Mathematical modelling and experimental investigation of drying … · 2017. 2. 20. · Table 2.1:...

Mathematical Modelling and

Experimental Investigation of

Drying of Piper Nigrum L.

Chong Chee Jiun

Faculty of Engineering, Computing and Science

Swinburne University of Technology

Sarawak Campus, Malaysia

Submitted for the degree of Master of Engineering

2013

i

ACKNOWLEDGEMENT I would like to express my deep appreciation and gratitude to my supervisor, Professor

Dr. Anatoli Vakhguelt, for the steadfast encouragement and mentorship he provided to

me, all the way from when I was first considering applying to the Master of Engineering,

through to completion of this degree. The completion of this thesis is impossible

without his guidance. His guidance helped me in all the time of research and writing of

this thesis. I could not have imagined having a better advisor and mentor for my Master

study.

Besides, Professor Justo Diaz plays an important role as my co-supervisor. His advice

on the effective use of software in compiling data also contributes to the completion of

this thesis.

My sincere thanks also go to Swinburne University of Technology Sarawak Campus for

waiving the tuition fee of the Master program I enrolled.

Special thanks to Mr Luk Tien Boh for helping in making the construction of the

custom made experimental setup for the forced convection trials possible.

I would like to express my gratitude to Malaysia Pepper Board who has been very

helpful in providing sample for all the experimental investigation. The body helped to

analyse the chemical constituents of the Piper Nigrum L. berries used or produced in the

experimental trials.

ii

DECLARATION

I hereby declare that this work contains no material which has been accepted for the

award to the candidate of any other degree or diploma, except where due reference is

made in the text of the examinable outcome; and

It is to the best of my knowledge that this work contains no material previously

published or written by another person except where due reference is made in the text of

the examinable outcome;

___________________

CHONG CHEE JIUN

February, 2013

iii

LIST OF PUBLICATIONS AS A RESULT OF THIS WORK

Chong, CJ & Vakhguelt, A, 2011, "Mathematical Modelling of Moisture Diffusions

During Drying of Piper Nigrum L.”, Proceedings of the Seventh Asia-Pacific Drying

Conference, 18th – 20th September, 2011, Tian Jin.

Vakhguelt, A, Chai, A, Luk, TB & Chong, CJ, 2010, “Extending the Drying Capability

Utilising Nature Airflow Booster for Convective Solar Dryer”, Proceeding of 19th

International Congress of Chemical and Process Engineering, 28th August – 1st

September 2010, Prague, Czech Republic.

Vakhguelt, A, Chong, CJ & Luk, TB, 2009, “Experimental Study of Drying Fresh

Pepper Berries In a Solar Dryer”, Proceeding of the 7th World Conference on

Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, 28th June – 03rd

July 2009, Krakow, Poland, pp. 1239-1245.

iv

ABSTRACT The aim of this study was to identify the optimum drying conditions of Piper Nigrum L.

berries that would yield quality black pepper.

Experimental trials were carried out to find out the drying characteristics of Piper

Nigrum L. berries. The berries were dried under natural convection and forced

convection. The effects of drying temperature and air flow on drying rate, drying

duration, retention of chemical constituents, and the changes to the internal structure of

the individual drupes were studied.

In natural convection trials, the drying rate was found to have increased at higher drying

temperatures. This reduced the drying duration, the moisture retained and hastened the

changes in the internal structure of individual drupe.

In forced convection trials, the increase in drying rate was obvious only within the first

24 hours of drying at 45oC and 55oC. The increase was significant throughout trials in

35oC. At different drying temperatures studied, the drying duration, the chemical

constituents, and the changes to the internal structure of individual drupes were

minimally affected by air flow.

The Fickian diffusion model for a spherical solid was used to describe the drying

characteristics of the berries. This model was solved via the analytic solution and the

finite difference method. The moisture distribution within the individual drupe for

different drying conditions was simulated. The results obtained from the solutions were

validated with the results obtained from experiments conducted in this work using the

bulk moisture loss method. The relationship of drying temperature and air flow with the

effective diffusivity of these chemical constituents was identified.

The validation of the results obtained from the solutions was satisfactory. The effective

diffusivity of piperine was much lower than the effective diffusivity of moisture in all

trials. The effective diffusivity of moisture was higher when berries were dried at higher

drying temperatures while the effective diffusivity of piperine in berries was about the

same at all drying temperatures studied except at 30oC.An increase in the speed of air

flow neither increased nor decreased the effective diffusivity of all the chemical

constituents at 35oC, 45oC and 55oC.

v

In this work, it is concluded that the air flow is a less influential driving force compared

to drying temperature on the drying of the berries. The optimum drying condition to

produce black pepper is a combination of drying temperature from 45oC to 55oC and air

flow from 0.5ms-1 to 1.0ms-1.

vi

TABLE OF CONTENTS

ACKNOWLEDGEMENT ............................................................................................... i

DECLARATION ............................................................................................................. ii

List of Publications as a Result of this Work............................................................... iii

ABSTRACT ............................................................................................................ iv

TABLE OF CONTENTS .............................................................................................. vi

LIST OF TABLES ......................................................................................................... ix

LIST OF FIGURES ........................................................................................................ x

NOMENCLATURE ...................................................................................................... xii

CHAPTER 1: Introduction ............................................................................................. 1

1.1 About the Piper Nigrum L. ......................................................................... 1

1.2 Contribution of Pepper as a Commodity in Malaysia ................................ 3

1.3 Drying Process to Produce Pepper ............................................................. 4

1.4 Problems in Relation to the Drying of Piper Nigrum L. Berries ................ 6

1.4.1 Objective of Research .............................................................................. 6

1.5 Scope of Experimental Study ..................................................................... 7

1.6 Structure of Thesis ...................................................................................... 7

CHAPTER 2: Literature Review ................................................................................... 8

2.1 History of Research and Development in Pepper ....................................... 8

2.1.1 Research and Development of the Piper Nigrum L. in Sarawak ............. 8

2.1.2 Research and Development on Drying of Piper Nigrum L. Berries in India ....................................................................................................... 10

2.2 Quality Assessment .................................................................................. 11

2.2.1 Current Assessment Methods ................................................................ 11

2.2.2 Problems in Relation to Current Assessment Methods ......................... 14

2.3 Mathematical Modelling .......................................................................... 16

2.3.1 Introduction ........................................................................................... 16

2.3.2 Research and Development of the Diffusion Model ............................. 17

2.3.3 Fick’s Second Law ................................................................................ 17

2.3.4 Methodology .......................................................................................... 18

2.3.5 Diffusion Coefficient ............................................................................. 20

2.3.6 Validation of Calculated Results with Experimental Results ................ 23

vii

2.3.7 Shrinkage Studies .................................................................................. 23

2.4 Mathematical Modelling used in this Study ............................................. 25

CHAPTER 3: Methodology .......................................................................................... 26

3.1 Experimental Study .................................................................................. 26

3.1.1 Materials and Methods of the Study ...................................................... 26

3.1.2 Procedures of Experimental Studies ...................................................... 30

3.2 Mathematical Modelling Study ................................................................ 33

3.2.1 Method of Analytic Solution ................................................................. 33

3.2.2 Method of Numerical Solution .............................................................. 35

CHAPTER 4: Results and Discussions ........................................................................ 42

4.1 Results and Discussions of Experimental Study for Natural Convection Trials ......................................................................................................... 42

4.1.1 Effects of Drying Temperature on Drying Rate .................................... 42

4.1.2 Effects of Drying Temperature on Duration for Drying ....................... 44

4.1.3 Effects of Drying Temperature on the Retention of Chemical Constituents ........................................................................................... 45

4.1.4 Optimum Drying Condition .................................................................. 46

4.1.5 Effects of Drying Temperature on the Changes to the Internal Structure of the Individual Drupe ......................................................................... 47

4.2 Results and Discussions of Experimental Study for Forced Convection Trials ......................................................................................................... 49

4.2.1 Effects of Air Flow on Drying Rate ...................................................... 49

4.2.2 Effects of Air Flow on Drying Duration ............................................... 51

4.2.3 Effects of Air Flow on the Retention of Chemical Constituents ........... 52

4.2.4 Ranking of Drying Conditions .............................................................. 54

4.2.5 Optimum Drying Condition .................................................................. 55

4.2.6 Effects of Air Flow on the Changes to the Internal Structure of the Individual Drupe .................................................................................... 56

4.3 Discussion on the Results of Mathematical Modelling used in the Study for Natural Convection Trials ................................................................... 58

4.3.1 Calculation Done to Determine the Effective Diffusivity of Moisture in Piper Nigrum L. Berries for Natural Convection Trials ........................ 58

4.3.2 Calculation Done to Determine the Effective Diffusivity of Piperine in Piper Nigrum L. Berries for Natural Convection Trials ........................ 58

4.3.3 Relation of Effective Diffusivity with Temperature ............................. 59

viii

4.3.4 Validation of Results of the Mathematical Model ................................ 62

4.4 Discussion on the Results of Mathematical Modelling used in the Study for Forced Convection Trials .................................................................... 63

4.4.1 Calculation Done to Determine the Effective Diffusivity of Moisture in Piper Nigrum L. Berries for Forced Convection Trials ......................... 63

4.4.2 Calculation Done to Determine the Effective Diffusivity of Piperine in Piper Nigrum L. Berries for Forced Convection Trials ......................... 64

4.4.3 Relation of Effective Diffusivity with Air Flow ................................... 64

4.4.4 Moisture Profile under Different Drying Conditions ............................ 66

4.4.5 Validation of Results of the Mathematical Model ................................ 68

CHAPTER 5: Conclusion ............................................................................................. 70

5.1 Natural Convection Trials ........................................................................ 70

5.2 Forced Convection Trials ......................................................................... 71

5.3 Recommendation For Future Work .......................................................... 73

REFERENCES ........................................................................................................... 75

Appendix 1: Calculation Work to Determine the Arrhenius Factor and Activation Energy ..................................................................................................... 80

Appendix 2: Calculation Work to Determine the Values of b and c in the Henderson's Equilibrium Moisture Content Equation ................................................. 81

Appendix 3: Calculation of Equilibrium Moisture Content, Me ..................................... 83

Appendix 4a: Calculation of Moisture Content in Piper Nigrum L. Berries with Time for Natural Convection Trials via The Analytic Solution ....................... 84

Appendix 4b: Calculation of Piperine Content in Piper Nigrum L. Berries with Time for Natural Convection Trials via The Analytic Solution .......................... 101

Appendix 5: Calculation of Mass Transfer Coefficient, hD .......................................... 118

Appendix 6a: Calculation of Moisture Content in Piper Nigrum L. Berries with Time for Forced Convection Trials via the Analytic Solution ....................... 120

Appendix 6b: Calculation of Piperine Contentin Piper Nigrum L. Berries with Time for Forced Convection Trials via the Analytic Solution ............................. 133

Appendix 7a: Moisture Profile of a Piper Nigrum L. Berry (Mi, j+1 ,Mn, j+1, Ms, j+1) .... 146

Appendix 7b: Piperine Profile of a Piper Nigrum L. Berry (Pi, j+1 ,Pn, j+1, Ps, j+1) ....... 159

Appendix 8: Calculation of the Average Moisture Content Based on the Moisture Profile of a Berry................................................................................... 172

Appendix 9: Calculation of the Average Piperine Content Based on the Piperine Profile of a Berry .............................................................................................. 182

ix

LIST OF TABLES

Table 1.1: Comparing the Chemical Quality in Different Varieties of Pepper (Paulus 2006, pp. 12-13) ............................................................................................. 3

Table 2.1: Benchmark Specified in the European Spice Association Quality Minima Document (European Spice Association 2007, pp. 9) ................................. 12

Table 2.2: Part of the Standards Developed by ISO (Ravidran 2000, pp. 154) .............. 13 Table 2.3: Comparing the Amount of Chemical Constituents in the Berries of Different

Varieties of Piper Nigrum L. in Sarawak (Paulus 2006, pp. 12-13) ............ 14 Table 2.4: Comparing the Amount of Chemical Constituents in the Berries Yield by

Different Varieties of Piper Nigrum L. in India (Ravidran & Johnny 2000, pp. 69) .......................................................................................................... 14

Table 2.5: Thin Layer Models that are Commonly Used to Describe the Thin Layer Drying of Agricultural Products (Gunhan et al. 2005, pp. 1670) ................ 16

Table 2.6: Differential Equations Representing Fick’s Second Law in Various Coordinate Systems (Crank 1975) ............................................................... 17

Table 2.7: Commonly Used Analytic Solutions of Fick’s Second Law Model in Describing the Drying Behaviour of Solids with Different Shapes (Kamil & Ahmet 2007, pp. 83-84) ............................................................................... 19

Table 3.1: Input Parameters ............................................................................................ 35 Table 3.2: Input Parameters ............................................................................................ 39 Table 3.3: Discretization of the function, f(r) ................................................................. 40 Table 4.1: Amount of Moisture Retained, Amount of Piperine Retained and Drying

Duration at Different Drying Temperatures ................................................. 46 Table 4.2 : Drying Duration under Different Air Flow Speeds at 35oC, 45oC, and 55oC

...................................................................................................................... 51 Table 4.3: Amount of Moisture Retained, Amount of Piperine Retained, and Drying

Duration at Different Drying Conditions ..................................................... 55 Table 4.4: Calculation Done to Determine the Effective Diffusivity of Moisture in Piper

Nigrum L. Berries for Natural Convection Trials ........................................ 58 Table 4.5: Calculation Done to Determine the Effective Diffusivity of Piperine in Piper

Nigrum L. Berries for Natural Convection Trials ........................................ 59 Table 4.6: Calculation Done to Determine the Effective Diffusivity of Moisture in Piper

Nigrum L. Berries for Forced Convection Trials ......................................... 63 Table 4.7: Calculation Done to Determine the Effective Diffusivity of Piperine in Piper

Nigrum L. Berries for Forced Convection Trials ......................................... 64 Table 4.8: Effective Diffusivity of Moisture and Effective Diffusivity of Piperine under

Different Drying Conditions ........................................................................ 65 Table 4.9: Standard Error of Analytic Solution and Numerical Solution with the

Experimental Results. .................................................................................. 69

x

LIST OF FIGURES Figure 1.1: The Perennial Climbing Vine Piper Nigrum L. ............................................. 1 Figure 1.2: Piper Nigrum L. Berries in Spike ................................................................... 1 Figure 1.3: Black Pepper ................................................................................................... 2 Figure 1.4: White Pepper .................................................................................................. 2 Figure 1.5: Agricultural Products Exported from Sarawak in the year 2008 (Department

of Statistics Malaysia, Sarawak 2009, pp. 77-78) ....................................... 3 Figure 1.6: River Soaking (Paulus, Megir & Eng n.d., pp. 25) ........................................ 4 Figure 1.7: Soaking in Dam (Paulus, Megir & Eng n.d., pp. 25) ..................................... 4 Figure 1.8: Drying of White Pepper by Spreading Evenly on Mats (Paulus, Megir &

Eng n.d., pp.25) ............................................................................................ 5 Figure 1.9: Drying of Black Pepper (Paulus, Megir & Eng n.d., pp.24) .......................... 5 Figure 3.1: Experimental Setup for Natural Convection Trials ...................................... 28 Figure 3.2: Experimental Setup for Forced Convection Trials ....................................... 29 Figure 3.3: Cross Section of a Piper Nigrum L. Berry ................................................... 36 Figure 3.4: Model which Represents the Whole Drupe .................................................. 36 Figure 3.5: Equivalent Model which Represents the Whole Drupe ............................... 36 Figure 4.1: Mass Change of Piper Nigrum L. Berries at Different Drying Temperatures

................................................................................................................... 43 Figure 4.2: Drying Duration at Different Drying Temperatures ..................................... 44 Figure 4.3: Retention of Chemical Constituents After Drying at Different Drying

Temperatures ............................................................................................. 45 Figure 4.4: Internal Structural Changes of Individual Drupes at Different Drying

Temperatures ............................................................................................. 47 Figure 4.5: Longitudinal Section of Fruit (Chih & Sim 1977, pp. 14) ........................... 48 Figure 4.6: Shrinkage of Berries at Different Drying Temperatures .............................. 48 Figure 4.7: Mass Change During Drying under Different Air Flow Speeds at 35oC,

45oC, and 55oC ........................................................................................... 50 Figure 4.8: Drying Duration under Different Air Flow Speeds at 35oC, 45oC, and 55oC

................................................................................................................... 51 Figure 4.9: Retention of Chemical Constituents After Drying under Different Air Flow

Speeds ........................................................................................................ 53 Figure 4.10: Mass Change in Natural Convection Trials and Forced Convection Trials

................................................................................................................... 54 Figure 4.11: Internal Structural Changes of Individual Drupes at Different Air Flow

Speeds ........................................................................................................ 56 Figure 4.12: Shrinkage of Berries at Different Air Flow Speeds at 35oC, 45oC, and

55oC ........................................................................................................... 57 Figure 4.13: Relation of Effective Diffusivity of Moisture and Piperine with Drying

Temperature ............................................................................................... 60 Figure 4.14: Relation of Effective Diffusivity of Moisture with Drying Temperature .. 60 Figure 4.15: Fitting Data into Arrhenius Relation .......................................................... 61

xi

Figure 4.16: Comparing the Changes in Mass of Piper Nigrum L. Berries at Different Drying Temperatures ............................................................................... 62

Figure 4.17: Effective Diffusivity of Moisture and Effective Diffusivity of Piperine under Different Air Flow Speeds at 35oC, 45oC, and 55oC ..................... 65

Figure 4.18: Variation of Moisture Loss Along the Radius in Different Time Periods in a Berry under Different Drying Conditions ............................................ 67

Figure 4.19: Comparing the Changes in Mass of Piper Nigrum L. Berries under Different Drying Conditions ................................................................... 68

Figure 4.20: Comparing the Calculated Mass Change of Piper Nigrum L. Berries at Different Air Flows with the Experimental Results ................................ 69

xii

NOMENCLATURE

Notation Description Unit

MR, mr Moisture Ratio Dimensionless

k Drying Velocity Constant in Drying

Models

(Unit Time) -1

t Time Unit Time

a, c, n Dimensionless Drying Constant in Thin

Layer Models Dimensionless

D Diffusion Coefficient m2(unit time)-1

c Concentration of Diffusion Substance kgm-3

Φ Displacement in the Non-Radial Direction Unit Length

r Displacement in the Radial Direction Unit Length

θ Displacement in the Non-Radial Direction Unit angle

x Displacement in the Direction of x-axis Unit Length

y Displacement in the Direction of y-axis Unit Length

z Displacement in the Direction of z-axis Unit Length

Deff Effective Diffusivity m2(unit time)-1

m InstantaneousMoisture Content kg moisture(kg dry solid) -1

mo Initial Moisture Content kg moisture(kg dry solid) -1

me Equilibrium Moisture Content kg moisture(kg dry solid) -1

L Characteristic Length Unit Length

Li, i=1,2,3 Characteristic Length in ith dimension Unit Length

xiii

Notation Description Unit

bnm βm,

αnm, αn

Coefficient Dimensionless

D, Deff Diffusion Coefficient /

Effective Diffusivity

m2hr-1

M Local Moisture Content within Berry dimesionless

R Radius of Berry m

hD Mass Transfer Coefficient mhr-1

Ms Moisture Content at Surface of Berry kg moisture(kg dry solid) -1

Me Equilibrium Moisture Content kg moisture(kg dry solid) -1

Mi, j Moisture Content at Node i of Berry After

j hour kg moisture(kg dry solid) -1

b, c Constant dimensionless

RH Relative Humidity dimensionless

T Drying Temperature oC

Sh Sherwood Number dimensionless

d Diameter of the Berry m

Re Reynolds Number dimensionless

Sc Schmidt Number dimensionless

u Mean Velocity of the Drying Air mhr-1

ρ Density of the Drying Air kgm-3

μ Viscosity of the Drying Air kgm-1hr-1

CHAPT

1.1 Abo

The Piper

pp. 2). Se

‘Semongo

cultivated

varieties (

Figu

The fruits

In Malay

significanc

production

pepper an

pepper co

1977, pp.

TER 1:

out the Pipe

Nigrum L.

everal varie

ok Emas’ a

. This is b

Paulus 2006

ure 1.1: TheVine Pip

of the Pipe

ysia, peppe

ce. Exports

n in Saraw

nd white pep

nsists of dr

2).

INTROD

er Nigrum

is a type of

eties of Pip

and ‘Semon

because the

6, pp. 1-10)

e Perennial per Nigrum

er Nigrum L

er is the

s of spices

wak. Two c

pper. Black

ried fruit fro

DUCTIO

L.

f perennial

per Nigrum

ngok Aman

ey generall

).

Climbing L.

L. are used

only dome

s from Ma

ommon for

k pepper co

om which t

ON

climbing vi

m L. are a

’ are some

ly produce

Figure

d to produce

estically-pro

alaysia are

rms of pep

onsists of th

the pericarp

C

ine spice cr

vailable in

of the var

high yield

1.2: Piper N

Sp

e the world

oduced spi

currently d

pper are ma

he whole dr

p has been r

Chapter 1: In

rop (Chih &

Sarawak.

rieties prefe

ds compare

Nigrum L. B

pike

famous spi

ice with c

dominated

arketed, nam

ried fruit, w

removed (C

ntroduction

1

& Sim 1977,

‘Kuching’,

ferred to be

ed to other

Berries in

ice, pepper.

commercial

by pepper

mely black

while white

Chih & Sim

n

,

,

e

r

.

l

r

k

e

m

Chapter 1: Introduction

2

Figure 1.3: Black Pepper

Figure 1.4: White Pepper

Pepper is famous for its unique pungent smell. Piperine is the main agent contributing to

this pungent smell (Narayanan 2000, pp. 143). It is the most abundant alkaloid in pepper

(Narayanan 2000, pp. 150). The pepper is more pungent when the piperine content is

higher. The amount of piperine in the berries of the Piper Nigrum L. differs among the

different varieties of Piper Nigrum L.. The following table shows the amount of

piperine in berries of Piper Nigrum L. for different varieties in Sarawak.

Table 1.

During th

diffusing

possible w

quality.

1.2 Con

Up to year

was grown

commonly

Huzaimi 2

in Sarawa

the agricu

Sarawak e

of white p

Sarawak 2

Figure 1.5

.1: Compari

Chemical

Piperine %

he drying pr

substances

when the be

ntribution o

r 2003, 95%

n in other p

y known a

2003, pp. 39

ak since 196

ultural produ

exported as

pepper and

2009, pp. 77

5: Agricultu

o

ing the Che

Quality K

% (w/w)

rocess, the

besides m

rries underg

of Pepper a

% (10,100 h

parts of Ma

as Sarawak

9). Pepper h

67. In year 2

ucts exporte

much as 13

10,823 tonn

7).

ural Product

f Statistics M

emical Quali

2006, pp

Kuching S

3.5

piperine c

moisture. It

go drying a

as a Comm

hectares) of

alaysia. Due

k pepper in

has been on

2008, peppe

ed by Saraw

3,322 tonne

nes of black

ts Exported

Malaysia, S

ity in Differ

p. 12-13)

Var

Semongok E

3.4

ontent chan

is importan

as its level o

odity in Ma

the crop wa

e to this, the

n the worl

e of the mo

er was the th

wak after o

es of pepper

k pepper (D

from Saraw

Sarawak 200

C

rent Varieti

riety

Emas Sem

nges. Piperi

nt to retain

of pungency

alaysia

as grown in

e pepper pr

d market (

ost importan

hird largest

oil palm and

r which con

Department

wak in the y

09, pp. 77-7

Chapter 1: In

ies of Peppe

mongok Aman

5.4

ine is also

n as much

y contribute

n Sarawak an

roduced in M

(Liew, Ma

nt agricultur

commodity

d rubber. In

nsisted of 2,

of Statistic

year 2008 (D

78)

ntroduction

3

er (Paulus

n

one of the

piperine as

es to pepper

nd only 5%

Malaysia is

hendran &

ral products

y among all

n that year,

,499 tonnes

s Malaysia,

Department

n

3

e

s

r

%

s

&

s

l

,

s

,


4

1.3 Drying Process to Produce Pepper

The process of drying the berries of the Piper Nigrum L. to produce white pepper is

slightly different compared to black pepper. To produce white pepper, Piper Nigrum L.

berries are first soaked in running water for 10 to 14 days to soften the pericarp of the

berries. Running water can either be in a river, as shown in Figure 1.6, or in a

polyethylene tank connected by pipes. In areas where only low-level streams are

available, a dam is built in the stream to increase the level of the water of the stream to

the required level.

After soaking, the berries are trampled upon and washed several times to remove the

pericarp, stalks and light berries. Resulting peppercorns are then spread in thin layers on

mats or on polythene sheets (Paulus, Megir & Eng n.d., pp. 24).

Figure 1.6: River Soaking (Paulus, Megir & Eng n.d., pp. 25)

Figure 1.7: Soaking in Dam (Paulus, Megir & Eng n.d., pp. 25)


5

On the other hand, black pepper is traditionally produced via drying under the sun for

three to four days. Based on the description given by Chih and Sim (1977, pp. 36),

initially after the berries are harvested, they are kept overnight. Then, they are threshed

from spikes, spread on mats, and after that put under the sun.

Figure 1.8: Drying of White Pepper by Spreading Evenly on Mats

(Paulus, Megir & Eng n.d., pp.25)

Figure 1.9: Drying of Black Pepper (Paulus, Megir & Eng n.d., pp.24)

During the drying, the berries are turned frequently to ensure even drying and to prevent

the formation of mildew from developing. When evening approaches, the berries are

collected and enclosed in sacks. The berries are released again for drying the next day

until the berries are sufficiently dried.


6

1.4 Problems in Relation to the Drying of Piper Nigrum L. Berries

Continuous fine and sunny weather guarantees proper drying of pepper and renders a

more uniform appearance and less mouldy berries (Chih & Sim 1977, pp. 36). However,

sun drying has several limitations (Joy, George & Jose 2002, pp. 40). The main

disadvantage of sun drying is the lack of drying uniformity and the possibility of

contamination by microorganisms (Zachariah 2000, pp. 340). A solar dryer would be

one of the alternatives to create a more consistent environment which would hasten the

drying process and thus ensure the quality of pepper produced. In order to design a solar

dryer, information on the drying characteristics of Piper Nigrum L. berries is needed.

Drying characteristics of the berries such as drying period, optimum drying temperature

and diffusivity can be used to determine the design of a solar dryer. There is not much

information on the drying characteristics of Piper Nigrum L. berries in the literature.

The information available is not sufficient to determine optimum drying conditions to

produce quality black pepper. An experimental study is needed to find out the drying

characteristics of Piper Nigrum L. berries.

There is limited information on the development of a mathematical model for drying

Piper Nigrum L. berries in the literature. Thus, a mathematical model which is able to

describe the drying characteristics of Piper Nigrum L. berries has been developed in this

work. The diffusivity model which describes the diffusivity of individual berries was

adopted from the literature. The research and development of the mathematical

modelling of food drying is presented to identify suitable mathematical model. The

model developed could be used in designing a suitable solar dryer to dry the berries of

the Piper Nigrum L.

1.4.1 Objective of Research

This work aims to provide useful information for the design of solar dryer. Results from

this work will benefit design engineers who are working on the solar dryer since

optimum conditions that would induce fastest drying and quality black pepper will be

available. Besides, it also provides suitable mathematical model which is capable to

predict the drying time at a given drying temperature and speed of air flow, and the

dryness of berries at a given drying time.


7

1.5 Scope of Experimental Study

Experimental studies were conducted to look into the effects of different drying

temperatures (ranging from 30oC until 55oC) on pepper quality, to study the effects of

different air flow speeds (ranging from 0ms-1 until 1ms-1) on pepper quality, and to

determine the drying time needed to dry Piper Nigrum L. berries at different

combinations of drying temperatures and air flow speeds. These characteristics were

able to assist in determining the optimum conditions that would induce fastest drying

and high quality in the final yield. Chemical content, including the moisture content and

the piperine content, was used as a guideline to measure the quality of pepper in this

work. However, the chemical content of the dried berries differs between different

cultivars. The amount of chemical constituents retained in pepper during drying could

only act as an additional guideline to determine the optimum drying condition to dry the

berries. The optimum drying condition should be determined based on the ability to

yield black pepper with the least moisture retained, and, at the same time, have the

highest amount of piperine retained after the drying process is completed. This issue

will be further discussed in the next chapter.

1.6 Structure of Thesis

The drying process involved to produce black pepper is presented in this chapter. After

that, the need to carry out experimental studies to study the drying characteristics of the

berries of Piper Nigrum L. is pointed out. The scope of the experimental study is then

defined. The next chapter begins with a review of research on the drying of Piper

Nigrum L. berries to determine the current gaps in knowledge regarding drying

characteristics. It follows with current research trend in the mathematical modelling of

food drying. The scope of mathematical modelling studies is then defined. The third and

fourth chapters contain procedures of sample preparation and the procedures of the

experimental studies for each different type of trial. The results and discussion on each

of the trials are presented in this chapter too. The optimum drying condition to produce

black pepper is concluded based on the results and discussions presented. This thesis

ends with a review of the results and discussions together with the conclusions.

Chapter 2: Literature Review

8

CHAPTER 2: LITERATURE REVIEW

2.1 History of Research and Development in Pepper

2.1.1 Research and Development of the Piper Nigrum L. in Sarawak

The great achievement of pepper production in Sarawak was the result of research and

development work done by the Sarawak State Department of Agriculture. This research

started in the late 1950’s. Investigations were conducted with the aim to increase

production of pepper in Sarawak. Different approaches were used to find out the most

effective way to increase the yield of the Piper Nigrum L.. The yield of Piper Nigrum L.

for different varieties was studied, followed by the research efforts to improve the

existing method of culturing and providing suitable nutrition to the plant. A breeding

program was started in 1964 where the main objective was to combine the yielding

ability of the local cultivar, ‘Kuching’, with the foot-rot resistance of foreign cultivars

or other species of Piper (Moir 1982, pp. 103). Not many studies were done on the

drying characteristics of the berries of the Piper Nigrum L..

There were three studies on pepper processing and the improvement in pepper quality

for both black pepper and white pepper was conducted from 1972 to 1974 (Moir 1982,

pp. 167-169). The main aim of these investigations was to find the best way to dry Piper

Nigrum L. berries, with special attention to the quality of pepper in terms of the outer

appearance of the dried berries (Moir 1982, pp. 167). The first study looked into the

storage period of Piper Nigrum L. berries before being processed into black pepper or

white pepper. The second study compared the performance of different drying methods

(Moir 1982, pp. 168), while the third study estimated the conversion ratio or percentage

of mass remaining when the berries were dried to produce black pepper or to produce

white pepper (Moir 1982, pp. 169). These works were not comprehensive enough to

determine the optimal drying conditions of Piper Nigrum L. berries.

The aim of the first study was to determine the longest period possible to store the

berries of the Piper Nigrum L. at room temperature before they were processed into

black or white pepper. The longest storage period for a good quality final product was

recorded at 11 days (Moir 1982, pp. 168). This means farmers could store the freshly

harvested berries of the Piper Nigrum L. for up to 11 days before processing these

berries into black pepper.


9

The aim of the second study was to find out whether there was any significant

difference between the final yield of Piper Nigrum L. berries with hot water treatment

and the final yield of the berries without hot water treatment before they were subjected

to sun drying to obtain black pepper. The result obtained was that the berries treated

with hot water before sun drying did not show distinct advantages over the ones treated

without hot water. In addition, the cost of hot water treatment was found to be

impractical. The studies also compared the differences in colour and quality between

oven drying and sun drying for both white pepper and black pepper. The conclusions of

the study mentioned that white pepper produced via oven drying was more yellowish in

colour while there was no obvious difference in the colour of black pepper produced

using oven drying or sun drying (Moir 1982, pp. 168). Any difference in the quality of

the final product obtained was not pointed out.

The aim of the third study was to estimate the conversion ratio of black pepper and

white pepper produced from the drying of Piper Nigrum L. berries. The study of the

conversion ratio was carried out when a new cultivar was being cultivated. This is

because the conversion ratio may be different for different cultivars. This study assisted

farmers in estimating their profit from the pepper cultivated by them (Moir 1982, pp.

169). The conversion ratio served as a guide for farmers to estimate the amount of the

final yield obtained from the amount of berries harvested. The conversion ratio of Piper

Nigrum L. berries was found to be between 31% and 33%.

After 1974, the Sarawak State Department of Agriculture Sarawak hardly carried out

any research work on black pepper processing in Sarawak. Research work mostly

emphasized the variety of cultivation and improvement, and diseases of the Piper

Nigrum L. vine and its berries in Sarawak (Research Division Department of

Agriculture 2006, pp. 21-25). Currently, no study has been done to determine the most

suitable drying condition to dry the berries of the Piper Nigrum L.. The quality of the

pepper produced was not assessed throughout the studies done by the Department of

Agriculture Sarawak. From this review, it was concluded that a more comprehensive

study is needed to find out the drying characteristics of Piper Nigrum L. berries.


10

2.1.2 Research and Development on Drying of Piper Nigrum L. Berries in India

In India, research on the drying of Piper Nigrum L. berries has mainly focused on the

performance of different types of dryers (Patil 1989, pp. 230; Joy, George & Jose 2002,

pp. 40). However, the results of the study revealed some drying characteristics of Piper

Nigrum L. berries. Patil (1989, pp. 230) compared the performance of the polydryer and

solar cabinet dryer in drying Piper Nigrum L. berries. Open sun drying on black painted

mats or on jut bags were taken as the reference of comparison. The performance of each

drying method was rated. Based on his studies, it took five days to dry 12kg/m2 of Piper

Nigrum L. berries using the open sun drying method. The average ambient temperature

was recorded as 29.8oC. The open sun drying had a rating 1.0. The average temperature

inside the polydryer was reported to be 37oC and its performance was rated as 1.92. The

polydryer with a cover throughout one whole drying trial required five and a half days

to dry 12kg/m2 of Piper Nigrum L. berries. Conversely, a polydryer without a cover on

the first day of drying took only four days to dry 12kg/m2 of Piper Nigrum L. berries

(Patil 1989, pp. 230-231). According to Patil (1989, pp.231), drying in a polydryer

without cover on the first day allowed air flow to remove excessive moisture in the

dryer. From here, it could be observed that air flow plays an important role in the first

24 hours of drying.

The solar cabinet dryer was found to have the highest rating which was 2.88. The

average temperature inside the solar cabinet dryer was 45oC. Four days were needed to

dry 18kg/m2 of Piper Nigrum L. berries in a solar cabinet dryer at 45oC. The rating was

higher since an equal period of time could dry the berries of the Piper Nigrum L. with

higher initial spreading density (Patil 1989, pp. 230-231). Patil (1989, pp.231)

concluded that most probably the drying time needed to dry the berries of the Piper

Nigrum L. could be reduced significantly as drying temperature was increased. In order

to verify this, the effects of drying temperature in the drying process of Piper Nigrum L.

berries need to be studied. Also, there is a need to verify whether the duration for drying

will be reduced with the presence of air flow in the drying process.

On the other hand, a histochemical study on the blackening of Piper Nigrum L. berries

during drying was carried out in India. It was reported that the phenolic extractives and

moisture diffused from inside of the berry towards the surface of the berry when the

turgidity of the cell was lost during drying (Mangalakumari, Sreedharan & Mathew


11

1983, pp. 605). This insight is important in the study of the diffusion of constituents of

berries. From this observation, it can be deduced that the piperine within the berries

diffuses together along with the diffusion of moisture when the berries of Piper Nigrum

L. undergo drying. Therefore, effects of drying condition on the diffusion of these

constituents need to be studied.

This study can be treated as a continuation to the investigative work on the processing

of Piper Nigrum L. berries into black pepper. A series of experimental trials was

conducted to study the drying characteristics of the berries of Piper Nigrum L.. The

effects of drying temperature and speed of air flow on the drying rate, the drying

duration, and the diffusion of the constituents of berries were studied.

The next section explains current methods to assess the quality of pepper and the

disadvantages of these methods.

2.2 Quality Assessment

2.2.1 Current Assessment Methods

In general, black pepper has good quality if it contains an appropriate amount of

moisture. The reason is that there is no microbiological growth if black pepper is dry

enough. Too much moisture in black pepper induces mould growth. An alternative way

to determine suitable dryness is by cracking a black pepper corn with one’s teeth. If a

distinctive snapping sound is produced, it is considered well dried pepper (Chih & Sim

1977, pp. 39). Although this is not a very scientific method to determine suitable

dryness, it is very useful for farmers to determine the moisture content level in black

pepper when advanced equipment is not available.

There are two major international standards available in the world which specify the

amount of constituents in good quality pepper. One is set by an association in the

United States (U.S.), the American Spice Trade Association (ASTA), and the other one

is set by an association in the European Union, the European Spice Association (ESA).

ASTA was established at the beginning of the twentieth century (Muggeridge & Clay

2001, p. 16). It is a trade association that represents the U.S. spice industry. Members of

the ASTA manufacture and market the majority of spices sold in the U.S. to retail

outlets and food processing industries (American Spice Trade Association 2012). The

ESA is the umbrella organisation of the European spice industry. Members of the ESA


12

are the national federations of the spice industry in the member countries of the

European Union, Switzerland and Turkey (European Spice Association 2007, pp. 3).

ASTA standards are recognised and endorsed by the United States Food & Drug

Administration (USDA) since it has been always involved in regulating the quality of

herbs and spices entering the United States (Muggeridge & Clay 2001, pp. 16). On the

other hand, standards developed by the ESA are based on both the national standards

such as those issued by the French standards authority (AFNOR), the British Standards

Institute (BSI), and international standards issued by the International Standards

Organisation (ISO) (Muggeridge & Clay 2001, pp. 16). The ESA general standards are

said to be more relaxed in their quantitative figures as they represent minimum

standards allowable for trade. The buyer and seller could set other standards for their

own purposes as long as the minimum requirements are satisfied (Muggeridge & Clay

2001, pp. 18). The development of these standards is influenced by the standards set by

the major importing countries. It relies on the same general parameters which also exist

in those countries responsible for growing herbs and spices, for example, the Indian

Spices Board and the Pepper Marketing Board (Muggeridge & Clay 2001, pp. 14).

In the standards established by ASTA and ESA, the essential chemical constituents of

pepper used to determine the quality of black pepper are moisture content, piperine

content, and volatile oil content. According to the Malaysian Pepper Board, the

moisture content of black pepper should range within 9.0% - 12.0%. The amount of

piperine in pepper should be adequately high as it contributes to the essential pungent

smell of pepper (Ravidran & Johnny 2000, pp. 68). However, the European Spice

Association Quality Minima Document does not indicate the minimum amount of

piperine that the black pepper must contain.

Table 2.1: Benchmark Specified in the European Spice Association Quality Minima

Document (European Spice Association 2007, pp. 9)

Product Ash %W/W MAX

Acid Insoluble Ash %W/W MAX

Volatile Oils ml/100g

MIN

Moisture Content %W/W MAX

Black Pepper

7.0 1.5 2.0 12.0

On the other hand, the International Organization for Standardization (ISO) developed

standards for black pepper products which indicate the minimum amount of piperine


13

content in quality black pepper. These standards were developed based on the input

received from various exporting and importing countries, and also from end users.

Based on standards developed by the ISO, piperine content in black pepper should be at

least 4% to be considered quality black pepper.

Table 2.2: Part of the Standards Developed by ISO (Ravidran 2000, pp. 154)

Product Ash

%m/m MAX,

on dry basis

Non-volatile Ether Extract

% (m/m) MIN,

on dry basis

Volatile Oils

ml/100g MIN,

on dry basis

Piperine

%m/m MIN

Moisture Content %m/m MAX

Black Pepper

5.0 6.0 2.0 4.0 12.0

Currently, both the physical appearance of pepper and chemical constituents of pepper

are indicators of pepper prices in the market. The physical appearance of pepper refers

to the size of the pepper corn, the number of broken berries, and the amount of

extraneous matter. In the Indonesian market, the quality of pepper is determined by its

appearance. Buyers prefer bold-sized pepper corns with a uniform dark-brown to black

colour as they are considered to have the best quality. The aroma and flavour

contributed by the volatile oil is more significant than the pungency level contributed by

the piperine when the spice is sold for domestic culinary purposes (Risfaheri &

Nurdjannah 2000, pp. 356).


14

2.2.2 Problems in Relation to Current Assessment Methods

Although the physical appearance of pepper and its chemical constituents are being

used as quality indicators, they are not convenient to be used in a scientific study. The

figures proposed by these standards can only serve as a benchmark to eliminate the

drying trials which fail to produce black pepper with specifications required by the

standards. They are not sufficient to determine the optimum drying condition. This is

because different varieties of Piper Nigrum L. contain different amounts of piperine.

The following tables show that different varieties of Piper Nigrum L. produce berries

with different amounts of piperine, oleoresin, and volatile oil:

Table 2.3: Comparing the Amount of Chemical Constituents in the Berries of Different

Varieties of Piper Nigrum L. in Sarawak (Paulus 2006, pp. 12-13)

Variety Volatile Oil % (v/w)

Oleoresin % (w/w)

Piperine % (w/w)

Kuching 2.8 11.0 3.5

Semongok Emas 3.0 11.0 3.4

Semongok Aman 3.8 15.5 5.4

Table 2.4: Comparing the Amount of Chemical Constituents in the Berries Yield by

Different Varieties of Piper Nigrum L. in India (Ravidran & Johnny 2000, pp. 69)

SL.

No

Variety Volatile Oil

% (v/w)

Oleoresin

% (w/w)

Piperine

% (w/w)

1 Arikottanandan 4.75 12.9 4.5

2 Arakkulammunda 4.75 9.84 4.4

3 Blankotta 5.12 9.35 4.26

4 Ceylon 3.75 3.5 7.6

5 Cheriyakaniakkadan 3.75 9.05 3.95

6 Chumala 2.25 5.45 3.3

7 Doddigya 2.5 7.1 2.85

8 Kalluvally 3.25 8.8 4.24

9 Kalluvally (PTB) 0.4 10.9 4.65

10 Kalluvally type I 3 8.44 5.4

11 Kaniakkadan 4.75 11.6 6

12 Kottanadan 2.5 17.8 6.6

13 Karimunda 4 11 4.4

14 Karuvilanchy 3.5 9.7 4.3

15 Kumbbakodi 4.5 14.9 7.6

16 Kuthiravally 4.5 14.9 5.97

17 Munda 4.75 7 5.6

18 Mundi 3.5 7.5 3.6

SL.

No

Variety Volatile Oil

% (v/w)

Oleoresin

% (w/w)

Piperine

% (w/w)

19 Narayakkodi 4 10.85 5.4

20 Nilgiris 5.5 15.5 6.05

21 Palulauta 3 7.6 3.6

22 Panniyur I 3.5 9.52 3.6

23 Perumkodi 3 8.6 4

24 Perumunda 4 8 7.4

25 Shimoga 2.5 7.2 4.56

26 Sullia 4 6.8 3.6

27 TMB II 2.5 10.8 5.8

28 Uthirankotta 4.75 8.55 3.92

29 Vally 2.5 6.53 4.9

30 Aimpiriyan 2.63 15.7 4.69

31 Udhakara 3.82 8.61 2.36

32 Thommankodi 5.98 13.77 2.77

33 Sreekara 7 13 5.1

34 Subhakara 6 12.4 3.4

35 Panchami 3.4 12.5 4.7

36 Pournami 3.35 13.8 4.1


15

Since the amount of constituents of the berries differs between different varieties, the

amount of constituents retained in the berries during drying would be a more

appropriate guideline in determining the optimum drying condition to dry the berries.

The optimum drying condition should be determined based on the ability of the drying

condition to produce black pepper with the least moisture retained, and, at the same time,

to produce black pepper which has the highest amount of piperine retained. The amount

of chemical content would merely serve as a benchmark to ensure the final yield is still

within the acceptable range.

Drying duration itself is another important factor in producing quality black pepper. The

moisture content within the berries should be reduced to a minimum level within short

period of time. The drying rate needs to be adequately high to prevent any

microbiological growth on black pepper produced during the drying process. As for the

diffusion rate of piperine, it should be as low as possible in a drying process as greater

pungency is only possible with a higher amount of piperine retained in the berries.


16

2.3 Mathematical Modelling

2.3.1 Introduction

There are two approaches in the studies of mathematical modelling of food drying,

namely, the diffusivity model, and the thin layer model. The study of diffusivity gives

an idea of the actual diffusion rate within an individual berry during a drying process.

The study of diffusivity was a commonly adopted approach before the thin layer model

became more frequently used in the literature. The use of the thin layer model in

literature is ever increasing due to the fact that the drying constant, k, embodies all the

transport properties into a simple exponential function (Mujumdar 2007, pp. 100). The

following table shows thin layer models which are commonly used in modelling the thin

layer drying of agricultural products:

Table 2.5: Thin Layer Models that are Commonly Used to Describe the Thin Layer

Drying of Agricultural Products (Gunhan et al. 2005, pp. 1670)

Model Name Model Lewis )exp( ktM R

Page )exp( nR ktM

Modified Page nR ktM exp

Henderson and Pabis )exp( ktaM R

Logarithmic cktaM R )exp(

Kamil and Ahmet (2007, pp. 123) believed that the thin layer models are very useful for

automatic control processes since their derivation requires little information and is

easily obtained. The drawback of these models is that they are only valid within the

range of the experimental studies (Kamil & Ahmet 2007, pp. 123). Since this work aims

to provide a model which has a wider validity, the diffusion model is adopted in this

work.


17

2.3.2 Research and Development of the Diffusion Model

In 2007, Wang, Guohua and Arun reviewed the mathematical models of solid drying

developed over two decades. Based on their reviews, they concluded that it is not

possible to establish a general model which can represent the drying process for all

types of materials. Thus, this work does not aim to develop a general model to represent

the drying process for different types of materials.

2.3.3 Fick’s Second Law

Over the years, different drying models were introduced to describe various drying

behaviours of food. They were developed on the same basis but with different

assumptions, different boundary conditions, and different method of solutions (Hussain

& Dincer 2003; Janjai et al. 2008; Janjai et al. 2010; Jaruk& John 2008; Karim &

Hawlader 2005; Maroulis, Kiranoudis & Marinos-Kouris 1995; Patil 1988; Siva,

Somchart & Apichit 2000; Souraki & Mowla 2008; Takahiro et al. 2008). These models

were derived based on Fick’s second law. This law states that the change in

concentration of a diffusing substance in a material over time is equal to the change in

local diffusion flux. The following shows differential equations which represent Fick’s

second law in various coordinate systems:

Table 2.6: Differential Equations Representing Fick’s Second Law in Various

Coordinate Systems (Crank 1975)

Coordinate System Differential Equation including all dimensions

Cartesian

If diffusion coefficient, D, is a constant, then

2

2

2

2

2

2

z

c

y

c

x

cD

t

c.

If diffusion coefficient, D, is a function of x, y, z, c, then

z

cD

zy

cD

yx

cD

xt

c.

Cylindrical

z

crD

z

c

r

D

r

crD

rrt

c

1

Spherical Polar

c

Dc

Dr

cDr

rrt

c2

22 sin

1sin

sin

11


18

A differential equation is to be used to accommodate the different shapes of food. The

diffusion equation in a cylindrical coordinate system is more suitable to describe the

diffusion in food with a cylindrical shape compared to other coordinate systems. The

spherical polar coordinate system is more suitable to describe the diffusion in food with

a spherical shape. The differential equations listed in the table (Crank 1975) could be

simplified depending on the assumptions made by the researcher in the model.

2.3.4 Methodology

Diffusion models shown in Table 2.6 could be solved via two main approaches:

1. Analytic solution

(Crank 1975; Souraki & Mowla 2008; Takahiro et al. 2008)

2. Numerical solutions:

a. Finite difference

method

(Hussain & Dincer

2003; Patil 1988; Jaruk

& John 2008; Karim &

Hawlader 2005)

b. Finite element method

(Janjai et al. 2008; Janjai et al. 2010)

Table 2.7 shows the commonly used analytic solutions in describing the drying

behaviour of solids with different shapes. The solution reflects the total amount of

moisture retained in different shapes of a drying body at time t.

Analytic solutions are not preferred by the researcher as the evaluation of terms in the

analytic solution is usually not trivial (Crank 1975), especially for forced convection

drying. Since most studies focused on forced convection drying (Hussain & Dincer

2003; Jaruk & John 2008; Karim & Hawlader 2005; Siva, Somchart & Apichit 2000),

an easier alternative is preferable. Another reason is that analytic solutions are mostly

restricted to simple geometries, linear forms of the diffusion equation, boundary

conditions, and diffusion coefficient (Crank 1975, pp. 137; Zhanyong, Noriyuki &


19

Table 2.7: Commonly Used Analytic Solutions of Fick’s Second Law Model in

Describing the Drying Behaviour of Solids with

Different Shapes (Kamil & Ahmet 2007, pp. 83-84)

Shape Analytic Solution

Infinite Slab mr =

2

2

2

122 4

)12(exp)12(

18

L

tDn

neff

n

Semi-Infinite

Slab mr =

2

2

2

2

122

1

2

2

12

2

2 4)12(exp

)12(

1

4)12(exp

)12(

18

L

tDn

nL

tDn

neff

n

eff

n

Finite Slab

mr =

2

3

2

2

12

2

2

2

2

122

1

2

2

12

3

2

4)12(exp

)12(

1

4)12(exp

)12(

1

4)12(exp

)12(

18

L

tDn

n

L

tDn

nL

tDn

n

eff

n

eff

n

eff

n

Sphere mr =

2

22

122

exp16

L

tDn

neff

n

Hemisphere mr = tDb nmeff

n mnm

2

1 1

exp

Infinite

Cylinder mr =

12

2

2exp

4

n

eff

n

n L

tD

Finite

Cylinder mr =

2

22

1 1222*

exp18

L

tD

leff

mnn m mn

Masanobu 2004, pp. 650). Crank (1975, pp. 137) claims that this can be a severe

limitation when the diffusion coefficient is concentration dependent. In addition,

analytic solutions cannot offer an insight into the moisture distribution within the drying

object during the drying process. In other words, the analytic solution can only estimate

diffusivity on average and it is not able to estimate diffusivity at different layers of the

drying object when a drying object consists of heterogeneous layers. In this work, the

Piper Nigrum L. berry is assumed to be a sphere drupe. Thus, based on Crank’s

suggestion (1975, pp. 91), the analytic solution is used to solve the diffusion model.

With the help of computational software such as Microsoft Excel, the evaluation of the

term in the analytic solution becomes feasible.


20

The numerical solution is an alternative to analytic solutions because it can predict the

moisture profile within a single drupe throughout the whole drying process although it

offers simulation insight only. The numerical solution has its own advantages over

analytic solutions. It was concluded by Crank (1975, pp. 137) that a more accurate

solution of diffusion equation is possible by using the methods of numerical analysis.

Therefore, one of the numerical solutions is used to model the drying behaviour of Piper

Nigrum L. berries.

The numerical solution is very useful when a food item has an irregular shape and

heterogeneous layers. Mango (Janjai et al. 2008) and litchi (Janjai et al. 2010) are food

items identified to have irregular shape and heterogeneous layers. In this case, the finite

element method has a great advantage over any other method. This method assumes that

any continuous quantity such as moisture content can be approximated by a discrete

model composed of a set of piecewise continuous functions defined over a finite

number of sub-domains or elements. Elements are connected at nodal points along the

boundaries and their equations are obtained by minimising a function of the physical

problem (Janjai et al. 2008, pp. 524). The complex features offered by the numerical

solution cannot possibly be offered by analytic solutions which consider the drying

object to have a simple geometry with homogeneous layers.

The disadvantage of the finite element method is that it is relatively more complicated

to be programmed and more time-consuming compared to the finite difference method.

Its program requires a Central Processing Unit (CPU) with larger memory if were to run

three-dimensional problems. The computation cost of the finite difference method is

relatively lower compared to the finite element method (Zhanyong, Noriyuki

&Masanobu 2004, pp. 652). In addition, it is able to provide adequate accuracy. Based

on Hussain and Dincer studies (2003), they concluded that the finite difference method

has a higher agreement with experimental results for moisture distribution compared to

analytic solutions. Therefore, the finite difference method is used to solve the

mathematical model which describes the drying behaviour of Piper Nigrum L. berries.

2.3.5 Diffusion Coefficient

The diffusion coefficient is a value which represents the rate of a substance passing

through a unit area of cross section. The diffusion coefficient can be considered either a

constant or can be considered to be influenced by the concentration of a diffusing


21

substance. In many investigations, the diffusion coefficient was considered to be a

constant. The analytic solution of Fick’s second law together with experimental data is

used to determine the diffusion coefficient. Currently, this method is known as the

Simplified Method in literature (Kamil & Ahmet 2007, pp. 130-132).

Researchers adopting the Simplified Method usually use only the first term of the series

as it is generally accepted to be sufficient (Souraki & Mowla 2008; Takahiro et al.

2008). The first step in the implementation of this method is plotting a semi logarithm

graph of dimensionless moisture ratio, mr =

e

e

mm

mm

0

, against time. This graph represents

the straight line equation tr

Dm eff

r 2

2

2

6lnln

, where the slope of the straight line is

2

2

r

Deff and the y-intercept is

2

6ln

on the tmr ln plane. The straight line equation

is derived from the simplified version of the analytic solution to the diffusion model of a

spherical drying body. The slope of the straight line is used to calculate the value of the

diffusion coefficient.

However, according to Patil (1988, pp. 25), it is not appropriate to consider the

diffusion coefficient as a constant throughout a drying process when the diffusion

process is concentration dependent. When the diffusion coefficient is concentration

dependent, the Simplified Method cannot be adopted anymore. This is because the

diffusion model is no longer linear when the diffusion coefficient is concentration

dependent (Du 1998, pp. 342). Patil (1988, pp. 25) argued that considering the diffusion

coefficient as a constant in such a situation causes inaccuracy in the values of the

solution. For a non-linear model, there is no general analytic solution and numerical

methods are then employed to solve the diffusion equation (Du 1998, pp. 342). For this

reason, some researchers are looking at using either the regular regime method or other

numerical methods to write the diffusion coefficient as a function of moisture content

and temperature (Zogzas, Maroulis & Marinos-Kouris 1994; Marcela, Roberto &

Constantino 1997).

Regular regime is a drying stage when the moisture distribution in a drying body is no

longer dependent on the initial moisture distribution (Schoeber 1976, pp. 4; Zogzas,

Maroulis & Marinos-Kouris 1994, pp. 503-504; Tong & Lund 1990, pp. 67). This


22

period occurs only when the amount of moisture content within a body is less than the

critical moisture content. The method assumes that the material of the drying body is

homogeneous and nonporous which could include food that has cellular tissue such as

the apple and potato (Kamil & Ahmet 2007, pp. 132). A requirement for the application

of this technique is the knowledge of the regular regime curve, which has been

determined experimentally at the desired temperature for the case of constant surface

concentration. One of the advantages of the regular regime method is that it can be

applied to systems with any degree of shrinkage since a reference component mass-

centred coordinate is used (Tong & Lund 1990, pp. 67). However, the regular regime

method is complicated and it needs successive interpolation and differentiation of the

experimental data (Kamil & Ahmet 2007, pp. 132).At this point in time, this work

assumes the diffusion coefficient as a constant during the drying process with a constant

drying temperature.

On the other hand, the diffusion coefficient has been accepted as a parameter that is

dependent on temperature. This has been accepted by all researchers and it has been re-

verified by several researchers who studied the drying of food (Souraki & Mowla 2008;

Takahiro et al. 2008). This relationship can be accurately described using the Arrhenius

equation

RT

EDD aexp0 , where D0 is the Arrhenius factor (m2s-1), Ea is the

activation energy (kJ/mol), R is the universal gas constant = 0.008314kJ/mol K, and T is

drying temperature (K). Therefore, it can be foreseen that the diffusion coefficient of

Piper Nigrum L. berries follows the Arrhenius relation. Ea and Do of Piper Nigrum L.

berries could be computed by calculating the slope, and the y -intercept of the straight

line lnD against 1/T.


23

2.3.6 Validation of Calculated Results with Experimental Results

Experimental validation of the solutions involving diffusion of an individual kernel is

rare (Souraki & Mowla 2008; Takahiro et al. 2008). These models are usually validated

via bulk moisture loss since it is assumed that diffusion in the individual kernel

contributes to the overall drying. The computed local moisture within the kernel is taken

in total and is compared with the value of the bulk moisture loss. Recently, there were

attempts to verify temperature distribution and moisture distribution at different cross

sections and time intervals within a drying body using magnetic resonance imaging,

MRI (Ghosh et al. 2008a; Ghosh et al. 2008b). The results of the comparison were

considered acceptable by Ghoshet alia (2008a, 2008b). Unfortunately, the cost of the

computation and experimental setup involved in the MRI study is relatively high

compared to the bulk moisture loss method. Thus, validation was done via the bulk

moisture loss method.

2.3.7 Shrinkage Studies

Recently, the shrinkage phenomenon began to gain the attention of researchers who are

studying the mathematical modelling of drying (Katekawa & Silva 2006, pp. 5). Dissa,

Desmorieux, Savadogo, Segda, and Koulidiati (2009) found that the effective diffusivity

which considers the shrinkage effect is much smaller than the one neglecting shrinkage

effect. They concluded that effective diffusivity of moisture which neglects the

shrinkage phenomenon overestimates the diffusivity of moisture. Katekawa & Silva

(2006, p. 5) mention that shrinkage occurring in food during the drying process should

not be ignored. They cite the example from research done by Frías, Foucat, Bimbenet,

and Bonazzi (2002) that a 5% reduction in radius of paddy rice could affect the

diffusivity of moisture in paddy rice. Shrinkage studies done by other researchers also

proved that the calculated results improved after including the shrinkage effect (Janjai et

al. 2008; Janjai et al. 2010; Souraki & Mowla 2008).

To develop a mathematical model of volumetric shrinkage, one of the most important

considerations is that the volume change due to the shrinkage of the drying body is

equal to the volume of water evaporated (Janjai et al. 2008). With the introduction of

the shrinkage phenomenon, its differential equation differs slightly compared to the

differential equation in Table 2.6 (Souraki & Mowla 2008, pp. 10):


24

V

mXD

t

X dddeff

d

where, )(.

)(,

where t is time, X is local moisture content, Deff is effective diffusivity, md is mass of

dry solid, and V is sample volume. The methodology used in getting the solution can be

either analytic (Souraki & Mowla 2008) or numerical (Janjai et al. 2008; Janjai et al.

2010) as mentioned in the methodology section previously. Souraki and Mowla (2008,

pp. 18) proposed to calculate the volume of the drying solid at various moisture content

levels in order to reflect the change in the volume of the drying body as a function of

moisture content. They claimed that the results yielded by the solution which considers

shrinkage are more reliable than those which do not consider shrinkage.

However, during preliminary studies on including shrinkage effects, it was found that

the moisture is not the only diffusing substance in the berry of the Piper Nigrum L.. The

piperine also diffuses during the drying process. Currently, it cannot be concluded that

the volume change in Piper Nigrum L. berries during the drying process is equal to the

volume of moisture loss during the drying process. Taking into account the shrinkage of

Piper Nigrum L. berries might result in underestimating the amount of moisture lost

through diffusion. Thus, the shrinkage effect is not included in the model of this work.

Besides shrinkage studies, there have been researchers who studied the strain and stress

which take place in the drying process due to shrinkage (Arrieche, Corrêa & Sartori

2009). A mechanical model was established from the elasticity theory. This model is

meant to predict deformation and cracks in the food material. At the moment,

deformation prediction is not a great concern of studies. Currently, this work focuses on

the ability to illustrate the moisture diffusion and the piperine diffusion of the individual

drupe.

The next section explains the mathematical modelling used in this work.


25

2.4 Mathematical Modelling used in this Study

In this work, the diffusion model assumes the Piper Nigrum L. berry to be a sphere

drupe. It considers both the diffusion of moisture and the diffusion of piperine to occur

simultaneously during a drying process. These diffusions within the drupe are in the

radial direction only. The analytic solution is used to model the drying behaviour of

Piper Nigrum L. berries in natural convection and in forced convection. The finite

difference method is used in forced convection to reveal the moisture distribution of

Piper Nigrum L. berries during forced convection drying. The scheme was initiated and

derived by Patil (1988) who believed that by accurately studying the individual

diffusion at each different location in an individual kernel, an accurate estimation on the

bulk moisture loss could be established. He also proposed the use of convective

boundary condition in modelling the forced convection drying. For now, this work

assumes the diffusion coefficient as a constant during drying at a constant drying

temperature. Shrinkage is not included in this model.

The effective diffusivity of moisture and piperine in the berry of Piper Nigrum L. is

estimated using the simplified method. Correlation of effective diffusivity with

temperature is studied. The data is fitted into the Arrhenius relation to estimate the

Arrhenius factor and activation energy of Piper Nigrum L. berries. Results calculated

via both the analytic and numerical solution of the diffusion model are validated with

the experimental results. Validation via bulk moisture loss is used.

The procedures used to conduct the experimental studies on the drying of Piper Nigrum

L. berries are outlined later. Results and discussions on the trials are presented after that.

Chapter 3: Methodology

26

CHAPTER 3: METHODOLOGY The study was conducted in two subsequent stages which are the experimental stage

followed by the mathematical modelling stage. The experimental study was carried out

by drying the berries under natural convection and forced convection. The natural

convection was used to study the effects of drying temperature on the drying process of

Piper Nigrum L. berries while the forced convection was used to study the effects of air

flow on the drying process of the berries. The details of the scope of experimental study

were outlined in section 1.5 while the procedures were outlined in section 3.1.1.1 and

3.1.1.2. The results obtained from the experimental study were used in the mathematical

modelling stage to validate the results simulated.

3.1 Experimental Study

In the experiment trials that involve the use of natural convection, a confined volume is

used to keep drying temperature at a constant level (Guiné & Fernandes 2006, p. 461).

Guiné & Fernandes (2006, p.461) suggested the use of a natural convection oven to

create the required controlled environment in the study. They obtained a satisfactory

experimental drying curve. On the other hand, a custom-made drying system was

constructed to create a controlled environment within a confined volume to carry out

the experiment trials that involve the use of forced convection. The detailed structure of

the drying system is shown in Figure 3.2 below.

3.1.1 Materials and Methods of the Study

3.1.1.1 Natural Convection Trials

Adopting the suggested method, six different drying temperatures ranging from 30oC to

55oC at 5oC intervals were selected in this experimental study. Drying temperatures

higher than 55oC were not studied as drying at higher temperatures produces a burning

smell which affects the quality of the pepper. In each trial, Piper Nigrum L. berries were

left in a natural convection oven, Binder ED53, at a constant temperature. The

relationship of the mass changes of Piper Nigrum L. berries with time was monitored in


27

every trial. The mass of the berries was measured using the Kyowa Miniature Load Cell,

LMA-A-10N, and was recorded by data logger at 30-minute intervals. The change of

the internal structure of individual berries with time was monitored as well.

Samples of Piper Nigrum L. berries used in natural convection trials were of the

Semongok Emas variety. The samples were divided into smaller samples for

experiments and each sample was sealed in a plastic package to minimize the change in

initial moisture content. These packages were stored in a refrigerator at low

temperatures ranging from 6oC to 8oC to prolong the freshness of the berries.

In each trial, only a pack of berries was used. Each package of Piper Nigrum L. berries

used was weighed at the beginning of each drying experiment. Before starting a trial,

the selected pack of berries was released from the sealed package. Berries were threshed

and a few berries were chosen. The remaining of the berries was weighed. Then, these

berries were left in the convection oven until the mass of the berries reached about 33%

of the initial mass of berries, which is the mass of threshed berries before drying. This is

the usual range to produce pepper with about 12% wb moisture content or less. After

the completion of each experiment, the berries were sent to the Malaysian Pepper Board

to determine the moisture content and the piperine content of the berries.

On the other hand, the few berries chosen earlier were placed on a specially designed

tray. These berries were selected so that the change in the internal structure of the

individual drupes during each trial could be observed. Observation was done before

each trial and every 12 hours after the start. During each observation, two berries were

selected. The image of the internal structure was captured via a webcam installed on

one of the eye pieces of a stereoscopic zoom microscope SMZ 445. After that, the drupe

was sectioned into two halves and the images for one of the halves were captured under

the stereoscopic zoom microscope. The radius of the berries were measured from the

images captured using the software AnalyzingDigitalImages, version 11.0. The detail of

the software is mentioned in section 3.1.2.4.


28

Figure 3.1: Experimental Setup for Natural Convection Trials

3.1.1.2 Forced Convection Trials

Two different air flow speeds was used: 0.5ms-1, and 1.0ms-1. The drying temperatures

in the drying system were chosen to be at 35oC, 45oC, and 55oC for each air flow speed.

In each trial, the berries were left in the drying system at constant temperatures and

consistent air flow. The relationship between the mass of Piper Nigrum L. berries with

time was monitored during each trial. The change in the internal structure of individual

berries with time was monitored as well. The mass of the berries was measured using

the Mettler Toledo Digital Balance with an accuracy of ±0.01g.

Samples of Piper Nigrum L. berries used in forced convection trials were of the

Semongok Aman variety. The samples were treated similarly as mentioned in the

second paragraph of section 3.1.1.1.

In each trial, only a pack of berries was used. Each package of Piper Nigrum L. berries

was used was weighed at the beginning of each drying experiment. The berries were

handled similarly before starting a trial as mentioned in the third paragraph of section

3.1.1.1. Then, these berries were left in the drying system at constant temperatures and

consistent air flow. At the beginning of the drying experiment, the reading was recorded

Room with controlled humidity

Adjustable Vent

Convection Oven

Plate

Specially Designed

Tray

Temperature cum Relative Humidity Sensor

Berries


29

at 30-minute intervals. The interval was prolonged to 60 minutes and later 120 minutes

before the drying ended. Each experiment was stopped when the mass of Piper Nigrum

L. berries reached about 34% of its initial mass. After the completion of each

experiment, the berries were sent to the Malaysian Pepper Board to determine the

moisture content and the piperine content of the berries.

On the other hand, the few berries chosen earlier were placed on a specially designed

tray. The observation and procedure is similar to the one mentioned in the fourth

paragraph of section 3.1.1.1.

Figure 3.2: Experimental Setup for Forced Convection Trials

Front ViewSide View Side View

Air Velocity Sensor

Pepper

Heating Element

Fan

Tray

Salt

Divider Divider

Channel

Wall

Channel

Wall

Forced

Convection Air

Tray


30

3.1.2 Procedures of Experimental Studies

3.1.2.1 Natural Convection Trials

The procedure below was followed to configure the setup of each trial and to carry out

the study proposed:

1. A pack of berries was withdrawn from storage and left at room temperature for

three hours.

2. The convection oven was switched on and the drying temperature required was

set. The adjustable vent was opened to a maximum.

3. Relative humidity and temperature within the oven and outside the oven were

monitored via sensors. A sensor was placed outside the oven to monitor relative

humidity and temperature outside the oven. Another sensor was placed inside

oven to monitor relative humidity and temperature near the surface of the berries.

4. A data logger was switched on to monitor the reading of sensors mentioned in

Step 3.

5. After three hours, the sample was released from the sealed plastic bag and the

excessive moisture on the surface of the spikes of the berries was wiped using a

dry cloth.

6. The berries were threshed from the spikes by hand to obtain the berries.

7. A number of berries was selected and placed on a specially designed tray in

order to observe the changes of the internal structure of individual berries.

Another two berries were selected to capture the initial cross section of Piper

Nigrum L. berries. The details of the procedure related to this observation are

provided in the next section.

8. The remaining berries were weighed and the weights were recorded. This

reading was the initial mass of the Piper Nigrum L. berries.

9. After weighing, these berries were placed on a plate.

10. A trial was considered to have started once the plate with berries was put in the

convection oven.

11. During the trial, the weight of the berries was sensed by a load cell. Readings

from the load cell were recorded at 30-minute intervals via the data logger

mentioned in Step 4.

12. A trial was stopped when the mass of the berries reached about 33% of the

initial mass.


31

13. A trial which yielded berries with a reduced mass of more than 33% after 72

hours was stopped immediately. This is because berries, which were dried

excessively, produce a bad odour after 72 hours.

3.1.2.2 Forced Convection Trials

The procedure below was followed to configure the setup of each trial and to carry out

the study proposed:

1. A pack of berries was withdrawn from storage and left at room temperature for

three hours.

2. The blower of the drying system was switched on and adjusted to the required

air velocity. The heating element of the drying system was switched on as well.

3. At the same time, the data logger was turned on to monitor the reading of all

sensors installed inside the channel before each trial started to ensure the speed

of air flow and the drying temperature of the drying system is at the level

required.

4. After three hours, the sample was released from the sealed plastic bag and the

excessive moisture on the surface of the spikes of the berries was wiped using a

dry cloth.

5. The berries were threshed from the spikes by hand to obtain the berries.

6. A number of berries was selected and placed on a specially designed mesh in

order to observe the change of the internal structure of individual berries.

Another two berries were selected to capture the initial cross section of Piper

Nigrum L. berries. The details of the procedure related to this observation are

provided in the next section.

7. The remaining berries were weighed and the weights were recorded. This

reading was the initial mass of Piper Nigrum L. berries.

8. After weighing, these berries were placed on a tray.

9. A trial was considered to have started once the tray with berries was put in the

oven.

10. At the beginning of the drying, the tray was withdrawn from the oven every 30

minutes to record the mass of the berries. When the loss in mass first reached 50%

of the previous amount lost, the interval was prolonged to 60 minutes. This

interval was maintained until the loss in mass reduced a further 50%. Then the

interval was prolonged to 120 minutes.


32

11. A trial was stopped when the mass of the berries reached about 34% of the

initial mass.

12. A trial which yielded berries with a reduced mass of more than 34% after 72

hours was stopped immediately. This is because berries dried excessively

produced bad odour after 72 hours of drying.

3.1.2.3 Observations of Internal Changes

In order to observe the changes to the internal structure of each drupe during each trial,

the following steps were taken:

1. Berries were retrieved from the specially-designed tray (natural convection trials)

or mesh (forced convection trials) every 12 hours.

2. The surface of each berry was observed and captured using a web cam, Sensonic,

installed on one of the eye pieces of Stereoscopic Zoom Microscope SMZ445.

3. After that, the berries were sectioned into two halves.

4. One of the halves was chosen and its inner structure was observed and captured

using devices mentioned in Step 2.

3.1.2.4 Measurement of Radius of Black Pepper Yield

The radius of the pepper berry was measured from the images captured using the

software AnalyzingDigitalImages, version 11.0. This software was developed by

Lawrence Hall of Science. The radius chosen for calculation is an average value of all

the measurements done on the samples.

3.1.2.5 Measurement of Moisture Content of Black Pepper Yield

After the completion of each experiment, the berries were sent to the Malaysian Pepper

Board to determine the moisture content of the berries. The moisture content was

determined using the distillation method following the procedures outlined in the ASTA

Method No. 2.0, the Official Analytical Methods of the American Spices Trade

Association.

3.1.2.6 Measurement of Piperine Content of Black Pepper Yield

Malaysian Pepper Board assisted in measuring the piperine content of the black pepper

yield from each experiment as well. The piperine content was determined using the

spectrophotometric procedure following the procedures outlined in the ASTA Method

No. 2.0, the Official Analytical Methods of the American Spices Trade Association.


33

3.2 Mathematical Modelling Study

Based on Crank’s recommendation (1975), the analytic solution was used to describe

the drying behaviour of Piper Nigrum L. berries in natural convection trials. The results

were computed via the Microsoft Excel 2007 and are presented in Appendix 4a and 4b.

These results were validated with experimental data.

The model established in Patil’s work (1988) was adopted to describe the drying

behaviour of the berries in forced convection trials. It involved the use of finite

difference method in solving the Fick’s second law, particularly the diffusion equation

of a sphere in the radial direction. The moisture profile within the berry at different

drying temperatures was simulated using this method. These results are shown in

Appendix 7a and 7b. The analytic solution, which was used to describe the drying

behaviour of the berries, was also used to describe the drying behaviour of the berries in

forced convection trials. The results computed are presented in Appendix 6a and 6b.

These results were validated with experimental data. The scope of the mathematical

model used in this study is outlined in section 2.4.

3.2.1 Method of Analytic Solution

The diffusion equation of a sphere in radial direction for a constant diffusion coefficient

is given by

2

22

r

M

r

M

rD

t

M. (1)

Based on Crank’s suggestion (1975), the analytic solution is used to solve equation (1).

The analytic solution is given by

2

22

220

exp16

r

tDn

nMM

MMM eff

e

er

. (2)

With the help of computational software such as Excel, the evaluation of the term in the

analytical solution becomes feasible. It was found that the first three terms of the series

in equation (2) is sufficient to describe the actual drying behaviour. The Appendix 4a

and 4b show the evaluations done to calculate the moisture content and piperine content

at different drying temperatures.


34

3.2.1.1 Input Parameters

The time step, t , used in the computation was 0.5 hours. The value of the radius of a

berry was 3.05mm. The diffusion coefficient was assumed to be constant in this work

and it was determined via the Simplified Method. The value of the diffusion coefficient

D or the effective diffusivity Deff for moisturewas calculated using a simplified equation

modified from equation (2). The following equation shows the simplified equation (2):

tr

DM

eff

r 2

2

2

6lnln

. (3)

Equation (3) is a straight line with the slope, m = 2

2

r

Deff and with the y-intercept at

2

6ln

on the plane with rMln being the vertical axis and t being the horizontal axis.

Then, Deff was calculated from 2

2

mr

Deff . Effective diffusivity for piperine was

calculated using the same methods. Section 3.4.1 and 3.4.2 present the calculation

involved to determine the effective diffusivity of moisture and piperine respectively at

different drying temperatures.

The equilibrium moisture content, Me, was determined using Henderson’s Equilibrium

Moisture Content equation:

beMTcExpRH 1002731 . (4)

The Appendix 3 displays the value of Me obtained using the equation above.

Based on the experimental data, the value of b was estimated to be 2.035 while the

value of c was estimated to be 1.697E-05. The details of the calculation to estimate the

value of b and c are presented in the Appendix 2. The following table shows the input

parameter used in the analytical solution:


35

Table 3.1: Input Parameters

Drying Conditions Properties of the Piper Nigrum L. Berry T, oC

RH, %

μ, kgm-1hr-1

u, mhr-1

Initial Moisture Content, db,

decimal

Initial Piperine Content, db,

decimal

r, m

30 61.36 6.790E-02 0 2.022 5.955E-02 3.047E-03

35 49.14 6.877E-02 0 2.022 5.955E-02 3.047E-03

40 35.24 6.964E-02 0 2.022 5.955E-02 3.047E-03

45 28.27 7.050E-02 0 2.022 5.955E-02 3.047E-03

50 22.33 7.136E-02 0 2.022 5.955E-02 3.047E-03

55 16.22 7.221E-02 0 2.022 5.955E-02 3.047E-03

3.2.1.2 Validation of Results of the Mathematical Model

In order to compare the calculated results with the experimental results, the amount of

average moisture content calculated was added with the amount of average piperine

content calculated and the amount of dry matter of Piper Nigrum L. berries calculated to

make up the mass of the berries.

3.2.2 Method of Numerical Solution

Assumptions made (Patil 1988, pp. 27) when deriving the model were:

1. No thermal gradient exists within Piper Nigrum L. berries. Based on a study by

Hussain and Dincer (2003), the temperature within a spherical object reaches its

equilibrium in the first hour of drying. The drying of Piper Nigrum L. berries

took at least 24 hours to complete. Hence, temperature gradient is negligible.

2. A berry consists of “n” equally thick, concentric spherical shells of

homogeneous material. Each of these shells represents the moisture profile at

interior nodes, the centre, and the surface of the berry at unit time intervals.

Refer to Figure 3.3, Figure 3.4, and Figure 3.5.

3. The moisture movement within the berry is radial. It has been observed by

Hussain and Dincer (2003) that the moisture movement in a spherical object

only occurs in radial direction.

4. The shrinkage which occurs during the diffusion process is negligible.


36

Figure 3.3: Cross Section of a Piper Nigrum L. Berry

Figure 3.4: Model which Represents the Whole Drupe

Figure 3.5: Equivalent Model which Represents the Whole Drupe


37

Boundary conditions used (Patil 1988, pp. 27) were:

1. At t = 0, the berry had a uniform moisture content in the different layers of

shells at interior nodes.

2. The moisture profile at the centre of the drupe was equal to the moisture profile

of its neighbouring shell throughout the process.

3. The moisture profile at the surface, Ms,j, was calculated from the convective

boundary condition using the following equation:

eSDS

MMhr

MD

. (5)

3.2.2.1 Finite Difference Equations

Applying the finite difference method, each differential in Equation (1) could be written

as

t

MM

t

M jiji

,1,

for i = 1, 2, 3, ..., n, (6)

r

MM

r

M jiji

,,1

for i = 1, 2, 3, ..., n, and (7)

2

,1,,1

2

2

)(

2

r

MMM

r

M jijiji

for i = 1, 2, 3, ..., n. (8)

Substituting Equations (6), (7), and (8) into Equation (1) yields

jijijijiji MM

i

iM

i

i

r

D

t

MM,1,,12

,1,

12

24

12

32

)( . (9)

Rearranging Equation (9),

jijijijiji MMi

iM

i

i

r

tDMM ,1,,12,1, 12

24

12

32

)(

. (10)

Equation (10) is only applicable for interior nodes, or i = 1, 2, 3, ..., n-1. Some

modification was done to to calculate moisture content at i = n.


38

As distance between surface and node i = n is half the distance between i = n - 1

and i = n, so,

r

MM

r

MM

r

M jnjsjnjn

,,,1, 2

. (11)

Also,

2

,1,,

2

2

)(

32

r

MMM

r

M jnjnjs

. (12)

Substituting Equations (6), (11), and (12) into Equation (1) yields

2

,1,,,,,1, 322

12

4

r

MMM

r

MM

nrD

t

MM jnjnjsjnjsjnjn

.

(13)

Rearranging Equation (13),

jnjnjsjnjn MMn

nM

n

n

r

tDMM ,1,,2,1, 12

56

12

64

)(

. (14)

To compute Ms,j from Equation (5), Equation (11) is substituted into it to have

ejsDjnjs MMh

r

MMD

,

,, 22

. (15)

Rearranging Equation (15) gives

rhD

rMhDMM

D

eDjnjs

2

2 ,, . (16)

The Appendix 7a and 7b show the computation performed to determine the moisture

profile and piperine profile within a berry under different drying conditions.

The value of the diffusion coefficient D of moisture is calculated using the Simplified

Method. The effective diffusivity for piperine is calculated using the same method as


39

well. The section 4.4.1 and 4.4.2 present the calculation involved to determine the

effective diffusivity of moisture and piperine respectively under different drying

conditions.

3.2.2.2 Input Parameters

The time step, t , used in the computation was 0.5 hours. The values of equilibrium

moisture content, Me, for forced convection trials used were similar to the values used

in natural convection trials as shown in Appendix 3.

The mass transfer coefficient, hD, was calculated using the mass correlations (Bird,

Stewart & Lightfoot 2002) which has the equation,

]800,2[Re ,Re552.02 3

1

2

1

ScD

dhSh D (17)

,Reud

where (18)

.D

Sc

(19)

The Appendix 5 displays the values of parameters used to compute the value of hD for

different drying conditions.

The following table shows the input parameters used in the mathematical model derived:

Table 3.2: Input Parameters

Drying Conditions Properties of Piper Nigrum L. Berry u,

ms-1

T,

oC

RH,

%

μ,

kgm-1hr-1

hD,

mhr-1

Initial Moisture Content, db,

decimal

Initial Piperine Content, db,

decimal

d,

m

n

0.5 35 49.14 6.877E-02 5.777E-03 1.986 5.108E-02 6.093E-03 4

0.5 45 28.27 7.050E-02 9.436E-03 1.986 5.108E-02 6.093E-03 4

0.5 55 16.22 7.221E-02 1.520E-02 2.077 5.042E-02 6.093E-03 4

1.0 35 49.14 6.877E-02 1.035E-02 2.022 5.955E-02 6.093E-03 4

1.0 45 28.27 7.050E-02 1.784E-02 2.030 4.987E-02 6.093E-03 4

1.0 55 16.22 7.221E-02 2.440E-02 2.077 5.042E-02 6.093E-03 4


40

3.2.2.3 Validation of Results of the Mathematical Model

In order to compare the calculated results with the experimental results, the amount of

average moisture content calculated was added to the amount of average piperine

content calculated and the amount of dry matter of Piper Nigrum L. berries calculated to

make up the mass of the berries.

The average moisture content was computed using the formula,

Rr

rdrMr

RM

0

23

3 (20)

Equation (20) was solved using the trapezoidal rule. The methodology was as follows:

Let f(r) = Mr2. f(r) be discretized and divided into different functions based on the

different locations in the berries:

Table 3.3: Discretization of the function, f(r)

Different Locations in Berries f(r)

Center of Berry f(rcenter) = f(rc) =Mc,j(02) = M1,j (0

2) = 0

Interior of Berry f(ri) =Mi,jri2, where ri= iδr, i = 1, 2, 3, ..., n.

Surface of Berry f(rsurface = R) =Ms,j( nδr + 0.5δr )2

Applying the trapezoidal rule yields,

)()(2

1

)()(2)(

)()(2

1

2)(

1

21

1

Rfrf

rfrfrf

rfrf

rdrrf

n

n

n

ii

c

. (21)

Substituting the functions listed in Table 3.3,

2,

2,

2,

1

2

2,

2,1

2,1

))5.0(()(2

1

)()(2)1(

)1(02

1

2)(

rnMrnM

rnMriMrM

rM

rdrrf

jsjn

jn

n

ijij

j

and


41

jsjn

jn

n

ijij

j

MnMn

MnMiM

M

R

r

drrfR

M

,2

,2

,2

1

2,

2,1

,1

3

3

3

)5.0(2

1

2

2

1

2

3

)(3

. (22)

The average piperine content was computed as well using the same methodology

explained above. The Appendix 8 and 9 present the computation of the average

moisture content and piperine content respectively using the methodology above.

Chapter 4: Results and Discussions

42

CHAPTER 4: RESULTS AND DISCUSSIONS

4.1 Results and Discussions of Experimental Study for Natural Convection

Trials

Based on studies done by Demir et al. (2007), Garau et al. (2006), Guiné & Fernandes

(2006), Gunhan et al. (2005) and Nourhène et al. (2008), it was expected that the mass

of the Piper Nigrum L. berries would reduce exponentially with time. Moreover, from

Patil’s studies (1989, pp. 231), the drying time of Piper Nigrum L. berries would likely

reduce significantly as drying temperature was increased. Results from the natural

convection trials met these expectations.

4.1.1 Effects of Drying Temperature on Drying Rate

From the experimental results, it was found that the mass of the Piper Nigrum L. berries

reduced exponentially with time at all drying temperatures studied. The results are

shown in Figure 4.1. In general, there was more loss in the mass of Piper Nigrum L.

berries when they were dried at a higher drying temperature. The drop was significant

when the drying temperature was raised from 30oC to 35oC, from 35oC to 40oC, and

from 40oC to 45oC. The drop was less significant when the drying temperature was

raised from 45oC to 50oC and from 50oC to 55oC. This implies the drying rate of Piper

Nigrum L. berries increased as drying temperature was raised. Thus, the drying rate of

Piper Nigrum L. berries was the highest at 55oC while it was the lowest at 30oC.


43

Figure 4.1: Mass Change of Piper Nigrum L. Berries at Different Drying Temperatures

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

0 12 24 36 48 60 72 84

Dim

ensionless Mass

Elapsed Time (Hour)

Mass Change at Different Drying Temperatures

30C

35C

40C

45C

50C

55C

30oC

35oC

40oC

45oC

50oC

55oC


44

4.1.2 Effects of Drying Temperature on Duration for Drying

From Figure 4.2, it can be seen that the duration for drying is shorter at a higher drying

temperature. This duration reduced exponentially with an increase in drying

temperature. Drying trials done at drying temperatures of 45oC and 50oC showed that

the mass of berries reached less than 33% of its initial mass within the same period of

time, which is 36 hours. The duration was the shortest (24 hours) at the highest

temperature (55oC) used in the natural convection trials.

Figure 4.2: Drying Duration at Different Drying Temperatures

0

12

24

36

48

60

72

84

30 35 40 45 50 55

Drying Duration (hour)

Drying Temperature (oC)

Drying Duration at Different Drying Temperatures


45

4.1.3 Effects of Drying Temperature on the Retention of Chemical Constituents

In this study, initial moisture content of berries in all the trials was about 66.91% wb.

From Figure 4.3, it was found that the retention of piperine is much higher than

moisture for all drying temperatures. This means the diffusivity of moisture within the

berries is much higher than the diffusivity of piperine within the berries.

In general, the amount of moisture retained in berries dropped as drying temperature

was raised. There was less moisture retained in berries at drying temperature 45oC,

50oC and 55oC compared to 30oC, 35oC and 40oC. These observations imply that the

effective diffusivity of moisture increased as drying temperature was raised. The

increment of effective diffusivity of moisture in Piper Nigrum L. berries was higher

when drying temperature was raised from 30oC to 35oC, and from 40oC to 45oC. The

increment of effective diffusivity of moisture in Piper Nigrum L. berries was lower

when drying temperature was raised from 45oC to 55oC.

On the other hand, the amount of piperine retained in berries did not deviate much at

drying temperatures studied except at 30oC. There was much more piperine retained in

berries at 30oC compared to berries dried at other higher drying temperatures. This

suggests that the effective diffusivity of piperine in the berries dried at 30oC is much

lower than effective diffusivity of piperine of the berries dried at other higher drying

temperatures.

Figure 4.3: Retention of Chemical Constituents After Drying at Different Drying

Temperatures

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

0.00%

5.00%

10.00%

15.00%

20.00%

30 35 40 45 50 55

Piperin

e Retain

ed (g/g)

Moisture Retained (ml/ml)

Temperature (oC)

Retention of Chemical Constituents After Drying at Different

Drying Temperatures

Moisture Retained (%) Piperine Retained (%)


46

4.1.4 Optimum Drying Condition

Berries dried at drying temperatures 30oC and 35oC did not reach less than 33% within

three days suggesting that these were not the optimum temperature to dry berries of

Piper Nigrum L.. This means that the drying temperature used to dry the berries of Piper

Nigrum L. should be at least above 35oC. The optimum drying condition should be a

condition which is able to produce black pepper with the lowest moisture content and

highest piperine content in the shortest drying duration. Table 4.1 shows the amount of

moisture retained, amount of piperine retained and drying duration at different drying

temperatures. The data in Table 4.1 is arranged based on the drying condition from the

highest to the lowest temperature. Since drying rate is the highest at the highest

temperature, 55oC is placed at the top in the table while 30oC is placed at the bottom.

Since the first three conditions were able to produce black pepper within the shortest

drying duration with the lowest moisture content and highest piperine content, it is

concluded that the drying temperatures 45oC, 50oC and 55oC are the optimum drying

conditions.

Table 4.1: Amount of Moisture Retained, Amount of Piperine Retained and Drying

Duration at Different Drying Temperatures

Drying Condition

oC

Moisture Content Retained (ml/ml)

Piperine Content Retained

(g/g)

Drying Duration

(Hours)

55 5.43% 32.34% 2450 4.78% 30.46% 3645 6.28% 31.57% 3640 12.34% 34.93% 4835 11.00% 35.43% 7230 15.48% 50.09% 72

oC


47

4.1.5 Effects of Drying Temperature on the Changes to the Internal Structure of

the Individual Drupe

Figure 4.4: Internal Structural Changes of Individual Drupes at Different Drying

Temperatures

From experimental results, it was found that the drying of Piper Nigrum L. berries

caused the formation of holes in the middle of the berries. Refer to Figure 4.4. The hole

observed in the berries was an extension of the inherited central cavity in the seed. This

cavity was observed by researcher in the Sarawak State Department of Agriculture as

shown in Figure 4.5. The extension of the cavity in the berries was caused by the

shrinkage of berries which occurs during the drying process.

Blackening

Starting Time

Cavity

Extension

Starting Time

Shrinkage

under the

stresses in

the volum

volume by

temperatu

expansion

temperatu

formed at

Dimensionless Characteristic Length

Figure 4.5:

e of dried m

influence o

n the proces

me Piper Ni

y the end of

ure was rai

n rate in Fig

ure. At 30oC

the 12th hou

Figure 4.6

0.7000

0.8000

0.9000

1.0000

1.1000

0

S

Longitudin

material is u

of internal s

ss of drying

igrum L. be

f drying. Fi

ised higher

gure 4.4. Th

C, the cavity

ur of drying

: Shrinkage

12

Shrinkage a

nal Section o

usually attr

stresses in t

g can lead to

erries event

igure 4.6 sh

r. This ma

he cavity e

y formed at

g.

e of Berries

24 36

Elapsed

at Differen

Cha

of Fruit (Ch

ributed to th

the materia

o cracks. Fr

tually reduc

hows that sh

atches with

extension oc

the 72nd ho

at Differen

48

d Time (Hour)

nt Drying Te

apter 4: Re

hih & Sim 1

he fact that

l. The relat

rom the ana

ced to 72%

hrinkage occ

h the obser

ccurred earl

our of dryin

t Drying Te

60 72

)

emperatur

esults and D

1977, pp. 14

t the capilla

tive growth

alysis of the

% - 83% of

curred faste

rvation in

lier at a hig

ng. At 55oC

emperatures

2 84

res

Discussions

48

4)

aries shrink

of internal

e shrinkage,

its original

er as drying

the cavity

gher drying

C, the cavity

s

30C

35C

40C

45C

50C

55C

30oC

35oC

40oC

45oC

50oC

55oC

8

k

l

,

l

g

y

g

y


49

The formation of cavity reduced the pore size of the internal structure. This caused an

increase in the resistance of moisture diffusion. So, moisture diffusivity may reduce

greatly after cavity extension takes place. However, based on the drying curve in Figure

4.1, cavity formation took place at a time when the concentration of moisture reached

an equilibrium state. Thus, the shrinkage of Piper Nigrum L. berries does not have a

great influence on drying rate of Piper Nigrum L. berries.

From Figure 4.4, the natural convection trials confirmed that the drying of Piper

Nigrum L. berries caused blackening in the pericarp of the berries. This phenomenon

occurred faster in a system with a higher drying temperature. At 30oC, the blackening of

the pericarp took place after three days of drying. At 55oC, the blackening of pericarp

started after 12 hours of drying.

4.2 Results and Discussions of Experimental Study for Forced Convection Trials

Based on studies done by Kaya et al. (2007a) and Kaya et al. (2007b), the increase of

drying air velocity will decrease the drying duration. Based on studies by Ye et al.

(2008), drying air velocity only affects the drying rate at the initial stage. Results from

forced convection trials showed that the force convection did cause a slight

improvement in reducing drying duration but not significantly. The results also showed

that the drying air velocity not only affects the drying rate at the initial stage, it affects

the drying process entirely.

4.2.1 Effects of Air Flow on Drying Rate

Figure 4.7 shows the experimental results for forced convection trials. From the figure,

it was found that the mass of Piper Nigrum L. berries reduced faster when the higher

speed of air flow was used at drying temperatures 35oC, 45oC, and 55oC. This implies

that the drying rate of Piper Nigrum L. berries increased when a higher speed of air

flow was used at drying temperatures 35oC, 45oC, and 55oC. The drying rate was higher

in the first 24 hours of drying when forced convection was introduced in the drying

system. After 24 hours of drying, the drying rate at all air flow speeds was similar. This

result confirms the significance of air flow in the first 24 hours of drying at 45oC as

claimed by Patil (1989). At 35oC, air flow speed played an important role at all time. It

could be deduced that air flow speed is less significant in a system with a higher drying

temperature than 55oC.


50

Figure 4.7: Mass Change During Drying under Different Air Flow Speeds at

35oC, 45oC, and 55oC

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

0 12 24 36 48 60 72 84

Dim

ensionless M

ass

Elapsed Time (Hour)

Mass Change During Drying under

Different Air Flow Speeds at 35oC

0.0ms^‐1 0.5ms^‐1 1.0ms^‐10.5ms‐1 1.0ms‐10.0ms‐1

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

0 12 24 36 48 60 72 84

Dimensionless M

ass

Elapsed Time (Hour)



0.0ms^‐1 0.5ms^‐1 1.0ms^‐10.5ms‐1 1.0ms‐10.0ms‐1

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)



0.0ms^‐1 0.5ms^‐1 1.0ms^‐10.5ms‐1 1.0ms‐10.0ms‐1


51

4.2.2 Effects of Air Flow on Drying Duration

From Table 4.2 and Figure 4.8, the presence of forced convection decreased the drying

duration at 35oC, 45oC, and 55oC. The difference was slightly more obvious when the

speed of air flow was raised from 0.5ms-1 to 1.0ms-1. This means the duration of a

drying process could be shorten at higher speed of air flow. However, the difference

was not much compared to effect of drying temperatures. The increase of speed in air

flow did not decrease the drying duration as much as the increase of drying temperature

did.

Table 4.2 : Drying Duration under Different Air Flow Speeds at 35oC, 45oC, and 55oC

Figure 4.8: Drying Duration under Different Air Flow Speeds at 35oC, 45oC, and 55oC

0 0.5 1

35 72 72 50.545 36 34 2255 24 18 14.5

Drying Temperature,

T, degree Celcius

Air Flow Speed(ms-1)

Drying Duration(Hour)

Air Flow Speed(ms-1)Drying

Temperature(oC)

0

12

24

36

48

60

72

84

0.0 0.5 1.0

Drying Duration (hour)

Air Flow Speed (ms‐1)

Drying Duration under Different Air Flow Speeds at


55oC 45oC 35oC45oC55oC 35oC


52

4.2.3 Effects of Air Flow on the Retention of Chemical Constituents

The initial moisture content of berries in forced convection trials was about 67.00% wb.

In general, the speed of air flow did not affect retention of chemical constituents at 55oC.

The presence of air flow increased the diffusivity of moisture in berries at a drying

temperature 35oC but reduced the diffusivity of piperine in berries at a drying

temperature 45oC.

At a drying temperature of 35oC, a significant drop in the moisture retained in Piper

Nigrum L. berries could be observed as the speed of air flow was raised. At drying

temperatures of 45oC and 55oC, the moisture retained in Piper Nigrum L. berries was

about the same for all speeds of air flow used. This suggests that forced convections do

not have much impact on the moisture retained in Piper Nigrum L. berries at 45oC and

55oC. The presence of forced convection in a drying system with drying temperature

35oC could increase the diffusivity of moisture in Piper Nigrum L. berries but not in

drying temperatures 45oC and 55oC.

On the other hand, the amount of piperine retained in Piper Nigrum L. berries was

similar for all the speeds of air flow at drying temperature 35oC and 55oC. There was

more piperine retained in Piper Nigrum L. berries with the presence of forced

convection at a drying temperature of 55oC. Figure 4.9 shows that less moisture was

retained in berries while more piperine was retained when berries were dried under

forced convection at a drying temperature of 45oC and 55oC. This indicates 45oC and

55oC might be the optimum drying temperatures in a drying system with forced

convection.


53

Figure 4.9: Retention of Chemical Constituents After Drying under

Different Air Flow Speeds

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.0 0.5 1.0

Piperin

e Retain

ed (g/g)

Moisture Retained

(ml/ml)


Retention of Chemical Constituents After Drying under Different Air Flows at 35oC


0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.0 0.5 1.0

Piperin

e Retain

ed (g/g)

Moisture Retained

(ml/ml)




0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.0 0.5 1.0

Piperin

e Retain

ed (g/g)

Moisture Retained

(ml/ml)





54

4.2.4 Ranking of Drying Conditions

In this section, the performance of natural convection trials and forced convection trials

are ranked. Figure 4.10 shows the mass change in natural convection trials and forced

convection trials at 35oC, 45oC, and 55oC. The ranking was done based on the drying

rates. The drying condition with the highest drying rate was ranked in the highest

position in the legend of Figure 4.10. This figure shows that drying rates of 55oC at

1ms-1 is the highest while drying rates of 35oC at 0ms-1 is the lowest. Based on the

drying rates of 55oC at 1ms-1 is the best drying condition.

Figure 4.10: Mass Change in Natural Convection Trials and Forced Convection Trials

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

1.1000

0 12 24 36 48 60 72 84

Dim

ensionless M

ass

Elapsed Time (Hour)

Mass Change Under Different Drying Conditions

55C, 1ms‐1

55C, 0.5ms‐1

45C, 1ms‐1

55C, 0ms‐1

45C, 0.5ms‐1

45C, 0ms‐1

35C, 1.0ms‐1

35C, 0.5ms‐1

35C, 0ms‐1

55oC, 0.0ms‐1

55oC, 0.5ms‐1

55oC, 1.0ms‐1

45oC, 0.0ms‐1

35oC, 0.5ms‐1

35oC, 0.0ms‐1

45oC, 0.5ms‐1

45oC, 1.0ms‐1

35oC, 1.0ms‐1


55

4.2.5 Optimum Drying Condition

The optimum drying condition should be a condition which is able to produce black

pepper with the lowest moisture content and highest piperine content in the shortest

drying duration. Table 4.3 above shows the amount of moisture retained, amount of

piperine retained, and drying duration at different drying conditions. The data in Table

4.3 was arranged according to the ranking done in previous section. As drying rate

increased, the moisture retained in Piper Nigrum L. berries decreased. The amount of

piperine retained in Piper Nigrum L. berries was about the same in all natural

convection trials and forced convection trials except at 45oC, 1ms-1 and 45oC, 0.5ms-1.

In general, as drying rate increased, drying duration decreased. Since the first four

conditions were able to produce black pepper within the shortest drying duration at the

highest drying rate, with the lowest moisture content, and with the highest piperine

content, it is concluded that a combination of drying temperature from 45oC to 55oC and

air flow speed from 0.5ms-1 to 1.0ms-1 provides the optimum drying condition.

Table 4.3: Amount of Moisture Retained, Amount of Piperine Retained, and Drying

Duration at Different Drying Conditions

Drying Condition

Moisture Content Retained (ml/ml)

Piperine Content Retained

(g/g)

Drying Duration

(Hour)

55 C, 1.0ms 4.75% 30.78% 14.555 C, 0.5ms 4.59% 31.52% 1845 C, 1.0ms 5.95% 28.61% 2255 C, 0.0ms 5.43% 32.34% 2445 C, 0.5ms 6.02% 30.50% 3445 C, 0.0ms 6.28% 31.57% 3635 C, 1.0ms 7.29% 30.57% 50.535 C, 0.5ms 9.52% 33.08% 7235 C, 0.0ms 11.00% 35.43% 72

o -1

o -1

o -1

o -1

o -1

o -1

o -1

o -1

o -1

oC


56

4.2.6 Effects of Air Flow on the Changes to the Internal Structure of the

Individual Drupe

Figure 4.11: Internal Structural Changes of Individual Drupes at Different Air Flow

Speeds

From Figure 4.11, there was no obvious trend in the rate of blackening when the air

flow speed was raised. At 55oC, blackening occurred at a similar time for all the speeds

of air flow used. At 45oC, blackening occurred 12 hours earlier in forced convection

trials when compared to natural convection trials. At 35oC, 0.5ms-1, blackening

occurred 12 hours later compared to natural convection trials. At 35oC, 1.0ms-1,

blackening occurred 24 hours earlier than 35oC, 0.5ms-1. Thus, a higher speed of air

flow did not imply a higher rate of blackening in the berries.

In forced convection trials, the inherited cavity was more obvious. This is due to

different varieties used in these trials compared to natural convection trials. From

shrinkage studies, the volume of Piper Nigrum L. berries eventually reduced to

72% - 82% of its original volume at the end of drying. There was no obvious trend in

shrinkage rate when the speed of air flow was raised. A higher speed of air flow did not

imply a higher shrinkage rate.

Blackening

Starting Time


57

Figure 4.12: Shrinkage of Berries at Different Air Flow Speeds at


0.6000

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

0 12 24 36 48 60 72 84

Dim

ensionless Characteristic Length

Elapsed Time (Hour)

Shrinkage Change During Drying at Different Air Flow Speeds at 35oC

0ms^‐1 0.5ms^‐1 1.0ms^‐10.5ms‐1 1.0ms‐10.0ms‐1

0.6000

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

0 12 24 36 48 60 72 84

Dim

ensionless Characteristic Len

gth

Elapsed Time (Hour)


0.0ms‐1 0.5ms‐1 1.0ms‐10.5ms‐1 1.0ms‐10.0ms‐1

0.6000

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

1.0500

0 12 24 36 48 60 72 84

Dimensionless Characteristic Length

Elapsed Time (Hour)


0.0ms‐1 0.5ms‐1 1.0ms‐10.5ms‐1 1.0ms‐10.0ms‐1


58

4.3 Discussion on the Results of Mathematical Modelling used in the Study for

Natural Convection Trials

From the experimental results shown in section 4.1.1, there was more loss in the mass

of Piper Nigrum L. berries when they were dried at higher drying temperatures. An

increase in the effective diffusivity of moisture of Piper Nigrum L. berries was expected

when the drying temperature is higher. Results from the Simplified Method employed

showed that the effective diffusivity of moisture in Piper Nigrum L. berries did increase

with an increase in drying temperature. This meets the expectations of the experimental

results.

4.3.1 Calculation Done to Determine the Effective Diffusivity of Moisture in

Piper Nigrum L. Berries for Natural Convection Trials

Table 4.4 shows the calculation involved via the Simplified Method to calculate the

value of the effective diffusivity of moisture in Piper Nigrum L. for natural convection

trials.

Table 4.4: Calculation Done to Determine the Effective Diffusivity of Moisture in Piper

Nigrum L. Berries for Natural Convection Trials

ln | Mr | t m Deff Drying

Temperature(oC)

Air Flow Speed (m/s)

y2 y1 x2 x1 (y2 - y1) / (x2 - x1)

-mr2 / π2

55 0.0 -3.319E+00 0.0 24.0 0.0 -1.383E-01 1.300E-07 50 0.0 -3.741E+00 0.0 36.0 0.0 -1.039E-01 9.773E-08 45 0.0 -3.289E+00 0.0 36.0 0.0 -9.137E-02 8.592E-08 40 0.0 -2.259E+00 0.0 48.0 0.0 -4.706E-02 4.425E-08 35 0.0 -2.544E+00 0.0 72.0 0.0 -3.534E-02 3.323E-08 30 0.0 -2.419E+00 0.0 72.0 0.0 -3.360E-02 3.159E-08

4.3.2 Calculation Done to Determine the Effective Diffusivity of Piperine in

Piper Nigrum L. Berries for Natural Convection Trials

shows the calculation involved via the Simplified Method to calculate the value of the

effective diffusivity of piperine in Piper Nigrum L. for natural convection trials.


59


value of the effective diffusivity of piperine in Piper Nigrum L. for natural convection

trials.

Table 4.5: Calculation Done to Determine the Effective Diffusivity of Piperine in Piper

Nigrum L. Berries for Natural Convection Trials


Temperature (oC)


y2 y1 x2 x1 (y2 - y1) / (x2 - x1)

-mr2 / π2

55 0.0 -1.350E-01 0.0 24.0 0.0 -5.614E-03 5.280E-09 50 0.0 -3.210E-01 0.0 36.0 0.0 -8.906E-03 8.375E-09 45 0.0 -2.450E-01 0.0 36.0 0.0 -6.808E-03 6.402E-09 40 0.0 -2.520E-01 0.0 48.0 0.0 -5.258E-03 4.945E-09 35 0.0 -1.280E-01 0.0 72.0 0.0 -1.781E-03 1.675E-09 30 0.0 -7.700E-02 0.0 72.0 0.0 -1.064E-03 1.000E-09

4.3.3 Relation of Effective Diffusivity with Temperature

From the calculation done, it was found that the effective diffusivity of piperine was

much lower than the effective diffusivity of moisture. The effective diffusivity for

piperine ranged from 1.086E-9m2/hr to 8.375E-9m2/hr while the effective diffusivity of

moisture ranged from 3.159E-8m2/hr to 1.300E-7m2/hr.

At drying temperatures ranging from 30oC to 55oC, the effective diffusivity of moisture

in Piper Nigrum L. berries increased with drying temperatures. From Figure 4.13, an

obvious increase was observed when the drying temperature rose from 40oC to 45oC.

This result matches the observation in the mass change of berries obtained from

experimental results. The drying rate of the berries increased when berries were dried in

a system with a higher drying temperature.

Looking at the piperine, its effective diffusivity reached its highest point at 50oC. This

means that the retention of piperine was lowest at 50oC. It can be concluded that the

drying temperature at 45oC or 55oC retains more piperine compared to 50oC while

keeping a minimum amount of moisture within Piper Nigrum L. berries. However, the


60

difference in the piperine retained in berries was insignificant when berries were dried

at 45oC, 50oC and 55oC. So, 50oC is still within the range of optimum drying conditions.

Figure 4.13: Relation of Effective Diffusivity of Moisture and Piperine with

Drying Temperature

A high correlation was found between the effective diffusivity of moisture and drying

temperature as can be seen in Figure 4.14. The value of R2 was estimated to be 0.9313.

Data was later fitted into the Arrhenius equation

RT

EDD aexp0 , where D0 is the

Arrhenius factor (m2s-1), Ea is the activation energy (kJ/mol), R is the universal gas

constant = 8.314J/mol K, and T is drying temperature (K). From the fit, the Arrhenius

factor was estimated to be 22.779m2s-1 and activation energy was estimated

to be 51.743kJ/mol. The details of the calculation to estimate the value of the Arrhenius

factor and activation energy of the berry are presented in the Appendix 1.

Figure 4.14: Relation of Effective Diffusivity of Moisture with Drying Temperature

0.0000E+00

2.0000E‐08

4.0000E‐08

6.0000E‐08

8.0000E‐08

1.0000E‐07

1.2000E‐07

1.4000E‐07

25 30 35 40 45 50 55 60

Effective Diffusivity, D

(m

2/hr)

Drying Temperature, T (oC)

Relation of Effective Diffusivity of Moisture for Different Drying Temperatures

0.0000E+00

1.0000E‐09

2.0000E‐09

3.0000E‐09

4.0000E‐09

5.0000E‐09

6.0000E‐09

7.0000E‐09

8.0000E‐09

9.0000E‐09

25 30 35 40 45 50 55 60


(m

2 /hr)

Drying Temperature, T (oC)

Relation of Effective Diffusivity of Piperine for Different Drying Temperatures

R² = 0.9313

0.0000E+00

2.0000E‐08

4.0000E‐08

6.0000E‐08

8.0000E‐08

1.0000E‐07

1.2000E‐07

1.4000E‐07

300 305 310 315 320 325 330

Effective Diffusivity, m

2/hr

Drying Temperature (K)

Deff vs T


61

Figure 4.15: Fitting Data into Arrhenius Relation

y = ‐62237x + 3.1259

‐1.7600E+01

‐1.7400E+01

‐1.7200E+01

‐1.7000E+01

‐1.6800E+01

‐1.6600E+01

‐1.6400E+01

‐1.6200E+01

‐1.6000E+01

‐1.5800E+01

‐1.5600E+01

3.0000E‐03 3.0500E‐03 3.1000E‐03 3.1500E‐03 3.2000E‐03 3.2500E‐03 3.3000E‐03 3.3500E‐03

ln(Effective Diffusivity)

1/Drying Temperature (1/K)

ln (Effective Diffusivity) vs 1/(Drying Temperature)


62

4.3.4 Validation of Results of the Mathematical Model

From Figure 4.16, it can be observed that the results yielded by the analytic solution

shows good agreement with the change in mass from the experimental results.

Figure 4.16: Comparing the Changes in Mass of Piper Nigrum L. Berries at Different Drying Temperatures

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)

Calculated Mass Change and Experimental Mass Change at 55oC

Cal

Exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dim

ensionless Mass

Elapsed Time (Hour)


Cal

Exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)


Cal

Exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)


Cal

Exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)


Cal

Exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72 84

Dimensionless Mass

Elapsed Time (Hour)


Cal

Exp


63

4.4 Discussion on the Results of Mathematical Modelling used in the Study for

Forced Convection Trials

This section presents the results and discussions from the mathematical modelling study

of forced convection drying. From the experimental results shown in Figure 4.7, the

mass of Piper Nigrum L. berries reduced faster when a higher speed of air flow was

used at drying temperature 35oC, 45oC, and 55oC. It was expected to observe an

increase in the effective diffusivity of moisture of the berries of Piper Nigrum L. when a

higher speed of air flow is used at drying temperatures 35oC, 45oC, and 55oC. The

retention of moisture and piperine from the experimental results show that the effective

diffusivity for both the moisture and piperine should increase when a higher speed of air

flow was used at drying temperatures studied. The results of the calculation done met

the expectation.

4.4.1 Calculation Done to Determine the Effective Diffusivity of Moisture in

Piper Nigrum L. Berries for Forced Convection Trials


value of the effective diffusivity of moisture in Piper Nigrum L. for forced convection

trials.

Table 4.6: Calculation Done to Determine the Effective Diffusivity of Moisture in Piper

Nigrum L. Berries for Forced Convection Trials


Temperature(oC)


y2 y1 x2 x1 (y2 - y1) / (x2 - x1)

-mr2 / π2

55 0.5 -3.714E+00 0.0 18.0 0.0 -2.063E-01 1.940E-07 1.0 -3.620E+00 0.0 14.5 0.0 -2.496E-01 2.348E-07

45 0.5 -3.401E+00 0.0 34.0 0.0 -1.000E-01 9.405E-08 1.0 -3.396E+00 0.0 22.0 0.0 -1.543E-01 1.451E-07

35 0.5 -3.422E+00 0.0 72.0 0.0 -4.753E-02 4.470E-08 1.0 -3.420E+00 0.0 50.5 0.0 -6.772E-02 6.368E-08


64

4.4.2 Calculation Done to Determine the Effective Diffusivity of Piperine in

Piper Nigrum L. Berries for Forced Convection Trials


value of the effective diffusivity of piperine in Piper Nigrum L. for forced convection

trials.

Table 4.7: Calculation Done to Determine the Effective Diffusivity of Piperine in Piper

Nigrum L. Berries for Forced Convection Trials


Temperature (oC)


y2 y1 x2 x1 (y2 - y1) / (x2 - x1)

-mr2 / π2

55 0.5 -1.948E-01 0.0 18.0 0.0 -1.082E-02 1.018E-08 1.0 -2.400E-01 0.0 14.5 0.0 -1.656E-02 1.558E-08

45 0.5 -2.615E-01 0.0 34.0 0.0 -7.692E-03 7.233E-09 1.0 -3.482E-01 0.0 22.0 0.0 -1.583E-02 1.488E-08

35 0.5 -3.000E-02 0.0 72.0 0.0 -4.230E-04 3.978E-10 1.0 -2.900E-01 0.0 50.5 0.0 -5.743E-03 5.400E-09

4.4.3 Relation of Effective Diffusivity with Air Flow

At all the drying temperatures studied, the effective diffusivity of moisture increased

when the speed of air flow was raised. This tally with the increase observed in the

drying rate of Piper Nigrum L. when a higher speed of air flow is used at drying

temperature 35oC, 45oC, and 55oC. In fact, a strong correlation was found between the

effective diffusivity of moisture with the speed of air flow at all drying temperature

studied. The slope of the increment in the effective diffusivity of moisture increases

when the drying temperature was raised higher. This means more moisture could be

removed under air flow with higher speed when the drying temperature is raised.

As for the effective diffusivity of piperine, an increase trend was observed as well.

From Figure 4.17, the effective diffusivity of piperine was found to be much lower than

the effective diffusivity of moisture in forced convection trials. There was less piperine

retained when the speed of air flow used was higher.

From Figure 4.17, a combination of higher temperature and air flow speed, in general,

yield higher effective diffusivity of piperine. Thus, when the amount of piperine

retained in black pepper became significant and a drying temperature more than 45oC


65

will be used in a drying system, it is recommended not to choose a speed of air flow

with more than 1.0ms-1.

Table 4.8: Effective Diffusivity of Moisture and Effective Diffusivity of Piperine under

Different Drying Conditions

Figure 4.17: Effective Diffusivity of Moisture and Effective Diffusivity of Piperine

under Different Air Flow Speeds at 35oC, 45oC, and 55oC

0 0.5 1

55 1.3004E-07 1.9403E-07 2.3476E-0745 8.5923E-08 9.4055E-08 1.4514E-0735 3.3232E-08 4.4700E-08 6.3680E-0855 5.2797E-09 1.0178E-08 1.5576E-0845 6.4025E-09 7.2331E-09 1.4884E-0835 1.6747E-09 3.9780E-10 5.4005E-09


Drying Temperature, T, degree Celcius

Moisture Effective Diffusivity, D, m^2/hr

Piperine Effective Diffusivity, D, m^2/hr


Drying Temperature(oC)

Effective Diffusivity of Moisture

(m2hr -1)

Effective Diffusivity of Piperine

(m2hr -1)

R² = 0.9838

R² = 0.8508

R² = 0.9801

0.0000E+00

4.0000E‐08

8.0000E‐08

1.2000E‐07

1.6000E‐07

2.0000E‐07

2.4000E‐07

0.0 0.5 1.0


(m

2/hr)


Effective Diffusivity of Moisture under Different Air Flow Speeds at 35oC, 45oC, and 55oC


0.0000E+00

4.0000E‐08

8.0000E‐08

1.2000E‐07

1.6000E‐07

2.0000E‐07

2.4000E‐07

0.0 0.5 1.0


(m

2 /hr)


Effective Diffusivity of Piperine under Different Air Flow Speeds at 35oC, 45oC, and 55oC



66

4.4.4 Moisture Profile under Different Drying Conditions

Figure 4.18 shows the moisture profile at different layers of a Piper Nigrum L. berry

dried under different conditions and at different drying times. Layer 4.5 indicates the

surface of the berry. In general, moisture diffused faster at layers nearer to the surface

vicinity at all drying conditions studied. From Figure 4.18, it could be observed that the

higher speed of air flow increased moisture diffusion rate at layers nearer to the centre

of the berry.

The difference in the moisture diffusion rate caused by different air flow speeds was

less obvious at higher drying temperatures. After 12 hours of drying, the moisture

content at all layers was lower than 85% at 35oC and 0.5ms-1 while the moisture content

at all layers of berry was lower than 70% at 35oC and 1.0ms-1. The difference was about

15% for 35oC. On the other hand, after 12 hours of drying, the moisture content at all

layers of berry was lower than 15% at 55oC and 0.5ms-1 and the moisture content at all

layers was lower than 10% at 55oC and 1.0ms-1. The difference at 55oC was about 5%.

This was less than forced convection trials at 35oC.

After 12 hours of drying, a significant drop was observed for the moisture at layers

nearer to the centre of the berry when drying temperature was raised from 35oC to 45oC

at 0.5ms-1. The moisture content at all layers was lower than 85% at 35oC while the

moisture content at all layers of the berry was lower than 45% at 45oC. The difference is

40%. A slightly greater drop was observed for a similar raise in drying temperature at

1.0ms-1. The drop was from 70% to 25%, which is 45%. Although the drop from 45oC

to 55oC at all speed of air flow studied is less but the moisture profile shows that the

drying condition 55oC at 0.5ms-1 and 1.0ms-1 are able to reduce the moisture at the

centre greatly from 100% to less than 15% in 12 hours of time. With the increase in the

rate of diffusion in moisture, the rate of shrinkage of the capillaries inside the berry

increase. Thus, increase the shrinkage rate with the increase in the speed of air flow.


67

Figure 4.18: Variation of Moisture Loss Along the Radius in Different Time Periods

in a Berry under Different Drying Conditions

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dim

ensionless M

oisture Content

Layer

Variation of Moisture Loss Along the Radius in Different

Time Periods in a Berry at 55oC, 0.5ms‐1

12.0

18.0

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dim

ensionless M

oisture Content

Layer

Variation of Moisture Loss Along the Radius inDifferent Time Periods in a Berry at 55oC, 1.0ms‐1

12.0

14.5

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dim

ensionless M

oisture Content

Layer



12.0

18.0

24.0

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dimensionless M

oisture Content

Layer



12.0

18.0

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dim

ensionless M

oisture Content

Layer

Variation of Moisture Loss Along the Radius in Different Time Periods in a Berry at 35oC, 0.5ms‐1

12.0

18.0

24.0

0.0000E+00

1.0000E‐01

2.0000E‐01

3.0000E‐01

4.0000E‐01

5.0000E‐01

6.0000E‐01

7.0000E‐01

8.0000E‐01

9.0000E‐01

0 1 2 3 4 5

Dimensionless M

oisture Content

Layer



12.0

18.0

24.0


68

4.4.5 Validation of Results of the Mathematical Model

4.4.5.1 The Analytic Solution

The calculated results yielded from the analytic solution show a satisfactory agreement

with experimental results. This means that the summation of the first three terms is

sufficient to describe the drying behaviour of Piper Nigrum L. berry.

Figure 4.19: Comparing the Changes in Mass of Piper Nigrum L. Berries under

Different Drying Conditions

4.4.5.2 The Numerical Solution

From Figure 4.19 and Figure 4.20, it can be observed that the change in mass from the

experimental results shows better agreement with the model proposed by Patil (1988)

compared to the analytic solution. Table 4.9 shows the standard error of analytic

solution and numerical solution with the experimental results. From the table, it could

be observed that the standard error in numerical solution is less than analytic solution.

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)

Calculated Mass Change and Experimental Mass Change at 55oC, 0.5ms‐1

55C, 0.5ms‐1, cal

55C, 0.5ms‐1, exp

55oC, 0.5ms‐1 , cal

55oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


55C, 1.0ms‐1, cal

55C, 1.0ms‐1, exp

55oC, 1.0ms‐1 , cal

55oC, 1.0ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


45C, 0.5ms‐1, cal

45C, 0.5ms‐1, exp

45oC, 0.5ms‐1 , cal

45oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


45C, 1.0ms‐1, cal

45C, 1.0ms‐1, exp

45oC, 1.0ms‐1 , cal

45oC, 1.0ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


35C, 0.5ms‐1, cal

35C, 0.5ms‐1, exp

35oC, 0.5ms‐1 , cal

35oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


35C, 1.0ms‐1, cal

35C, 1.0ms‐1, exp

35oC, 1.0ms‐1 , cal

35oC, 1.0ms‐1 , exp


69

This implies that the numerical solution produced a slightly better estimation of change

in mass compared to the analytic solution.

Figure 4.20: Comparing the Calculated Mass Change of Piper Nigrum L. Berries at

Different Air Flows with the Experimental Results

Table 4.9: Standard Error of Analytic Solution and Numerical Solution with the Experimental Results.

Drying Temperature

(oC)


Standard Error (Dimensionless)

Analytic Solution

Numerical Solution

55 0.5 9.985E-03 6.197E-03 1.0 7.620E-03 5.869E-03

45 0.5 1.228E-02 1.063E-02 1.0 8.853E-03 3.471E-03

35 0.5 1.135E-02 6.253E-03 1.0 1.581E-02 1.095E-02

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


55C, 0.5ms‐1, cal

55C, 0.5ms‐1, exp

55oC, 0.5ms‐1 , cal

55oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


55C, 1.0ms‐1, cal

55C, 1.0ms‐1, exp

55oC, 1.0ms‐1 , cal

55oC, 1.0ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


45C, 0.5ms‐1, cal

45C, 0.5ms‐1, exp

45oC, 0.5ms‐1 , cal

45oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


45C, 1.0ms‐1, cal

45C, 1.0ms‐1, exp

45oC, 1.0ms‐1 , cal

45oC, 1.0ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)


35C, 0.5ms‐1, cal

35C, 0.5ms‐1, exp

35oC, 0.5ms‐1 , cal

35oC, 0.5ms‐1 , exp

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

0 12 24 36 48 60 72

Dim

ensionless M

ass

Elapsed Time (Hour)

Calculated Mass Change and Experimental Mass Change at35oC, 1.0ms‐1

35C, 1.0ms‐1, cal

35C, 1.0ms‐1, exp

35oC, 1.0ms‐1 , cal

35oC, 1.0ms‐1 , exp

Chapter 5: Conclusion

70

CHAPTER 5: CONCLUSION

5.1 Natural Convection Trials

Natural convection trials show the effects of drying temperature on the drying process

of the Piper Nigrum L. berries. The experimental results obtained show that a higher

drying temperature induces a higher drying rate of the Piper Nigrum L. berries. It also

shows that the drying duration reduces as a higher drying temperature is used in the

drying process. It suggests that the drying temperature must be at least above 35oC in

order to produce black pepper within three days. Drying at 55oC requires the least time

to dry berries until 33% of its initial mass. From the optimum drying condition studies

done, the optimum drying temperature range is concluded to range from 45oC to 55oC.

From the observation of the changes to the internal structure of individual drupe, it is

confirmed that the drying of Piper Nigrum L. berries causes blackening at the pericarp

of the berries. Blackening of the berries occurs faster in a system with higher drying

temperatures. From shrinkage studies, the volume Piper Nigrum L. berries eventually

reduced to 72% - 83% of its original volume by the end of drying. Shrinkage occurs

faster as drying temperature is raised. This correlates with the observation in the cavity

expansion rate in Figure 4.4. Cavity extension occurs earlier at higher drying

temperatures.

From the experimental results and calculation results, it was also found that the

transport of moisture within the berries is much higher than the transport of piperine.

This statement is supported by observation done on chemical constituent retention

within the Piper Nigrum L. berries and the calculation of effective diffusivity via the

Simplified Method. From the observation done, moisture retained in the Piper Nigrum L.

berries ranged from 4.78% to 15.48% while piperine retained in the berries ranged from

30.46% to 50.09%. From calculation done, the effective diffusivity of moisture in

berries ranged from 3.159E-8m2/hr to 1.300E-7m2/hr while the effective diffusivity of

piperine in berries ranged from 1.086E-9m2/hr to 8.375E-9m2/hr at all drying

temperatures studied. From these results, it is concluded that the effective diffusivity of

moisture in berries is higher when berries are dried at higher drying temperatures while

the effective diffusivity of piperine in berries is about the same at all drying

temperatures studied except at 30oC. The effective diffusivity of piperine in berries


71

dried at 30oC is much lower than the effective diffusivity of piperine in berries dried at

other higher drying temperatures.

The analytical solution is sufficient in describing the bulk moisture loss of drying in

natural convection system. The results calculated were compared with the experimental

results. The validation was satisfactory. The effective diffusivity of moisture was fitted

into the Arrhenius Equation. The Arrhenius factor was estimated to be 22.779m2s-1 and

activation energy was estimated to be 51.7kJ/mol.

In an actual drying situation, forced convection takes place most of the time due to the

existence of wind. Also, from Patil’s studies (1989), drying duration reduces by one day

when air flow is introduced in a drying process.

5.2 Forced Convection Trials

Forced convection trials show the effects of air flow on the drying process of the Piper

Nigrum L. berries. From the experimental results, the presence of forced convection

decreased drying duration at drying temperatures of 35oC, 45oC and 55oC. The

difference was slightly more obvious when the speed of air flow was raised from 0.5ms-

1 to 1.0ms-1. This means the duration of a drying process could be shorten at higher

speed of air flow. However, the difference was not much compared to effect of drying

temperatures. The increase of speed in air flow did not decrease the drying duration as

much as the increase of drying temperature did.

The experimental results confirm the significance of air flow in the first 24 hours of

drying at 45oC and 55oC as claimed by Patil (1989). After 24 hours of drying, the drying

rate was similar at all speeds of air flow used. At 35oC, air flow plays an important role

throughout the drying process. It was deduced that the effects of air flow are less

significant in a drying system with a drying temperature of more than 55oC. In the

ranking of the drying conditions, the drying condition of 55oC at 1.0ms-1 ranked on top

while the drying condition of 35oC at 0.0ms-1 had the lowest rank. Thus, the drying

condition of 55oC at 1ms-1 is deduced to be the best based on its drying rate. From the

optimum drying condition studies, it can be concluded that a combination of a drying

temperature from 45oC to 55oC and a speed of air flow from 0.5ms-1 to 1ms-1 is the

optimum drying condition. This combination is able to produce black pepper within the


72

shortest drying duration at the highest drying rate, with the lowest moisture content, and

with the highest piperine content.

In general, there is no obvious trend in the rate of blackening when the speed of air flow

used was raised at all drying temperatures studied. A higher speed of air flow increases

the blackening rate of the berry slightly. Compare to the natural convection trials, the

drying temperature has a greater influence in speeding the blackening of the berries

during drying.

From shrinkage studies, the volume of Piper Nigrum L. berries eventually reduced to

72% - 82% of its original volume by the end of drying. There is no obvious trend in

shrinkage rate when the speed of air flow was raised. In general, introducing forced

convection in a drying system would induce higher shrinkage rate.

From calculation done, it was observed that there was an increase in the effective

diffusivity of moisture of the berries of Piper Nigrum L. at a higher speed of air flow.In

fact, a strong correlation was found between the effective diffusivity of moisture with

the speed of air flow at all drying temperature studied. This tally with the increase

observed in the drying rate of Piper Nigrum L. when a higher speed of air flow is used

at drying temperature 35oC, 45oC, and 55oC. As for the effective diffusivity of piperine,

there was no obvious trend when the speed of air flow was raised. A combination of

higher temperature and air flow speed, in general, yield higher effective diffusivity of

piperine.

From the experimental results and calculation results, it was also found that the

transport of moisture within the berries is much higher than the transport of piperine.

This statement is supported by observation done on chemical constituent retention

within the Piper Nigrum L. berries and the calculation of effective diffusivity via the

Simplified Method. From the observation done, moisture retained in the Piper Nigrum L.

berries ranged from4.59% to 11.00% while piperine retained in the berries ranged from

29.31% to 35.43%. From calculation done, the effective diffusivity of moisture in

berries ranged from 4.470E-08m2/hr to 2.348E-07m2/hr while the effective diffusivity

of piperine in berries ranged from 3.978E-10m2/hr to 1.558E-08m2/hr at all speed of air

flow studied.


73

In general, an increase in the speed of air flow increases the effective diffusivity of

moisture and piperine. A strong correlation was found between the effective diffusivity

of moisture with the speed of of air flow at all drying temperatures studied. When the

drying temperature was raised, the rate of moisture diffusion increase. As for the

effective diffusivity of piperine, there was less piperine retained with the increase in the

speed of air flow. When the amount of piperine retained in black pepper become

significant and a drying temperature of more than 45oC will be used in a drying system,

it is recommended not to use forced convection.

Both the analytic solution and numerical solution were able to describe the drying

behaviour of the Piper Nigrum L. in forced convection. The results yielded by both of

the solutions were validated with the experimental results and the comparison was

satisfactory. The numerical solution could estimate slightly better than the analytic

solution. In addition, the numerical solution could illustrate the moisture distribution

within a berry of the Piper Nigrum L.. Thus, numerical solution is recommended to be

used if one prefers a more accurate prediction and an insight of the moisture distribution

within a berry of Piper Nigrum L.

From forced convection trials, it is concluded that the air flow is a less influential

driving force compared to drying temperature on the drying of the berries of the Piper

Nigrum L.. The advantage of the presence of forced convection in the drying is that

drying duration could be decreased significantly. More drying could be done with the

decrease of drying time for a drying cycle. In addition, mould growth could be avoided

when drying has to be done at a lower drying temperature.

5.3 Recommendation For Future Work

This work has been limited to the study of producing black pepper. The drying process

to produce white pepper is another major area to be studied. The study of drying Piper

Nigrum L. berries to produce white pepper requires the knowledge on the removal of

the pericarp of the berries and how different removal methods would affect the drying

behaviour of berries. The process to remove the pericarp might affect the profile of

chemical constituents in berries. At the moment, there are two different methods to

remove the pericarp of the berries (Paulus, Megir & Eng n.d., pp. 25-26). The first

removal method would be by soaking the berries in water with room temperature and to

be trampled and washed several times after that as mentioned in section 1.3. The other


74

method would be to boil the berries in water for about 20 minutes to soften the pericarp

and rubbed off the pericarp manually or mechanically via a decorticator (Paulus, Megir

& Eng n.d., pp. 25-26).

In addition, the drying behaviour of the berries without the pericarp would be different

from the current study. After the pericarp was removed, the berries would be smaller in

size. Diffusion within the berries in the radial direction could be faster since the radius

of the berries reduced. The amount of moisture retained in the berries would differ as

well depending on the method of pericarp removal employed. The aroma of the white

pepper is a very important component and it could be affected by the amount of time

taken to remove the pericarp of the berries. Any study related to the production of white

pepper is recommended to include the study of volatile oil retained in berries after the

drying process of the berries.

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75

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Appendices

80

APPENDIX 1: CALCULATION WORK TO DETERMINE THE ARRHENIUS

FACTOR AND ACTIVATION ENERGY

The best least-squares fit to the following data is y = -62237x + 3.1259.

ln Do = y-intercept = 3.1259E-01

Do = Exp(3.1259E-01) = 2.2779E+01 m2s-1 = Arrhenius Factor

Ea = -m*R, R = universal gas constant = 8.314 J/mol K

Ea = -(-6.2237E+03)*8.314

Ea = 51743.3842J/mol

X Y

n

Drying Temperature

T (oC)

Drying Temperature T

Diffusivity

Deff(m^2/hr)

1/T

(1/oK)

ln (Deff )

(m^2/hr)X^2 Y^2 XY

1 55 328 1.3004E-07 3.0488E-03 -1.5855E+01 9.2951E-06 2.5139E+02 -4.8340E-022 50 323 9.7727E-08 3.0960E-03 -1.6141E+01 9.5851E-06 2.6053E+02 -4.9972E-023 45 318 8.5923E-08 3.1447E-03 -1.6270E+01 9.8888E-06 2.6471E+02 -5.1163E-024 40 313 4.4251E-08 3.1949E-03 -1.6933E+01 1.0207E-05 2.8674E+02 -5.4100E-025 35 308 3.3232E-08 3.2468E-03 -1.7220E+01 1.0541E-05 2.9652E+02 -5.5908E-026 30 303 3.1594E-08 3.3003E-03 -1.7270E+01 1.0892E-05 2.9826E+02 -5.6998E-02

1.9031E-02 -9.9690E+01 6.0410E-05 1.6582E+03 -3.1648E-01Total

Drying Temperature

(oC) (oK) (m2/hr) (m2/hr)(1/oK)

X2 Y2

Appendices

81

APPENDIX 2: CALCULATION WORK TO DETERMINE THE VALUES OF b

AND c IN THE HENDERSON'S EQUILIBRIUM MOISTURE

CONTENT EQUATION

Using the Henderson’s Equilibrium Moisture Content,

beMTcExpRH 1002731 ,

Rearranging the equation yield

273

1ln100

Tc

RHM b

e .

The following experimental data obtained from preliminary studies were used to form a

system of linear equations to solve for b and c:

Data Set Equilibrium Moisture Content, Me

(Dry Basis, Decimal)

Relative Humidity, RH

(Decimal)

Drying Temperature, T

(oC) 1 0.1300 0.6136 30 2 0.0200 0.02562 100

Using data set 1, equation becomes

b

b

c

cc

00.13

003138.0

003138.01

27330

6136.01ln1300.0100

Using data set 2, equation becomes

b

b

c

cc

00.2

10958.6

10958.61

273100

02562.01ln0200.0100

5

5

So,

Appendices

82

035.2

10958.6

003138.0ln

00.2

00.13ln

10958.6

003138.0

00.2

00.13

00.2

10958.6

00.13

003138.0

5

5

5

b

b

b

bb

and

5

035.210697.1

00.13

003138.0 c

Appendices

83

APPENDIX 3: CALCULATION OF EQUILIBRIUM MOISTURE CONTENT,

Me

Using the results in Appendix 6, the equation 273

1ln100

Tc

RHM b

e become

27310067.2

1ln100

5

035.2

T

RHMe .

The following table shows the parameter used in the calculations to calculate

equilibrium moisture content, Me.

Drying Temperature, T

(oC)

Relative Humidity in Dryer, RH (%)

Equilibrium Moisture Content, Me

(kg/kg d.b.) 55 16.22 4.969 E-02 50 22.33 5.964 E-02 45 28.27 6.874 E-02 40 35.24 7.904 E-02 35 49.14 9.900 E-02 30 61.36 1.180 E-01

Appendices

84

APPENDIX 4A: CALCULATION OF MOISTURE CONTENT IN PIPER

NIGRUM L. BERRIES WITH TIME FOR NATURAL

CONVECTION TRIALS VIA THE ANALYTIC SOLUTION

T=55oC u=0.0m/s

1 2 30.5 9.332E-01 1.896E-01 5.964E-02 1.182E+00 7.188E-01 1.467E+00 59.471.0 8.709E-01 1.438E-01 3.201E-02 1.047E+00 6.363E-01 1.305E+00 56.611.5 8.127E-01 1.090E-01 1.718E-02 9.389E-01 5.708E-01 1.175E+00 54.032.0 7.584E-01 8.270E-02 9.220E-03 8.503E-01 5.169E-01 1.069E+00 51.672.5 7.077E-01 6.272E-02 4.949E-03 7.754E-01 4.714E-01 9.794E-01 49.483.0 6.604E-01 4.756E-02 2.656E-03 7.107E-01 4.320E-01 9.018E-01 47.423.5 6.163E-01 3.607E-02 1.426E-03 6.538E-01 3.975E-01 8.336E-01 45.464.0 5.751E-01 2.736E-02 7.651E-04 6.033E-01 3.667E-01 7.730E-01 43.604.5 5.367E-01 2.075E-02 4.107E-04 5.579E-01 3.391E-01 7.186E-01 41.815.0 5.009E-01 1.573E-02 2.204E-04 5.168E-01 3.142E-01 6.694E-01 40.105.5 4.674E-01 1.193E-02 1.183E-04 4.795E-01 2.915E-01 6.246E-01 38.456.0 4.362E-01 9.049E-03 6.349E-05 4.453E-01 2.707E-01 5.836E-01 36.856.5 4.070E-01 6.862E-03 3.408E-05 4.139E-01 2.516E-01 5.460E-01 35.327.0 3.798E-01 5.204E-03 1.829E-05 3.851E-01 2.341E-01 5.114E-01 33.847.5 3.545E-01 3.947E-03 9.817E-06 3.584E-01 2.179E-01 4.795E-01 32.418.0 3.308E-01 2.993E-03 5.269E-06 3.338E-01 2.029E-01 4.499E-01 31.038.5 3.087E-01 2.270E-03 2.828E-06 3.110E-01 1.890E-01 4.225E-01 29.709.0 2.881E-01 1.722E-03 1.518E-06 2.898E-01 1.762E-01 3.972E-01 28.439.5 2.688E-01 1.306E-03 8.146E-07 2.701E-01 1.642E-01 3.736E-01 27.2010.0 2.509E-01 9.901E-04 4.372E-07 2.519E-01 1.531E-01 3.517E-01 26.0210.5 2.341E-01 7.509E-04 2.347E-07 2.349E-01 1.428E-01 3.313E-01 24.8811.0 2.185E-01 5.695E-04 1.259E-07 2.190E-01 1.332E-01 3.123E-01 23.8011.5 2.039E-01 4.319E-04 6.760E-08 2.043E-01 1.242E-01 2.947E-01 22.7612.0 1.903E-01 3.275E-04 3.628E-08 1.906E-01 1.159E-01 2.782E-01 21.7612.5 1.775E-01 2.484E-04 1.947E-08 1.778E-01 1.081E-01 2.629E-01 20.8113.0 1.657E-01 1.884E-04 1.045E-08 1.659E-01 1.008E-01 2.486E-01 19.9113.5 1.546E-01 1.429E-04 5.610E-09 1.548E-01 9.408E-02 2.352E-01 19.0414.0 1.443E-01 1.083E-04 3.011E-09 1.444E-01 8.778E-02 2.228E-01 18.2214.5 1.346E-01 8.216E-05 1.616E-09 1.347E-01 8.190E-02 2.112E-01 17.4415.0 1.256E-01 6.231E-05 8.673E-10 1.257E-01 7.642E-02 2.004E-01 16.7015.5 1.173E-01 4.726E-05 4.655E-10 1.173E-01 7.131E-02 1.903E-01 15.9916.0 1.094E-01 3.584E-05 2.498E-10 1.095E-01 6.654E-02 1.809E-01 15.3216.5 1.021E-01 2.718E-05 1.341E-10 1.021E-01 6.209E-02 1.722E-01 14.6917.0 9.529E-02 2.061E-05 7.197E-11 9.531E-02 5.794E-02 1.640E-01 14.0917.5 8.892E-02 1.563E-05 3.863E-11 8.894E-02 5.407E-02 1.563E-01 13.5218.0 8.298E-02 1.185E-05 2.073E-11 8.299E-02 5.045E-02 1.492E-01 12.98

nt (hour)

Total Grand Total Mr (dry basis) Mr (Wet Basis)

Appendices

85

1 2 318.5 7.744E-02 8.990E-06 1.113E-11 7.745E-02 4.708E-02 1.426E-01 12.4819.0 7.227E-02 6.818E-06 5.972E-12 7.227E-02 4.394E-02 1.363E-01 12.0019.5 6.744E-02 5.171E-06 3.206E-12 6.744E-02 4.100E-02 1.306E-01 11.5520.0 6.293E-02 3.921E-06 1.720E-12 6.294E-02 3.826E-02 1.252E-01 11.1220.5 5.873E-02 2.974E-06 9.234E-13 5.873E-02 3.570E-02 1.201E-01 10.7221.0 5.481E-02 2.255E-06 4.956E-13 5.481E-02 3.332E-02 1.154E-01 10.3521.5 5.114E-02 1.710E-06 2.660E-13 5.115E-02 3.109E-02 1.110E-01 9.9922.0 4.773E-02 1.297E-06 1.428E-13 4.773E-02 2.902E-02 1.069E-01 9.6622.5 4.454E-02 9.837E-07 7.663E-14 4.454E-02 2.708E-02 1.031E-01 9.3523.0 4.156E-02 7.461E-07 4.113E-14 4.156E-02 2.527E-02 9.952E-02 9.0523.5 3.879E-02 5.658E-07 2.207E-14 3.879E-02 2.358E-02 9.619E-02 8.7824.0 3.620E-02 4.291E-07 1.185E-14 3.620E-02 2.200E-02 9.309E-02 8.52

t (hour)

n Total Grand Total Mr (dry basis) Mr (Wet Basis)

Appendices

86

T=50oC u=0.0m/s

1 2 30.5 9.494E-01 2.031E-01 6.961E-02 1.222E+00 7.429E-01 1.518E+00 60.281.0 9.013E-01 1.650E-01 4.361E-02 1.110E+00 6.747E-01 1.384E+00 58.051.5 8.557E-01 1.340E-01 2.732E-02 1.017E+00 6.183E-01 1.273E+00 56.002.0 8.123E-01 1.089E-01 1.711E-02 9.383E-01 5.704E-01 1.179E+00 54.112.5 7.712E-01 8.843E-02 1.072E-02 8.704E-01 5.291E-01 1.098E+00 52.333.0 7.322E-01 7.184E-02 6.717E-03 8.107E-01 4.928E-01 1.027E+00 50.663.5 6.951E-01 5.835E-02 4.208E-03 7.576E-01 4.606E-01 9.635E-01 49.074.0 6.599E-01 4.740E-02 2.636E-03 7.099E-01 4.316E-01 9.066E-01 47.554.5 6.265E-01 3.851E-02 1.651E-03 6.666E-01 4.053E-01 8.549E-01 46.095.0 5.948E-01 3.128E-02 1.035E-03 6.271E-01 3.812E-01 8.077E-01 44.685.5 5.646E-01 2.541E-02 6.481E-04 5.907E-01 3.591E-01 7.643E-01 43.326.0 5.360E-01 2.064E-02 4.060E-04 5.571E-01 3.387E-01 7.243E-01 42.006.5 5.089E-01 1.677E-02 2.544E-04 5.259E-01 3.197E-01 6.871E-01 40.737.0 4.831E-01 1.362E-02 1.594E-04 4.969E-01 3.021E-01 6.525E-01 39.487.5 4.587E-01 1.106E-02 9.983E-05 4.698E-01 2.856E-01 6.202E-01 38.288.0 4.354E-01 8.988E-03 6.254E-05 4.445E-01 2.702E-01 5.899E-01 37.108.5 4.134E-01 7.302E-03 3.918E-05 4.207E-01 2.558E-01 5.616E-01 35.969.0 3.925E-01 5.931E-03 2.455E-05 3.984E-01 2.422E-01 5.350E-01 34.859.5 3.726E-01 4.818E-03 1.538E-05 3.774E-01 2.294E-01 5.099E-01 33.7710.0 3.537E-01 3.914E-03 9.634E-06 3.577E-01 2.174E-01 4.863E-01 32.7210.5 3.358E-01 3.179E-03 6.035E-06 3.390E-01 2.061E-01 4.641E-01 31.7011.0 3.188E-01 2.583E-03 3.781E-06 3.214E-01 1.954E-01 4.431E-01 30.7011.5 3.027E-01 2.098E-03 2.369E-06 3.048E-01 1.853E-01 4.232E-01 29.7412.0 2.873E-01 1.704E-03 1.484E-06 2.891E-01 1.757E-01 4.045E-01 28.8012.5 2.728E-01 1.384E-03 9.296E-07 2.742E-01 1.667E-01 3.867E-01 27.8913.0 2.590E-01 1.125E-03 5.824E-07 2.601E-01 1.581E-01 3.699E-01 27.0013.5 2.459E-01 9.136E-04 3.648E-07 2.468E-01 1.500E-01 3.540E-01 26.1514.0 2.334E-01 7.421E-04 2.286E-07 2.342E-01 1.424E-01 3.390E-01 25.3214.5 2.216E-01 6.029E-04 1.432E-07 2.222E-01 1.351E-01 3.247E-01 24.5115.0 2.104E-01 4.897E-04 8.970E-08 2.109E-01 1.282E-01 3.112E-01 23.7315.5 1.997E-01 3.978E-04 5.620E-08 2.001E-01 1.217E-01 2.984E-01 22.9816.0 1.896E-01 3.232E-04 3.520E-08 1.899E-01 1.155E-01 2.862E-01 22.2516.5 1.800E-01 2.625E-04 2.205E-08 1.803E-01 1.096E-01 2.747E-01 21.5517.0 1.709E-01 2.133E-04 1.382E-08 1.711E-01 1.040E-01 2.638E-01 20.8717.5 1.622E-01 1.732E-04 8.656E-09 1.624E-01 9.874E-02 2.534E-01 20.2218.0 1.540E-01 1.407E-04 5.423E-09 1.542E-01 9.372E-02 2.436E-01 19.59

t (hour)


Appendices

87

1 2 318.5 1.462E-01 1.143E-04 3.397E-09 1.463E-01 8.897E-02 2.342E-01 18.9819.0 1.388E-01 9.286E-05 2.128E-09 1.389E-01 8.445E-02 2.254E-01 18.3919.5 1.318E-01 7.543E-05 1.333E-09 1.319E-01 8.017E-02 2.170E-01 17.8320.0 1.251E-01 6.128E-05 8.352E-10 1.252E-01 7.610E-02 2.090E-01 17.2920.5 1.188E-01 4.978E-05 5.233E-10 1.188E-01 7.224E-02 2.014E-01 16.7621.0 1.128E-01 4.044E-05 3.278E-10 1.128E-01 6.858E-02 1.942E-01 16.2621.5 1.071E-01 3.285E-05 2.054E-10 1.071E-01 6.511E-02 1.874E-01 15.7822.0 1.016E-01 2.668E-05 1.287E-10 1.017E-01 6.181E-02 1.809E-01 15.3222.5 9.650E-02 2.168E-05 8.060E-11 9.652E-02 5.868E-02 1.748E-01 14.8823.0 9.161E-02 1.761E-05 5.049E-11 9.163E-02 5.570E-02 1.689E-01 14.4523.5 8.697E-02 1.430E-05 3.163E-11 8.699E-02 5.288E-02 1.634E-01 14.0524.0 8.257E-02 1.162E-05 1.982E-11 8.258E-02 5.020E-02 1.582E-01 13.6624.5 7.839E-02 9.439E-06 1.241E-11 7.840E-02 4.766E-02 1.532E-01 13.2825.0 7.442E-02 7.667E-06 7.777E-12 7.443E-02 4.524E-02 1.484E-01 12.9225.5 7.065E-02 6.228E-06 4.872E-12 7.066E-02 4.295E-02 1.439E-01 12.5826.0 6.707E-02 5.059E-06 3.052E-12 6.708E-02 4.078E-02 1.397E-01 12.2526.5 6.368E-02 4.110E-06 1.912E-12 6.368E-02 3.871E-02 1.356E-01 11.9427.0 6.045E-02 3.339E-06 1.198E-12 6.046E-02 3.675E-02 1.318E-01 11.6427.5 5.739E-02 2.712E-06 7.505E-13 5.739E-02 3.489E-02 1.281E-01 11.3628.0 5.448E-02 2.203E-06 4.702E-13 5.449E-02 3.312E-02 1.246E-01 11.0828.5 5.173E-02 1.790E-06 2.945E-13 5.173E-02 3.145E-02 1.213E-01 10.8229.0 4.911E-02 1.454E-06 1.845E-13 4.911E-02 2.985E-02 1.182E-01 10.5729.5 4.662E-02 1.181E-06 1.156E-13 4.662E-02 2.834E-02 1.153E-01 10.3330.0 4.426E-02 9.594E-07 7.242E-14 4.426E-02 2.691E-02 1.124E-01 10.1130.5 4.202E-02 7.793E-07 4.537E-14 4.202E-02 2.554E-02 1.098E-01 9.8931.0 3.989E-02 6.331E-07 2.842E-14 3.989E-02 2.425E-02 1.072E-01 9.6831.5 3.787E-02 5.143E-07 1.781E-14 3.787E-02 2.302E-02 1.048E-01 9.4932.0 3.595E-02 4.177E-07 1.115E-14 3.595E-02 2.186E-02 1.025E-01 9.3032.5 3.413E-02 3.394E-07 6.988E-15 3.413E-02 2.075E-02 1.004E-01 9.1233.0 3.240E-02 2.757E-07 4.378E-15 3.241E-02 1.970E-02 9.830E-02 8.9533.5 3.076E-02 2.239E-07 2.743E-15 3.076E-02 1.870E-02 9.634E-02 8.7934.0 2.921E-02 1.819E-07 1.718E-15 2.921E-02 1.776E-02 9.448E-02 8.6334.5 2.773E-02 1.478E-07 1.076E-15 2.773E-02 1.686E-02 9.271E-02 8.4835.0 2.632E-02 1.200E-07 6.743E-16 2.632E-02 1.600E-02 9.104E-02 8.3435.5 2.499E-02 9.751E-08 4.224E-16 2.499E-02 1.519E-02 8.945E-02 8.2136.0 2.373E-02 7.921E-08 2.646E-16 2.373E-02 1.442E-02 8.794E-02 8.08

Total Grand Total Mr (dry basis) Mr (Wet Basis)t (hour)

n

Appendices

88

T=45oC u=0.0m/s

1 2 30.5 9.553E-01 2.082E-01 7.365E-02 1.237E+00 7.521E-01 1.538E+00 60.601.0 9.127E-01 1.735E-01 4.882E-02 1.135E+00 6.900E-01 1.416E+00 58.621.5 8.719E-01 1.445E-01 3.236E-02 1.049E+00 6.376E-01 1.314E+00 56.792.0 8.330E-01 1.204E-01 2.145E-02 9.748E-01 5.926E-01 1.226E+00 55.082.5 7.958E-01 1.003E-01 1.422E-02 9.103E-01 5.534E-01 1.150E+00 53.483.0 7.602E-01 8.351E-02 9.426E-03 8.532E-01 5.187E-01 1.082E+00 51.973.5 7.263E-01 6.957E-02 6.249E-03 8.021E-01 4.876E-01 1.021E+00 50.524.0 6.939E-01 5.795E-02 4.142E-03 7.559E-01 4.596E-01 9.664E-01 49.154.5 6.629E-01 4.827E-02 2.746E-03 7.139E-01 4.340E-01 9.165E-01 47.825.0 6.333E-01 4.021E-02 1.820E-03 6.753E-01 4.105E-01 8.706E-01 46.545.5 6.050E-01 3.349E-02 1.206E-03 6.397E-01 3.889E-01 8.284E-01 45.316.0 5.780E-01 2.790E-02 7.997E-04 6.067E-01 3.688E-01 7.891E-01 44.116.5 5.522E-01 2.324E-02 5.301E-04 5.759E-01 3.501E-01 7.526E-01 42.947.0 5.275E-01 1.936E-02 3.514E-04 5.472E-01 3.327E-01 7.185E-01 41.817.5 5.039E-01 1.612E-02 2.329E-04 5.203E-01 3.163E-01 6.866E-01 40.718.0 4.814E-01 1.343E-02 1.544E-04 4.950E-01 3.009E-01 6.566E-01 39.638.5 4.599E-01 1.119E-02 1.024E-04 4.712E-01 2.865E-01 6.283E-01 38.599.0 4.394E-01 9.319E-03 6.785E-05 4.488E-01 2.728E-01 6.017E-01 37.569.5 4.198E-01 7.763E-03 4.497E-05 4.276E-01 2.599E-01 5.765E-01 36.57

10.0 4.010E-01 6.466E-03 2.981E-05 4.075E-01 2.477E-01 5.527E-01 35.5910.5 3.831E-01 5.386E-03 1.976E-05 3.885E-01 2.362E-01 5.301E-01 34.6511.0 3.660E-01 4.487E-03 1.310E-05 3.705E-01 2.252E-01 5.087E-01 33.7211.5 3.497E-01 3.737E-03 8.683E-06 3.534E-01 2.149E-01 4.884E-01 32.8112.0 3.341E-01 3.113E-03 5.756E-06 3.372E-01 2.050E-01 4.691E-01 31.9312.5 3.191E-01 2.593E-03 3.815E-06 3.217E-01 1.956E-01 4.508E-01 31.0713.0 3.049E-01 2.160E-03 2.529E-06 3.070E-01 1.867E-01 4.333E-01 30.2313.5 2.913E-01 1.799E-03 1.677E-06 2.931E-01 1.782E-01 4.167E-01 29.4214.0 2.783E-01 1.499E-03 1.111E-06 2.798E-01 1.701E-01 4.009E-01 28.6214.5 2.658E-01 1.249E-03 7.367E-07 2.671E-01 1.624E-01 3.859E-01 27.8415.0 2.540E-01 1.040E-03 4.883E-07 2.550E-01 1.550E-01 3.715E-01 27.0915.5 2.426E-01 8.663E-04 3.237E-07 2.435E-01 1.480E-01 3.579E-01 26.3616.0 2.318E-01 7.216E-04 2.146E-07 2.325E-01 1.413E-01 3.448E-01 25.6416.5 2.214E-01 6.011E-04 1.422E-07 2.220E-01 1.350E-01 3.324E-01 24.9517.0 2.115E-01 5.007E-04 9.428E-08 2.120E-01 1.289E-01 3.205E-01 24.2717.5 2.021E-01 4.171E-04 6.250E-08 2.025E-01 1.231E-01 3.092E-01 23.6218.0 1.931E-01 3.474E-04 4.143E-08 1.934E-01 1.176E-01 2.984E-01 22.98

t (hour)


Appendices

89


t (hour)


Appendices

90

T=40oC u=0.0m/s

1 2 30.5 9.767E-01 2.275E-01 8.991E-02 1.294E+00 7.868E-01 1.608E+00 61.651.0 9.540E-01 2.071E-01 7.275E-02 1.234E+00 7.501E-01 1.537E+00 60.581.5 9.318E-01 1.885E-01 5.887E-02 1.179E+00 7.169E-01 1.472E+00 59.552.0 9.102E-01 1.716E-01 4.763E-02 1.129E+00 6.866E-01 1.413E+00 58.562.5 8.890E-01 1.562E-01 3.854E-02 1.084E+00 6.588E-01 1.359E+00 57.613.0 8.683E-01 1.421E-01 3.119E-02 1.042E+00 6.333E-01 1.309E+00 56.703.5 8.481E-01 1.294E-01 2.524E-02 1.003E+00 6.096E-01 1.264E+00 55.824.0 8.284E-01 1.177E-01 2.042E-02 9.666E-01 5.876E-01 1.221E+00 54.974.5 8.092E-01 1.072E-01 1.652E-02 9.329E-01 5.671E-01 1.181E+00 54.155.0 7.903E-01 9.755E-02 1.337E-02 9.013E-01 5.479E-01 1.144E+00 53.355.5 7.720E-01 8.878E-02 1.082E-02 8.716E-01 5.298E-01 1.109E+00 52.576.0 7.540E-01 8.081E-02 8.754E-03 8.436E-01 5.128E-01 1.075E+00 51.826.5 7.365E-01 7.355E-02 7.083E-03 8.171E-01 4.967E-01 1.044E+00 51.087.0 7.194E-01 6.694E-02 5.731E-03 7.920E-01 4.815E-01 1.015E+00 50.367.5 7.026E-01 6.093E-02 4.638E-03 7.682E-01 4.670E-01 9.864E-01 49.668.0 6.863E-01 5.546E-02 3.753E-03 7.455E-01 4.532E-01 9.596E-01 48.978.5 6.703E-01 5.048E-02 3.036E-03 7.238E-01 4.400E-01 9.341E-01 48.309.0 6.547E-01 4.594E-02 2.457E-03 7.031E-01 4.275E-01 9.096E-01 47.639.5 6.395E-01 4.182E-02 1.988E-03 6.833E-01 4.154E-01 8.862E-01 46.9810.0 6.246E-01 3.806E-02 1.609E-03 6.643E-01 4.039E-01 8.637E-01 46.3410.5 6.101E-01 3.464E-02 1.302E-03 6.461E-01 3.928E-01 8.422E-01 45.7211.0 5.959E-01 3.153E-02 1.053E-03 6.285E-01 3.821E-01 8.214E-01 45.1011.5 5.821E-01 2.870E-02 8.523E-04 6.116E-01 3.718E-01 8.015E-01 44.4912.0 5.685E-01 2.612E-02 6.896E-04 5.954E-01 3.619E-01 7.823E-01 43.8912.5 5.553E-01 2.377E-02 5.580E-04 5.797E-01 3.524E-01 7.637E-01 43.3013.0 5.424E-01 2.164E-02 4.515E-04 5.645E-01 3.432E-01 7.458E-01 42.7213.5 5.298E-01 1.970E-02 3.654E-04 5.499E-01 3.343E-01 7.285E-01 42.1514.0 5.175E-01 1.793E-02 2.956E-04 5.357E-01 3.257E-01 7.118E-01 41.5814.5 5.054E-01 1.632E-02 2.392E-04 5.220E-01 3.173E-01 6.956E-01 41.0215.0 4.937E-01 1.485E-02 1.936E-04 5.087E-01 3.093E-01 6.800E-01 40.4715.5 4.822E-01 1.352E-02 1.566E-04 4.959E-01 3.015E-01 6.648E-01 39.9316.0 4.710E-01 1.230E-02 1.267E-04 4.834E-01 2.939E-01 6.501E-01 39.4016.5 4.600E-01 1.120E-02 1.025E-04 4.713E-01 2.865E-01 6.358E-01 38.8717.0 4.493E-01 1.019E-02 8.298E-05 4.596E-01 2.794E-01 6.219E-01 38.3517.5 4.389E-01 9.276E-03 6.714E-05 4.482E-01 2.725E-01 6.085E-01 37.8318.0 4.287E-01 8.443E-03 5.433E-05 4.372E-01 2.658E-01 5.954E-01 37.32

t (hour)


Appendices

91


t (hour)


Appendices

92

1 2 336.5 1.795E-01 2.595E-04 2.150E-08 1.798E-01 1.093E-01 2.914E-01 22.5637.0 1.753E-01 2.362E-04 1.739E-08 1.756E-01 1.067E-01 2.864E-01 22.2637.5 1.712E-01 2.150E-04 1.407E-08 1.715E-01 1.042E-01 2.816E-01 21.9738.0 1.673E-01 1.957E-04 1.139E-08 1.675E-01 1.018E-01 2.768E-01 21.6838.5 1.634E-01 1.781E-04 9.215E-09 1.636E-01 9.943E-02 2.722E-01 21.4039.0 1.596E-01 1.621E-04 7.456E-09 1.597E-01 9.711E-02 2.677E-01 21.1239.5 1.559E-01 1.476E-04 6.033E-09 1.560E-01 9.485E-02 2.633E-01 20.8440.0 1.522E-01 1.343E-04 4.882E-09 1.524E-01 9.263E-02 2.590E-01 20.5740.5 1.487E-01 1.222E-04 3.950E-09 1.488E-01 9.047E-02 2.548E-01 20.3141.0 1.452E-01 1.113E-04 3.196E-09 1.454E-01 8.837E-02 2.507E-01 20.0541.5 1.419E-01 1.013E-04 2.586E-09 1.420E-01 8.631E-02 2.467E-01 19.7942.0 1.386E-01 9.217E-05 2.093E-09 1.387E-01 8.430E-02 2.428E-01 19.5442.5 1.353E-01 8.389E-05 1.693E-09 1.354E-01 8.233E-02 2.390E-01 19.2943.0 1.322E-01 7.636E-05 1.370E-09 1.323E-01 8.041E-02 2.353E-01 19.0543.5 1.291E-01 6.950E-05 1.109E-09 1.292E-01 7.854E-02 2.316E-01 18.8144.0 1.261E-01 6.326E-05 8.972E-10 1.262E-01 7.671E-02 2.281E-01 18.5744.5 1.232E-01 5.757E-05 7.260E-10 1.232E-01 7.492E-02 2.246E-01 18.3445.0 1.203E-01 5.240E-05 5.874E-10 1.204E-01 7.318E-02 2.212E-01 18.1245.5 1.175E-01 4.770E-05 4.753E-10 1.176E-01 7.148E-02 2.179E-01 17.8946.0 1.148E-01 4.341E-05 3.846E-10 1.148E-01 6.981E-02 2.147E-01 17.6746.5 1.121E-01 3.951E-05 3.112E-10 1.122E-01 6.819E-02 2.115E-01 17.4647.0 1.095E-01 3.596E-05 2.518E-10 1.096E-01 6.660E-02 2.084E-01 17.2547.5 1.070E-01 3.273E-05 2.038E-10 1.070E-01 6.505E-02 2.054E-01 17.0448.0 1.045E-01 2.979E-05 1.649E-10 1.045E-01 6.354E-02 2.025E-01 16.84

t (hour)


Appendices

93

T=35oC u=0.0m/s

1 2 30.5 9.825E-01 2.329E-01 9.477E-02 1.310E+00 7.965E-01 1.631E+00 61.991.0 9.653E-01 2.170E-01 8.084E-02 1.263E+00 7.679E-01 1.576E+00 61.181.5 9.484E-01 2.022E-01 6.896E-02 1.220E+00 7.414E-01 1.525E+00 60.392.0 9.318E-01 1.884E-01 5.882E-02 1.179E+00 7.168E-01 1.477E+00 59.632.5 9.154E-01 1.756E-01 5.017E-02 1.141E+00 6.938E-01 1.433E+00 58.903.0 8.994E-01 1.636E-01 4.279E-02 1.106E+00 6.722E-01 1.392E+00 58.193.5 8.837E-01 1.524E-01 3.650E-02 1.073E+00 6.521E-01 1.353E+00 57.504.0 8.682E-01 1.420E-01 3.113E-02 1.041E+00 6.331E-01 1.316E+00 56.834.5 8.530E-01 1.323E-01 2.656E-02 1.012E+00 6.151E-01 1.282E+00 56.185.0 8.380E-01 1.233E-01 2.265E-02 9.840E-01 5.982E-01 1.249E+00 55.545.5 8.234E-01 1.149E-01 1.932E-02 9.576E-01 5.821E-01 1.218E+00 54.926.0 8.089E-01 1.071E-01 1.648E-02 9.325E-01 5.669E-01 1.189E+00 54.326.5 7.948E-01 9.975E-02 1.406E-02 9.086E-01 5.523E-01 1.161E+00 53.737.0 7.808E-01 9.294E-02 1.199E-02 8.858E-01 5.385E-01 1.135E+00 53.157.5 7.672E-01 8.660E-02 1.023E-02 8.640E-01 5.252E-01 1.109E+00 52.598.0 7.537E-01 8.069E-02 8.724E-03 8.432E-01 5.126E-01 1.085E+00 52.038.5 7.405E-01 7.518E-02 7.442E-03 8.232E-01 5.004E-01 1.061E+00 51.499.0 7.276E-01 7.005E-02 6.348E-03 8.040E-01 4.888E-01 1.039E+00 50.959.5 7.148E-01 6.527E-02 5.414E-03 7.855E-01 4.775E-01 1.017E+00 50.43


t (hour)


Appendices

94


t (hour)


Appendices

95


t (hour)


Appendices

96


t (hour)


Appendices

97

T=30oC u=0.0m/s

1 2 30.5 9.833E-01 2.338E-01 9.552E-02 1.313E+00 7.980E-01 1.637E+00 62.081.0 9.670E-01 2.186E-01 8.212E-02 1.268E+00 7.706E-01 1.585E+00 61.321.5 9.509E-01 2.044E-01 7.060E-02 1.226E+00 7.452E-01 1.537E+00 60.582.0 9.350E-01 1.911E-01 6.069E-02 1.187E+00 7.215E-01 1.492E+00 59.872.5 9.194E-01 1.787E-01 5.217E-02 1.150E+00 6.993E-01 1.449E+00 59.173.0 9.041E-01 1.671E-01 4.485E-02 1.116E+00 6.785E-01 1.410E+00 58.503.5 8.891E-01 1.562E-01 3.856E-02 1.084E+00 6.589E-01 1.373E+00 57.854.0 8.743E-01 1.460E-01 3.315E-02 1.053E+00 6.404E-01 1.337E+00 57.224.5 8.597E-01 1.366E-01 2.850E-02 1.025E+00 6.230E-01 1.304E+00 56.605.0 8.454E-01 1.277E-01 2.450E-02 9.975E-01 6.064E-01 1.273E+00 56.005.5 8.313E-01 1.194E-01 2.106E-02 9.717E-01 5.907E-01 1.243E+00 55.416.0 8.174E-01 1.116E-01 1.811E-02 9.472E-01 5.758E-01 1.214E+00 54.846.5 8.038E-01 1.044E-01 1.557E-02 9.238E-01 5.616E-01 1.187E+00 54.287.0 7.904E-01 9.759E-02 1.338E-02 9.014E-01 5.480E-01 1.161E+00 53.737.5 7.773E-01 9.125E-02 1.150E-02 8.800E-01 5.350E-01 1.137E+00 53.208.0 7.643E-01 8.532E-02 9.890E-03 8.595E-01 5.225E-01 1.113E+00 52.678.5 7.516E-01 7.977E-02 8.503E-03 8.399E-01 5.106E-01 1.090E+00 52.169.0 7.391E-01 7.459E-02 7.310E-03 8.210E-01 4.991E-01 1.068E+00 51.659.5 7.268E-01 6.974E-02 6.284E-03 8.028E-01 4.880E-01 1.047E+00 51.1510.0 7.146E-01 6.521E-02 5.402E-03 7.853E-01 4.774E-01 1.027E+00 50.6610.5 7.027E-01 6.097E-02 4.644E-03 7.684E-01 4.671E-01 1.007E+00 50.1811.0 6.910E-01 5.701E-02 3.993E-03 7.520E-01 4.572E-01 9.885E-01 49.7111.5 6.795E-01 5.330E-02 3.432E-03 7.363E-01 4.476E-01 9.702E-01 49.2412.0 6.682E-01 4.984E-02 2.951E-03 7.210E-01 4.383E-01 9.526E-01 48.7912.5 6.571E-01 4.660E-02 2.537E-03 7.062E-01 4.293E-01 9.355E-01 48.3313.0 6.461E-01 4.357E-02 2.181E-03 6.919E-01 4.206E-01 9.189E-01 47.8913.5 6.354E-01 4.074E-02 1.875E-03 6.780E-01 4.122E-01 9.028E-01 47.4514.0 6.248E-01 3.809E-02 1.612E-03 6.645E-01 4.040E-01 8.872E-01 47.0114.5 6.144E-01 3.562E-02 1.386E-03 6.514E-01 3.960E-01 8.720E-01 46.5815.0 6.041E-01 3.330E-02 1.191E-03 6.386E-01 3.882E-01 8.572E-01 46.1615.5 5.941E-01 3.114E-02 1.024E-03 6.262E-01 3.807E-01 8.429E-01 45.7416.0 5.842E-01 2.912E-02 8.804E-04 6.142E-01 3.734E-01 8.289E-01 45.3216.5 5.744E-01 2.722E-02 7.568E-04 6.024E-01 3.662E-01 8.153E-01 44.9117.0 5.649E-01 2.545E-02 6.507E-04 5.910E-01 3.593E-01 8.021E-01 44.5117.5 5.555E-01 2.380E-02 5.594E-04 5.798E-01 3.525E-01 7.892E-01 44.1118.0 5.462E-01 2.225E-02 4.809E-04 5.689E-01 3.459E-01 7.766E-01 43.71

Total Grand Total Mr (dry basis) Mr (Wet Basis)t (hour)

n

Appendices

98


t (hour)


Appendices

99


t (hour)


Appendices

100


t (hour)


Appendices

101

APPENDIX 4B: CALCULATION OF PIPERINE CONTENT IN PIPER

NIGRUM L. BERRIES WITH TIME FOR NATURAL


T=55oC u=0.0m/s

1 2 30.5 9.972E-01 2.472E-01 1.083E-01 1.353E+00 8.224E-01 5.607E-02 5.311.0 9.944E-01 2.444E-01 1.056E-01 1.344E+00 8.173E-01 5.598E-02 5.301.5 9.916E-01 2.417E-01 1.030E-01 1.336E+00 8.124E-01 5.588E-02 5.292.0 9.888E-01 2.390E-01 1.004E-01 1.328E+00 8.075E-01 5.578E-02 5.282.5 9.861E-01 2.364E-01 9.793E-02 1.320E+00 8.027E-01 5.569E-02 5.283.0 9.833E-01 2.337E-01 9.548E-02 1.312E+00 7.979E-01 5.560E-02 5.273.5 9.805E-01 2.311E-01 9.310E-02 1.305E+00 7.932E-01 5.550E-02 5.264.0 9.778E-01 2.285E-01 9.078E-02 1.297E+00 7.885E-01 5.541E-02 5.254.5 9.751E-01 2.260E-01 8.851E-02 1.290E+00 7.839E-01 5.532E-02 5.245.0 9.723E-01 2.234E-01 8.630E-02 1.282E+00 7.794E-01 5.523E-02 5.235.5 9.696E-01 2.210E-01 8.415E-02 1.275E+00 7.749E-01 5.515E-02 5.236.0 9.669E-01 2.185E-01 8.205E-02 1.267E+00 7.705E-01 5.506E-02 5.226.5 9.642E-01 2.160E-01 8.001E-02 1.260E+00 7.661E-01 5.497E-02 5.217.0 9.615E-01 2.136E-01 7.801E-02 1.253E+00 7.618E-01 5.489E-02 5.207.5 9.588E-01 2.112E-01 7.606E-02 1.246E+00 7.575E-01 5.481E-02 5.208.0 9.561E-01 2.089E-01 7.417E-02 1.239E+00 7.533E-01 5.472E-02 5.198.5 9.534E-01 2.066E-01 7.231E-02 1.232E+00 7.491E-01 5.464E-02 5.189.0 9.507E-01 2.042E-01 7.051E-02 1.225E+00 7.450E-01 5.456E-02 5.179.5 9.481E-01 2.020E-01 6.875E-02 1.219E+00 7.409E-01 5.448E-02 5.17

10.0 9.454E-01 1.997E-01 6.704E-02 1.212E+00 7.369E-01 5.440E-02 5.1610.5 9.428E-01 1.975E-01 6.536E-02 1.206E+00 7.329E-01 5.433E-02 5.1511.0 9.401E-01 1.953E-01 6.373E-02 1.199E+00 7.290E-01 5.425E-02 5.1511.5 9.375E-01 1.931E-01 6.214E-02 1.193E+00 7.251E-01 5.417E-02 5.1412.0 9.348E-01 1.909E-01 6.059E-02 1.186E+00 7.212E-01 5.410E-02 5.1312.5 9.322E-01 1.888E-01 5.908E-02 1.180E+00 7.174E-01 5.402E-02 5.1313.0 9.296E-01 1.867E-01 5.761E-02 1.174E+00 7.137E-01 5.395E-02 5.1213.5 9.270E-01 1.846E-01 5.617E-02 1.168E+00 7.099E-01 5.388E-02 5.1114.0 9.244E-01 1.826E-01 5.477E-02 1.162E+00 7.062E-01 5.380E-02 5.1114.5 9.218E-01 1.805E-01 5.340E-02 1.156E+00 7.026E-01 5.373E-02 5.1015.0 9.192E-01 1.785E-01 5.207E-02 1.150E+00 6.990E-01 5.366E-02 5.0915.5 9.167E-01 1.765E-01 5.077E-02 1.144E+00 6.954E-01 5.359E-02 5.0916.0 9.141E-01 1.745E-01 4.950E-02 1.138E+00 6.919E-01 5.352E-02 5.0816.5 9.115E-01 1.726E-01 4.827E-02 1.132E+00 6.884E-01 5.346E-02 5.0717.0 9.090E-01 1.707E-01 4.707E-02 1.127E+00 6.849E-01 5.339E-02 5.0717.5 9.064E-01 1.688E-01 4.589E-02 1.121E+00 6.815E-01 5.332E-02 5.0618.0 9.039E-01 1.669E-01 4.475E-02 1.115E+00 6.781E-01 5.326E-02 5.06

t (hour)

n Total Grand Total Pr (dry basis) Pr (Wet Basis)

Appendices

102

1 2 318.5 9.013E-01 1.650E-01 4.363E-02 1.110E+00 6.748E-01 5.319E-02 5.0519.0 8.988E-01 1.632E-01 4.254E-02 1.105E+00 6.715E-01 5.312E-02 5.0419.5 8.963E-01 1.613E-01 4.148E-02 1.099E+00 6.682E-01 5.306E-02 5.0420.0 8.938E-01 1.595E-01 4.044E-02 1.094E+00 6.649E-01 5.300E-02 5.0320.5 8.913E-01 1.578E-01 3.944E-02 1.088E+00 6.617E-01 5.293E-02 5.0321.0 8.888E-01 1.560E-01 3.845E-02 1.083E+00 6.585E-01 5.287E-02 5.0221.5 8.863E-01 1.543E-01 3.749E-02 1.078E+00 6.554E-01 5.281E-02 5.0222.0 8.838E-01 1.525E-01 3.656E-02 1.073E+00 6.522E-01 5.275E-02 5.0122.5 8.813E-01 1.508E-01 3.565E-02 1.068E+00 6.491E-01 5.269E-02 5.0123.0 8.789E-01 1.491E-01 3.476E-02 1.063E+00 6.461E-01 5.263E-02 5.0023.5 8.764E-01 1.475E-01 3.389E-02 1.058E+00 6.430E-01 5.257E-02 4.9924.0 8.739E-01 1.458E-01 3.304E-02 1.053E+00 6.400E-01 5.251E-02 4.99

t (hour)


Appendices

103

T=50oC u=0.0m/s



t (hour)


Appendices

104

1 2 318.5 8.481E-01 1.293E-01 2.522E-02 1.003E+00 6.095E-01 5.191E-02 4.9419.0 8.443E-01 1.271E-01 2.423E-02 9.956E-01 6.053E-01 5.183E-02 4.9319.5 8.406E-01 1.248E-01 2.328E-02 9.887E-01 6.010E-01 5.175E-02 4.9220.0 8.368E-01 1.226E-01 2.237E-02 9.818E-01 5.969E-01 5.167E-02 4.9120.5 8.331E-01 1.204E-01 2.149E-02 9.751E-01 5.928E-01 5.159E-02 4.9121.0 8.294E-01 1.183E-01 2.064E-02 9.684E-01 5.887E-01 5.151E-02 4.9021.5 8.257E-01 1.162E-01 1.983E-02 9.618E-01 5.847E-01 5.143E-02 4.8922.0 8.221E-01 1.142E-01 1.905E-02 9.553E-01 5.808E-01 5.135E-02 4.8822.5 8.184E-01 1.122E-01 1.830E-02 9.489E-01 5.769E-01 5.128E-02 4.8823.0 8.148E-01 1.102E-01 1.759E-02 9.426E-01 5.730E-01 5.120E-02 4.8723.5 8.112E-01 1.082E-01 1.689E-02 9.363E-01 5.692E-01 5.113E-02 4.8624.0 8.076E-01 1.063E-01 1.623E-02 9.301E-01 5.654E-01 5.105E-02 4.8624.5 8.040E-01 1.044E-01 1.559E-02 9.240E-01 5.617E-01 5.098E-02 4.8525.0 8.004E-01 1.026E-01 1.498E-02 9.180E-01 5.581E-01 5.091E-02 4.8425.5 7.968E-01 1.008E-01 1.439E-02 9.120E-01 5.544E-01 5.084E-02 4.8426.0 7.933E-01 9.902E-02 1.383E-02 9.061E-01 5.509E-01 5.077E-02 4.8326.5 7.898E-01 9.727E-02 1.328E-02 9.003E-01 5.473E-01 5.070E-02 4.8327.0 7.863E-01 9.555E-02 1.276E-02 8.946E-01 5.438E-01 5.063E-02 4.8227.5 7.828E-01 9.386E-02 1.226E-02 8.889E-01 5.404E-01 5.056E-02 4.8128.0 7.793E-01 9.221E-02 1.178E-02 8.833E-01 5.370E-01 5.050E-02 4.8128.5 7.758E-01 9.058E-02 1.132E-02 8.777E-01 5.336E-01 5.043E-02 4.8029.0 7.724E-01 8.898E-02 1.087E-02 8.722E-01 5.303E-01 5.036E-02 4.7929.5 7.690E-01 8.741E-02 1.044E-02 8.668E-01 5.270E-01 5.030E-02 4.7930.0 7.655E-01 8.587E-02 1.003E-02 8.614E-01 5.237E-01 5.024E-02 4.7830.5 7.621E-01 8.435E-02 9.640E-03 8.561E-01 5.205E-01 5.017E-02 4.7831.0 7.588E-01 8.286E-02 9.261E-03 8.509E-01 5.173E-01 5.011E-02 4.7731.5 7.554E-01 8.140E-02 8.898E-03 8.457E-01 5.141E-01 5.005E-02 4.7732.0 7.520E-01 7.996E-02 8.548E-03 8.405E-01 5.110E-01 4.999E-02 4.7632.5 7.487E-01 7.855E-02 8.212E-03 8.354E-01 5.079E-01 4.993E-02 4.7633.0 7.454E-01 7.716E-02 7.890E-03 8.304E-01 5.048E-01 4.987E-02 4.7533.5 7.420E-01 7.580E-02 7.580E-03 8.254E-01 5.018E-01 4.981E-02 4.7434.0 7.388E-01 7.446E-02 7.282E-03 8.205E-01 4.988E-01 4.975E-02 4.7434.5 7.355E-01 7.315E-02 6.996E-03 8.156E-01 4.958E-01 4.969E-02 4.7335.0 7.322E-01 7.186E-02 6.721E-03 8.108E-01 4.929E-01 4.963E-02 4.7335.5 7.289E-01 7.059E-02 6.457E-03 8.060E-01 4.900E-01 4.958E-02 4.7236.0 7.257E-01 6.934E-02 6.203E-03 8.013E-01 4.871E-01 4.952E-02 4.72

t (hour)


Appendices

105

T=45oC u=0.0m/s



t (hour)


Appendices

106

1 2 318.5 8.817E-01 1.511E-01 3.576E-02 1.068E+00 6.496E-01 5.270E-02 5.0119.0 8.787E-01 1.490E-01 3.468E-02 1.062E+00 6.458E-01 5.262E-02 5.0019.5 8.757E-01 1.470E-01 3.364E-02 1.056E+00 6.422E-01 5.255E-02 4.9920.0 8.727E-01 1.450E-01 3.262E-02 1.050E+00 6.385E-01 5.248E-02 4.9920.5 8.697E-01 1.430E-01 3.164E-02 1.044E+00 6.349E-01 5.241E-02 4.9821.0 8.668E-01 1.411E-01 3.068E-02 1.039E+00 6.314E-01 5.234E-02 4.9721.5 8.638E-01 1.392E-01 2.976E-02 1.033E+00 6.279E-01 5.227E-02 4.9722.0 8.609E-01 1.373E-01 2.886E-02 1.027E+00 6.244E-01 5.220E-02 4.9622.5 8.580E-01 1.355E-01 2.799E-02 1.021E+00 6.209E-01 5.214E-02 4.9623.0 8.551E-01 1.336E-01 2.715E-02 1.016E+00 6.175E-01 5.207E-02 4.9523.5 8.521E-01 1.318E-01 2.633E-02 1.010E+00 6.142E-01 5.201E-02 4.9424.0 8.493E-01 1.300E-01 2.553E-02 1.005E+00 6.109E-01 5.194E-02 4.9424.5 8.464E-01 1.283E-01 2.476E-02 9.994E-01 6.076E-01 5.188E-02 4.9325.0 8.435E-01 1.265E-01 2.401E-02 9.941E-01 6.043E-01 5.181E-02 4.9325.5 8.406E-01 1.248E-01 2.329E-02 9.887E-01 6.011E-01 5.175E-02 4.9226.0 8.378E-01 1.231E-01 2.259E-02 9.835E-01 5.979E-01 5.169E-02 4.9126.5 8.349E-01 1.215E-01 2.191E-02 9.783E-01 5.947E-01 5.163E-02 4.9127.0 8.321E-01 1.198E-01 2.124E-02 9.732E-01 5.916E-01 5.156E-02 4.9027.5 8.293E-01 1.182E-01 2.060E-02 9.681E-01 5.885E-01 5.150E-02 4.9028.0 8.264E-01 1.166E-01 1.998E-02 9.630E-01 5.855E-01 5.144E-02 4.8928.5 8.236E-01 1.150E-01 1.938E-02 9.580E-01 5.824E-01 5.138E-02 4.8929.0 8.208E-01 1.135E-01 1.879E-02 9.531E-01 5.794E-01 5.133E-02 4.8829.5 8.180E-01 1.120E-01 1.823E-02 9.482E-01 5.764E-01 5.127E-02 4.8830.0 8.153E-01 1.104E-01 1.768E-02 9.434E-01 5.735E-01 5.121E-02 4.8730.5 8.125E-01 1.089E-01 1.714E-02 9.386E-01 5.706E-01 5.115E-02 4.8731.0 8.097E-01 1.075E-01 1.663E-02 9.338E-01 5.677E-01 5.110E-02 4.8631.5 8.070E-01 1.060E-01 1.612E-02 9.291E-01 5.648E-01 5.104E-02 4.8632.0 8.042E-01 1.046E-01 1.564E-02 9.245E-01 5.620E-01 5.099E-02 4.8532.5 8.015E-01 1.032E-01 1.517E-02 9.198E-01 5.592E-01 5.093E-02 4.8533.0 7.988E-01 1.018E-01 1.471E-02 9.153E-01 5.564E-01 5.088E-02 4.8433.5 7.961E-01 1.004E-01 1.426E-02 9.107E-01 5.537E-01 5.082E-02 4.8434.0 7.934E-01 9.904E-02 1.383E-02 9.062E-01 5.509E-01 5.077E-02 4.8334.5 7.907E-01 9.770E-02 1.342E-02 9.018E-01 5.482E-01 5.072E-02 4.8335.0 7.880E-01 9.638E-02 1.301E-02 8.974E-01 5.455E-01 5.066E-02 4.8235.5 7.853E-01 9.508E-02 1.262E-02 8.930E-01 5.429E-01 5.061E-02 4.8236.0 7.826E-01 9.379E-02 1.224E-02 8.887E-01 5.402E-01 5.056E-02 4.81

t (hour)


Appendices

107

T=40oC u=0.0m/s



t (hour)


Appendices

108

1 2 318.5 9.073E-01 1.694E-01 4.629E-02 1.123E+00 6.827E-01 5.334E-02 5.0619.0 9.049E-01 1.676E-01 4.521E-02 1.118E+00 6.795E-01 5.328E-02 5.0619.5 9.025E-01 1.659E-01 4.415E-02 1.113E+00 6.764E-01 5.322E-02 5.0520.0 9.002E-01 1.642E-01 4.312E-02 1.107E+00 6.732E-01 5.316E-02 5.0520.5 8.978E-01 1.624E-01 4.211E-02 1.102E+00 6.701E-01 5.310E-02 5.0421.0 8.955E-01 1.607E-01 4.113E-02 1.097E+00 6.671E-01 5.304E-02 5.0421.5 8.931E-01 1.591E-01 4.017E-02 1.092E+00 6.640E-01 5.298E-02 5.0322.0 8.908E-01 1.574E-01 3.923E-02 1.087E+00 6.610E-01 5.292E-02 5.0322.5 8.884E-01 1.557E-01 3.831E-02 1.082E+00 6.581E-01 5.286E-02 5.0223.0 8.861E-01 1.541E-01 3.741E-02 1.078E+00 6.551E-01 5.281E-02 5.0223.5 8.838E-01 1.525E-01 3.654E-02 1.073E+00 6.522E-01 5.275E-02 5.0124.0 8.814E-01 1.509E-01 3.568E-02 1.068E+00 6.493E-01 5.269E-02 5.0124.5 8.791E-01 1.493E-01 3.485E-02 1.063E+00 6.464E-01 5.263E-02 5.0025.0 8.768E-01 1.478E-01 3.403E-02 1.059E+00 6.436E-01 5.258E-02 5.0025.5 8.745E-01 1.462E-01 3.324E-02 1.054E+00 6.407E-01 5.252E-02 4.9926.0 8.722E-01 1.447E-01 3.246E-02 1.049E+00 6.379E-01 5.247E-02 4.9926.5 8.699E-01 1.432E-01 3.170E-02 1.045E+00 6.352E-01 5.242E-02 4.9827.0 8.676E-01 1.417E-01 3.096E-02 1.040E+00 6.324E-01 5.236E-02 4.9827.5 8.654E-01 1.402E-01 3.024E-02 1.036E+00 6.297E-01 5.231E-02 4.9728.0 8.631E-01 1.387E-01 2.953E-02 1.031E+00 6.270E-01 5.226E-02 4.9728.5 8.608E-01 1.373E-01 2.884E-02 1.027E+00 6.243E-01 5.220E-02 4.9629.0 8.586E-01 1.358E-01 2.816E-02 1.023E+00 6.216E-01 5.215E-02 4.9629.5 8.563E-01 1.344E-01 2.751E-02 1.018E+00 6.190E-01 5.210E-02 4.9530.0 8.541E-01 1.330E-01 2.686E-02 1.014E+00 6.164E-01 5.205E-02 4.9530.5 8.518E-01 1.316E-01 2.623E-02 1.010E+00 6.138E-01 5.200E-02 4.9431.0 8.496E-01 1.302E-01 2.562E-02 1.005E+00 6.112E-01 5.195E-02 4.9431.5 8.473E-01 1.289E-01 2.502E-02 1.001E+00 6.087E-01 5.190E-02 4.9332.0 8.451E-01 1.275E-01 2.444E-02 9.971E-01 6.062E-01 5.185E-02 4.9332.5 8.429E-01 1.262E-01 2.387E-02 9.930E-01 6.037E-01 5.180E-02 4.9233.0 8.407E-01 1.249E-01 2.331E-02 9.889E-01 6.012E-01 5.175E-02 4.9233.5 8.385E-01 1.236E-01 2.276E-02 9.848E-01 5.987E-01 5.170E-02 4.9234.0 8.363E-01 1.223E-01 2.223E-02 9.808E-01 5.962E-01 5.165E-02 4.9134.5 8.341E-01 1.210E-01 2.171E-02 9.768E-01 5.938E-01 5.161E-02 4.9135.0 8.319E-01 1.197E-01 2.120E-02 9.728E-01 5.914E-01 5.156E-02 4.9035.5 8.297E-01 1.185E-01 2.071E-02 9.689E-01 5.890E-01 5.151E-02 4.9036.0 8.275E-01 1.172E-01 2.022E-02 9.650E-01 5.866E-01 5.147E-02 4.89

t (hour)


Appendices

109

1 2 336.5 8.254E-01 1.160E-01 1.975E-02 9.611E-01 5.843E-01 5.142E-02 4.8937.0 8.232E-01 1.148E-01 1.929E-02 9.573E-01 5.820E-01 5.138E-02 4.8937.5 8.210E-01 1.136E-01 1.884E-02 9.535E-01 5.796E-01 5.133E-02 4.8838.0 8.189E-01 1.124E-01 1.840E-02 9.497E-01 5.773E-01 5.128E-02 4.8838.5 8.167E-01 1.112E-01 1.797E-02 9.459E-01 5.751E-01 5.124E-02 4.8739.0 8.146E-01 1.101E-01 1.755E-02 9.422E-01 5.728E-01 5.120E-02 4.8739.5 8.124E-01 1.089E-01 1.714E-02 9.385E-01 5.705E-01 5.115E-02 4.8740.0 8.103E-01 1.078E-01 1.673E-02 9.348E-01 5.683E-01 5.111E-02 4.8640.5 8.082E-01 1.067E-01 1.634E-02 9.312E-01 5.661E-01 5.107E-02 4.8641.0 8.061E-01 1.055E-01 1.596E-02 9.276E-01 5.639E-01 5.102E-02 4.8541.5 8.039E-01 1.044E-01 1.559E-02 9.240E-01 5.617E-01 5.098E-02 4.8542.0 8.018E-01 1.033E-01 1.522E-02 9.204E-01 5.595E-01 5.094E-02 4.8542.5 7.997E-01 1.023E-01 1.487E-02 9.169E-01 5.574E-01 5.089E-02 4.8443.0 7.976E-01 1.012E-01 1.452E-02 9.133E-01 5.552E-01 5.085E-02 4.8443.5 7.955E-01 1.001E-01 1.418E-02 9.098E-01 5.531E-01 5.081E-02 4.8444.0 7.934E-01 9.908E-02 1.385E-02 9.064E-01 5.510E-01 5.077E-02 4.8344.5 7.914E-01 9.805E-02 1.352E-02 9.029E-01 5.489E-01 5.073E-02 4.8345.0 7.893E-01 9.702E-02 1.321E-02 8.995E-01 5.468E-01 5.069E-02 4.8245.5 7.872E-01 9.601E-02 1.290E-02 8.961E-01 5.448E-01 5.065E-02 4.8246.0 7.851E-01 9.500E-02 1.260E-02 8.927E-01 5.427E-01 5.061E-02 4.8246.5 7.831E-01 9.401E-02 1.230E-02 8.894E-01 5.407E-01 5.057E-02 4.8147.0 7.810E-01 9.302E-02 1.202E-02 8.861E-01 5.387E-01 5.053E-02 4.8147.5 7.790E-01 9.205E-02 1.173E-02 8.828E-01 5.367E-01 5.049E-02 4.8148.0 7.769E-01 9.109E-02 1.146E-02 8.795E-01 5.347E-01 5.045E-02 4.80

t (hour)


Appendices

110

T=35oC u=0.0m/s



t (hour)


Appendices

111

1 2 318.5 9.676E-01 2.191E-01 8.260E-02 1.269E+00 7.717E-01 5.508E-02 5.2219.0 9.667E-01 2.184E-01 8.194E-02 1.267E+00 7.703E-01 5.506E-02 5.2219.5 9.659E-01 2.176E-01 8.129E-02 1.265E+00 7.689E-01 5.503E-02 5.2220.0 9.650E-01 2.168E-01 8.064E-02 1.262E+00 7.675E-01 5.500E-02 5.2120.5 9.642E-01 2.160E-01 7.999E-02 1.260E+00 7.661E-01 5.497E-02 5.2121.0 9.633E-01 2.153E-01 7.936E-02 1.258E+00 7.647E-01 5.495E-02 5.2121.5 9.624E-01 2.145E-01 7.872E-02 1.256E+00 7.633E-01 5.492E-02 5.2122.0 9.616E-01 2.137E-01 7.809E-02 1.253E+00 7.620E-01 5.489E-02 5.2022.5 9.607E-01 2.130E-01 7.747E-02 1.251E+00 7.606E-01 5.487E-02 5.2023.0 9.599E-01 2.122E-01 7.685E-02 1.249E+00 7.593E-01 5.484E-02 5.2023.5 9.590E-01 2.115E-01 7.624E-02 1.247E+00 7.579E-01 5.481E-02 5.2024.0 9.582E-01 2.107E-01 7.563E-02 1.245E+00 7.566E-01 5.479E-02 5.1924.5 9.573E-01 2.100E-01 7.503E-02 1.242E+00 7.552E-01 5.476E-02 5.1925.0 9.565E-01 2.092E-01 7.443E-02 1.240E+00 7.539E-01 5.474E-02 5.1925.5 9.556E-01 2.085E-01 7.383E-02 1.238E+00 7.526E-01 5.471E-02 5.1926.0 9.548E-01 2.077E-01 7.324E-02 1.236E+00 7.512E-01 5.468E-02 5.1826.5 9.539E-01 2.070E-01 7.266E-02 1.234E+00 7.499E-01 5.466E-02 5.1827.0 9.531E-01 2.063E-01 7.208E-02 1.231E+00 7.486E-01 5.463E-02 5.1827.5 9.522E-01 2.055E-01 7.150E-02 1.229E+00 7.473E-01 5.461E-02 5.1828.0 9.514E-01 2.048E-01 7.093E-02 1.227E+00 7.460E-01 5.458E-02 5.1828.5 9.505E-01 2.041E-01 7.037E-02 1.225E+00 7.447E-01 5.456E-02 5.1729.0 9.497E-01 2.033E-01 6.981E-02 1.223E+00 7.434E-01 5.453E-02 5.1729.5 9.488E-01 2.026E-01 6.925E-02 1.221E+00 7.421E-01 5.451E-02 5.1730.0 9.480E-01 2.019E-01 6.870E-02 1.219E+00 7.408E-01 5.448E-02 5.1730.5 9.471E-01 2.012E-01 6.815E-02 1.216E+00 7.395E-01 5.445E-02 5.1631.0 9.463E-01 2.005E-01 6.760E-02 1.214E+00 7.382E-01 5.443E-02 5.1631.5 9.454E-01 1.998E-01 6.706E-02 1.212E+00 7.370E-01 5.441E-02 5.1632.0 9.446E-01 1.990E-01 6.653E-02 1.210E+00 7.357E-01 5.438E-02 5.1632.5 9.438E-01 1.983E-01 6.600E-02 1.208E+00 7.344E-01 5.436E-02 5.1633.0 9.429E-01 1.976E-01 6.547E-02 1.206E+00 7.332E-01 5.433E-02 5.1533.5 9.421E-01 1.969E-01 6.495E-02 1.204E+00 7.319E-01 5.431E-02 5.1534.0 9.412E-01 1.962E-01 6.443E-02 1.202E+00 7.307E-01 5.428E-02 5.1534.5 9.404E-01 1.955E-01 6.392E-02 1.200E+00 7.294E-01 5.426E-02 5.1535.0 9.396E-01 1.948E-01 6.341E-02 1.198E+00 7.282E-01 5.423E-02 5.1435.5 9.387E-01 1.941E-01 6.290E-02 1.196E+00 7.269E-01 5.421E-02 5.1436.0 9.379E-01 1.934E-01 6.240E-02 1.194E+00 7.257E-01 5.419E-02 5.14

t (hour)


Appendices

112


t (hour)


Appendices

113


t (hour)


Appendices

114

T=30oC u=0.0m/s



t (hour)


Appendices

115


t (hour)


Appendices

116


t (hour)


Appendices

117


t (hour)


Appendices

118

APPENDIX 5: CALCULATION OF MASS TRANSFER COEFFICIENT, hD

Mass Transfer Coefficient, hD, is calculated from using the mass correlations (Bird,

Stewart & Lightfoot 2002) which is given by,

]800,2[Re ,Re552.02 3

1

2

1

ScD

dhSh D (17)

,Reud

where (18)

.D

Sc

(19)

In forced convection trials, the viscosity of air, µ, at different speed of air flow is needed

to compute hD. LMNO Engineering, Research, and Software, Ltd. (2003) uses the

Sutherland’s formula to determine µ. From LMNO Engineering, Research, and

Software, Ltd. (2003), Sutherland’s formula is given by

Air) Standard(at 120 Constant s'Sutherland

Air) Standarde(at centipois10827.1at centipoisein viscocityreference

at centipoisein viscocity

Air) Standard(at 524.07Rankie degreesin eTemperatur Reference

Rankie degreesin eTemperaturInput

555.0 ,555.0 ,

2o

o

2

3

C

T

T

RT

T

CTbCTawhereT

T

b

a

o

o

oo

o

Appendices

119

The following shows calculations done to determine µ and hD:

Drying Temperature,

T

(oC)

Drying Air Temperature,

T

(oR)

Air Flow

Speed, u

(m/s)

Air Flow

Speed, u

(m/hr)

Constant,

b (oR)

Viscocity of Drying

Air, µ

(kg/mhr)

Density of Drying

Air, ρ

(kg/m3)

Reynolds Number,

Re

(dimensionless)

Schmidt Number,

Sc

(dimentionless)

Mass Transfer

Coefficient, hD

(m/hr)

55 590.688 0.5 1800 4.478E+02 7.221E-02 1.085 1.647E+02 3.431E+05 1.520E-02 1.0 3600 4.478E+02 7.221E-02 1.085 3.295E+02 2.836E+05 2.440E-02

45 572.688 0.5 1800 4.378E+02 7.050E-02 1.118 1.739E+02 6.705E+05 9.436E-03 1.0 3600 4.378E+02 7.050E-02 1.118 3.478E+02 4.345E+05 1.784E-02

35 554.688 0.5 1800 4.279E+02 6.878E-02 1.146 1.828E+02 1.343E+06 5.777E-03 1.0 3600 4.279E+02 6.878E-02 1.146 3.655E+02 9.424E+05 1.035E-02

Appendices

120

APPENDIX 6A: CALCULATION OF MOISTURE CONTENT IN PIPER

NIGRUM L. BERRIES WITH TIME FOR FORCED


T=55oC u=0.5m/s

1 2 30.5 9.020E-01 1.655E-01 4.390E-02 1.111E+00 6.756E-01 1.419E+00 58.671.0 8.136E-01 1.095E-01 1.735E-02 9.404E-01 5.717E-01 1.209E+00 54.721.5 7.338E-01 7.249E-02 6.855E-03 8.132E-01 4.943E-01 1.052E+00 51.262.0 6.619E-01 4.798E-02 2.709E-03 7.126E-01 4.332E-01 9.279E-01 48.132.5 5.970E-01 3.176E-02 1.070E-03 6.298E-01 3.829E-01 8.259E-01 45.233.0 5.385E-01 2.102E-02 4.230E-04 5.599E-01 3.404E-01 7.397E-01 42.523.5 4.857E-01 1.391E-02 1.671E-04 4.998E-01 3.038E-01 6.656E-01 39.964.0 4.381E-01 9.208E-03 6.604E-05 4.474E-01 2.720E-01 6.010E-01 37.544.5 3.951E-01 6.095E-03 2.610E-05 4.013E-01 2.439E-01 5.442E-01 35.245.0 3.564E-01 4.034E-03 1.031E-05 3.605E-01 2.191E-01 4.939E-01 33.065.5 3.215E-01 2.670E-03 4.074E-06 3.241E-01 1.971E-01 4.492E-01 30.996.0 2.900E-01 1.767E-03 1.610E-06 2.917E-01 1.774E-01 4.092E-01 29.046.5 2.615E-01 1.170E-03 6.362E-07 2.627E-01 1.597E-01 3.735E-01 27.197.0 2.359E-01 7.742E-04 2.514E-07 2.367E-01 1.439E-01 3.414E-01 25.457.5 2.128E-01 5.124E-04 9.933E-08 2.133E-01 1.297E-01 3.125E-01 23.818.0 1.919E-01 3.392E-04 3.925E-08 1.923E-01 1.169E-01 2.866E-01 22.288.5 1.731E-01 2.245E-04 1.551E-08 1.733E-01 1.054E-01 2.633E-01 20.849.0 1.561E-01 1.486E-04 6.129E-09 1.563E-01 9.501E-02 2.423E-01 19.509.5 1.408E-01 9.835E-05 2.422E-09 1.409E-01 8.568E-02 2.234E-01 18.26


t (hour)


Appendices

121

T=45oC u=0.5m/s

1 2 30.5 9.512E-01 2.047E-01 7.084E-02 1.227E+00 7.458E-01 1.499E+00 59.981.0 9.048E-01 1.676E-01 4.517E-02 1.118E+00 6.794E-01 1.371E+00 57.831.5 8.607E-01 1.372E-01 2.880E-02 1.027E+00 6.241E-01 1.265E+00 55.862.0 8.187E-01 1.123E-01 1.836E-02 9.494E-01 5.772E-01 1.175E+00 54.032.5 7.788E-01 9.195E-02 1.171E-02 8.824E-01 5.364E-01 1.097E+00 52.323.0 7.408E-01 7.528E-02 7.464E-03 8.235E-01 5.006E-01 1.029E+00 50.703.5 7.046E-01 6.163E-02 4.759E-03 7.710E-01 4.687E-01 9.674E-01 49.174.0 6.703E-01 5.046E-02 3.034E-03 7.238E-01 4.400E-01 9.123E-01 47.714.5 6.376E-01 4.131E-02 1.934E-03 6.808E-01 4.139E-01 8.623E-01 46.305.0 6.065E-01 3.382E-02 1.233E-03 6.415E-01 3.900E-01 8.165E-01 44.955.5 5.769E-01 2.769E-02 7.863E-04 6.054E-01 3.680E-01 7.743E-01 43.646.0 5.488E-01 2.267E-02 5.014E-04 5.719E-01 3.477E-01 7.353E-01 42.376.5 5.220E-01 1.856E-02 3.197E-04 5.409E-01 3.288E-01 6.991E-01 41.157.0 4.965E-01 1.519E-02 2.038E-04 5.119E-01 3.112E-01 6.654E-01 39.957.5 4.723E-01 1.244E-02 1.299E-04 4.849E-01 2.948E-01 6.339E-01 38.808.0 4.493E-01 1.018E-02 8.285E-05 4.595E-01 2.794E-01 6.043E-01 37.678.5 4.274E-01 8.338E-03 5.282E-05 4.357E-01 2.649E-01 5.766E-01 36.579.0 4.065E-01 6.827E-03 3.368E-05 4.134E-01 2.513E-01 5.505E-01 35.519.5 3.867E-01 5.589E-03 2.147E-05 3.923E-01 2.385E-01 5.260E-01 34.47

10.0 3.678E-01 4.576E-03 1.369E-05 3.724E-01 2.264E-01 5.028E-01 33.4610.5 3.499E-01 3.746E-03 8.729E-06 3.536E-01 2.150E-01 4.809E-01 32.4711.0 3.328E-01 3.067E-03 5.565E-06 3.359E-01 2.042E-01 4.602E-01 31.5211.5 3.166E-01 2.511E-03 3.548E-06 3.191E-01 1.940E-01 4.406E-01 30.5912.0 3.011E-01 2.056E-03 2.262E-06 3.032E-01 1.843E-01 4.221E-01 29.6812.5 2.864E-01 1.683E-03 1.442E-06 2.881E-01 1.752E-01 4.046E-01 28.8013.0 2.725E-01 1.378E-03 9.196E-07 2.738E-01 1.665E-01 3.879E-01 27.9513.5 2.592E-01 1.128E-03 5.863E-07 2.603E-01 1.582E-01 3.721E-01 27.1214.0 2.465E-01 9.235E-04 3.738E-07 2.475E-01 1.504E-01 3.572E-01 26.3214.5 2.345E-01 7.561E-04 2.383E-07 2.353E-01 1.430E-01 3.429E-01 25.5415.0 2.231E-01 6.190E-04 1.520E-07 2.237E-01 1.360E-01 3.295E-01 24.7815.5 2.122E-01 5.068E-04 9.689E-08 2.127E-01 1.293E-01 3.166E-01 24.0516.0 2.018E-01 4.149E-04 6.177E-08 2.023E-01 1.230E-01 3.045E-01 23.3416.5 1.920E-01 3.397E-04 3.939E-08 1.923E-01 1.169E-01 2.929E-01 22.6517.0 1.826E-01 2.781E-04 2.511E-08 1.829E-01 1.112E-01 2.819E-01 21.9917.5 1.737E-01 2.277E-04 1.601E-08 1.739E-01 1.057E-01 2.715E-01 21.35

t (hour)


Appendices

122

1 2 318.0 1.652E-01 1.864E-04 1.021E-08 1.654E-01 1.006E-01 2.616E-01 20.7318.5 1.572E-01 1.526E-04 6.508E-09 1.573E-01 9.565E-02 2.521E-01 20.1419.0 1.495E-01 1.249E-04 4.149E-09 1.496E-01 9.097E-02 2.431E-01 19.5619.5 1.422E-01 1.023E-04 2.646E-09 1.423E-01 8.652E-02 2.346E-01 19.0020.0 1.353E-01 8.375E-05 1.687E-09 1.354E-01 8.230E-02 2.265E-01 18.4720.5 1.287E-01 6.856E-05 1.075E-09 1.288E-01 7.827E-02 2.188E-01 17.9521.0 1.224E-01 5.613E-05 6.857E-10 1.225E-01 7.445E-02 2.115E-01 17.4621.5 1.164E-01 4.596E-05 4.372E-10 1.165E-01 7.081E-02 2.045E-01 16.9822.0 1.108E-01 3.762E-05 2.787E-10 1.108E-01 6.736E-02 1.979E-01 16.5222.5 1.054E-01 3.080E-05 1.777E-10 1.054E-01 6.407E-02 1.916E-01 16.0823.0 1.002E-01 2.522E-05 1.133E-10 1.002E-01 6.094E-02 1.856E-01 15.6523.5 9.533E-02 2.065E-05 7.224E-11 9.535E-02 5.797E-02 1.799E-01 15.2424.0 9.068E-02 1.690E-05 4.606E-11 9.070E-02 5.514E-02 1.744E-01 14.8524.5 8.626E-02 1.384E-05 2.937E-11 8.627E-02 5.245E-02 1.693E-01 14.4825.0 8.205E-02 1.133E-05 1.872E-11 8.206E-02 4.989E-02 1.644E-01 14.1225.5 7.805E-02 9.276E-06 1.194E-11 7.806E-02 4.745E-02 1.597E-01 13.7726.0 7.424E-02 7.594E-06 7.611E-12 7.425E-02 4.514E-02 1.553E-01 13.4426.5 7.062E-02 6.217E-06 4.853E-12 7.062E-02 4.293E-02 1.511E-01 13.1227.0 6.717E-02 5.090E-06 3.094E-12 6.718E-02 4.084E-02 1.470E-01 12.8227.5 6.390E-02 4.167E-06 1.973E-12 6.390E-02 3.885E-02 1.432E-01 12.5328.0 6.078E-02 3.412E-06 1.258E-12 6.078E-02 3.695E-02 1.396E-01 12.2528.5 5.781E-02 2.793E-06 8.019E-13 5.782E-02 3.515E-02 1.361E-01 11.9829.0 5.499E-02 2.287E-06 5.113E-13 5.500E-02 3.343E-02 1.328E-01 11.7329.5 5.231E-02 1.872E-06 3.260E-13 5.231E-02 3.180E-02 1.297E-01 11.4830.0 4.976E-02 1.533E-06 2.078E-13 4.976E-02 3.025E-02 1.267E-01 11.2530.5 4.733E-02 1.255E-06 1.325E-13 4.733E-02 2.878E-02 1.239E-01 11.0231.0 4.502E-02 1.027E-06 8.448E-14 4.503E-02 2.737E-02 1.212E-01 10.8131.5 4.283E-02 8.411E-07 5.387E-14 4.283E-02 2.604E-02 1.187E-01 10.6132.0 4.074E-02 6.886E-07 3.434E-14 4.074E-02 2.477E-02 1.162E-01 10.4132.5 3.875E-02 5.638E-07 2.190E-14 3.875E-02 2.356E-02 1.139E-01 10.2333.0 3.686E-02 4.616E-07 1.396E-14 3.686E-02 2.241E-02 1.117E-01 10.0533.5 3.506E-02 3.779E-07 8.901E-15 3.506E-02 2.132E-02 1.096E-01 9.8834.0 3.335E-02 3.094E-07 5.675E-15 3.335E-02 2.028E-02 1.076E-01 9.72

t (hour)


Appendices

123

T=35oC u=0.5m/s

1 2 30.5 9.765E-01 2.273E-01 8.971E-02 1.294E+00 7.864E-01 1.583E+00 61.281.0 9.536E-01 2.067E-01 7.244E-02 1.233E+00 7.494E-01 1.513E+00 60.211.5 9.312E-01 1.880E-01 5.849E-02 1.178E+00 7.159E-01 1.450E+00 59.182.0 9.093E-01 1.709E-01 4.722E-02 1.127E+00 6.854E-01 1.392E+00 58.202.5 8.880E-01 1.554E-01 3.813E-02 1.082E+00 6.575E-01 1.340E+00 57.263.0 8.671E-01 1.413E-01 3.079E-02 1.039E+00 6.318E-01 1.291E+00 56.353.5 8.467E-01 1.285E-01 2.486E-02 1.000E+00 6.080E-01 1.246E+00 55.484.0 8.268E-01 1.169E-01 2.007E-02 9.638E-01 5.859E-01 1.205E+00 54.644.5 8.074E-01 1.063E-01 1.621E-02 9.299E-01 5.653E-01 1.166E+00 53.835.0 7.885E-01 9.662E-02 1.309E-02 8.982E-01 5.460E-01 1.129E+00 53.045.5 7.699E-01 8.786E-02 1.057E-02 8.684E-01 5.279E-01 1.095E+00 52.276.0 7.519E-01 7.989E-02 8.531E-03 8.403E-01 5.108E-01 1.063E+00 51.526.5 7.342E-01 7.264E-02 6.888E-03 8.137E-01 4.947E-01 1.032E+00 50.807.0 7.170E-01 6.606E-02 5.561E-03 7.886E-01 4.794E-01 1.004E+00 50.097.5 7.001E-01 6.007E-02 4.490E-03 7.647E-01 4.649E-01 9.762E-01 49.408.0 6.837E-01 5.462E-02 3.626E-03 7.419E-01 4.510E-01 9.501E-01 48.728.5 6.676E-01 4.966E-02 2.928E-03 7.202E-01 4.378E-01 9.252E-01 48.069.0 6.519E-01 4.516E-02 2.364E-03 6.995E-01 4.252E-01 9.014E-01 47.419.5 6.366E-01 4.106E-02 1.909E-03 6.796E-01 4.131E-01 8.786E-01 46.7710.0 6.217E-01 3.734E-02 1.541E-03 6.606E-01 4.016E-01 8.567E-01 46.1410.5 6.071E-01 3.395E-02 1.244E-03 6.423E-01 3.905E-01 8.358E-01 45.5311.0 5.928E-01 3.088E-02 1.005E-03 6.247E-01 3.798E-01 8.156E-01 44.9211.5 5.789E-01 2.807E-02 8.112E-04 6.078E-01 3.695E-01 7.962E-01 44.3312.0 5.653E-01 2.553E-02 6.550E-04 5.915E-01 3.596E-01 7.775E-01 43.7412.5 5.520E-01 2.321E-02 5.288E-04 5.758E-01 3.500E-01 7.595E-01 43.1613.0 5.391E-01 2.111E-02 4.270E-04 5.606E-01 3.408E-01 7.421E-01 42.6013.5 5.264E-01 1.919E-02 3.448E-04 5.459E-01 3.319E-01 7.253E-01 42.0414.0 5.140E-01 1.745E-02 2.784E-04 5.318E-01 3.233E-01 7.090E-01 41.4914.5 5.020E-01 1.587E-02 2.248E-04 5.180E-01 3.149E-01 6.933E-01 40.9415.0 4.902E-01 1.443E-02 1.815E-04 5.048E-01 3.069E-01 6.780E-01 40.4115.5 4.787E-01 1.312E-02 1.465E-04 4.919E-01 2.991E-01 6.633E-01 39.8816.0 4.674E-01 1.193E-02 1.183E-04 4.795E-01 2.915E-01 6.490E-01 39.3616.5 4.564E-01 1.085E-02 9.553E-05 4.674E-01 2.841E-01 6.351E-01 38.8417.0 4.457E-01 9.866E-03 7.713E-05 4.557E-01 2.770E-01 6.217E-01 38.3417.5 4.352E-01 8.972E-03 6.228E-05 4.443E-01 2.701E-01 6.086E-01 37.8418.0 4.250E-01 8.158E-03 5.029E-05 4.332E-01 2.634E-01 5.960E-01 37.34

t (hour)


Appendices

124


t (hour)


Appendices

125


t (hour)


Appendices

126


t (hour)


Appendices

127

T=55oC u=1.0m/s

1 2 30.5 8.827E-01 1.517E-01 3.613E-02 1.071E+00 6.508E-01 1.369E+00 57.791.0 7.791E-01 9.210E-02 1.175E-02 8.829E-01 5.368E-01 1.138E+00 53.221.5 6.877E-01 5.590E-02 3.820E-03 7.474E-01 4.543E-01 9.708E-01 49.262.0 6.070E-01 3.393E-02 1.242E-03 6.421E-01 3.904E-01 8.411E-01 45.682.5 5.357E-01 2.059E-02 4.039E-04 5.567E-01 3.385E-01 7.358E-01 42.393.0 4.729E-01 1.250E-02 1.313E-04 4.855E-01 2.951E-01 6.480E-01 39.323.5 4.174E-01 7.587E-03 4.271E-05 4.250E-01 2.584E-01 5.735E-01 36.454.0 3.684E-01 4.605E-03 1.389E-05 3.730E-01 2.268E-01 5.094E-01 33.754.5 3.252E-01 2.795E-03 4.516E-06 3.280E-01 1.994E-01 4.539E-01 31.225.0 2.870E-01 1.696E-03 1.468E-06 2.887E-01 1.755E-01 4.055E-01 28.855.5 2.533E-01 1.030E-03 4.775E-07 2.544E-01 1.546E-01 3.632E-01 26.646.0 2.236E-01 6.250E-04 1.553E-07 2.242E-01 1.363E-01 3.260E-01 24.596.5 1.974E-01 3.793E-04 5.049E-08 1.977E-01 1.202E-01 2.934E-01 22.687.0 1.742E-01 2.302E-04 1.642E-08 1.744E-01 1.060E-01 2.647E-01 20.937.5 1.538E-01 1.397E-04 5.338E-09 1.539E-01 9.356E-02 2.394E-01 19.318.0 1.357E-01 8.482E-05 1.736E-09 1.358E-01 8.256E-02 2.171E-01 17.838.5 1.198E-01 5.148E-05 5.644E-10 1.198E-01 7.286E-02 1.974E-01 16.489.0 1.057E-01 3.125E-05 1.835E-10 1.058E-01 6.430E-02 1.800E-01 15.269.5 9.333E-02 1.897E-05 5.968E-11 9.335E-02 5.675E-02 1.647E-01 14.1410.0 8.238E-02 1.151E-05 1.941E-11 8.239E-02 5.009E-02 1.512E-01 13.1410.5 7.271E-02 6.987E-06 6.310E-12 7.272E-02 4.421E-02 1.393E-01 12.2311.0 6.418E-02 4.241E-06 2.052E-12 6.418E-02 3.902E-02 1.288E-01 11.4111.5 5.665E-02 2.574E-06 6.672E-13 5.665E-02 3.444E-02 1.195E-01 10.6712.0 5.000E-02 1.562E-06 2.170E-13 5.000E-02 3.040E-02 1.113E-01 10.0212.5 4.413E-02 9.483E-07 7.055E-14 4.413E-02 2.683E-02 1.041E-01 9.4313.0 3.895E-02 5.756E-07 2.294E-14 3.895E-02 2.368E-02 9.769E-02 8.9013.5 3.438E-02 3.493E-07 7.459E-15 3.438E-02 2.090E-02 9.206E-02 8.4314.0 3.035E-02 2.120E-07 2.426E-15 3.035E-02 1.845E-02 8.709E-02 8.0114.5 2.679E-02 1.287E-07 7.887E-16 2.679E-02 1.628E-02 8.270E-02 7.64

t (hour)


Appendices

128

T=45oC u=1.0m/s

1 2 30.5 9.257E-01 1.836E-01 5.548E-02 1.165E+00 7.081E-01 1.458E+00 59.311.0 8.570E-01 1.348E-01 2.770E-02 1.020E+00 6.198E-01 1.284E+00 56.231.5 7.933E-01 9.903E-02 1.383E-02 9.062E-01 5.509E-01 1.149E+00 53.472.0 7.344E-01 7.273E-02 6.905E-03 8.140E-01 4.949E-01 1.039E+00 50.972.5 6.799E-01 5.341E-02 3.448E-03 7.367E-01 4.479E-01 9.473E-01 48.653.0 6.294E-01 3.922E-02 1.721E-03 6.703E-01 4.075E-01 8.681E-01 46.473.5 5.826E-01 2.881E-02 8.595E-04 6.123E-01 3.722E-01 7.989E-01 44.414.0 5.394E-01 2.116E-02 4.291E-04 5.609E-01 3.410E-01 7.376E-01 42.454.5 4.993E-01 1.554E-02 2.143E-04 5.150E-01 3.131E-01 6.829E-01 40.585.0 4.622E-01 1.141E-02 1.070E-04 4.737E-01 2.880E-01 6.336E-01 38.795.5 4.279E-01 8.380E-03 5.342E-05 4.363E-01 2.652E-01 5.890E-01 37.076.0 3.961E-01 6.154E-03 2.667E-05 4.023E-01 2.446E-01 5.485E-01 35.426.5 3.667E-01 4.520E-03 1.332E-05 3.712E-01 2.257E-01 5.114E-01 33.847.0 3.395E-01 3.319E-03 6.649E-06 3.428E-01 2.084E-01 4.775E-01 32.327.5 3.142E-01 2.438E-03 3.320E-06 3.167E-01 1.925E-01 4.464E-01 30.868.0 2.909E-01 1.790E-03 1.658E-06 2.927E-01 1.779E-01 4.178E-01 29.478.5 2.693E-01 1.315E-03 8.276E-07 2.706E-01 1.645E-01 3.914E-01 28.139.0 2.493E-01 9.656E-04 4.132E-07 2.503E-01 1.521E-01 3.672E-01 26.869.5 2.308E-01 7.091E-04 2.063E-07 2.315E-01 1.407E-01 3.448E-01 25.6410.0 2.136E-01 5.208E-04 1.030E-07 2.142E-01 1.302E-01 3.241E-01 24.4810.5 1.978E-01 3.825E-04 5.143E-08 1.982E-01 1.205E-01 3.050E-01 23.3711.0 1.831E-01 2.809E-04 2.568E-08 1.834E-01 1.115E-01 2.874E-01 22.3211.5 1.695E-01 2.063E-04 1.282E-08 1.697E-01 1.032E-01 2.711E-01 21.3312.0 1.569E-01 1.515E-04 6.402E-09 1.570E-01 9.547E-02 2.560E-01 20.3812.5 1.452E-01 1.113E-04 3.196E-09 1.454E-01 8.837E-02 2.421E-01 19.4913.0 1.345E-01 8.171E-05 1.596E-09 1.345E-01 8.179E-02 2.292E-01 18.6413.5 1.245E-01 6.001E-05 7.968E-10 1.245E-01 7.571E-02 2.172E-01 17.8514.0 1.152E-01 4.407E-05 3.979E-10 1.153E-01 7.008E-02 2.062E-01 17.0914.5 1.067E-01 3.237E-05 1.986E-10 1.067E-01 6.487E-02 1.960E-01 16.3915.0 9.875E-02 2.377E-05 9.918E-11 9.877E-02 6.004E-02 1.865E-01 15.7215.5 9.141E-02 1.746E-05 4.952E-11 9.143E-02 5.558E-02 1.778E-01 15.0916.0 8.462E-02 1.282E-05 2.473E-11 8.464E-02 5.145E-02 1.697E-01 14.5116.5 7.834E-02 9.415E-06 1.235E-11 7.835E-02 4.763E-02 1.622E-01 13.9517.0 7.252E-02 6.915E-06 6.164E-12 7.253E-02 4.409E-02 1.552E-01 13.4417.5 6.713E-02 5.078E-06 3.078E-12 6.714E-02 4.082E-02 1.488E-01 12.95

t (hour)


Appendices

129

1 2 318.0 6.215E-02 3.729E-06 1.537E-12 6.215E-02 3.778E-02 1.429E-01 12.5018.5 5.753E-02 2.739E-06 7.673E-13 5.753E-02 3.498E-02 1.373E-01 12.0819.0 5.326E-02 2.011E-06 3.831E-13 5.326E-02 3.238E-02 1.322E-01 11.6819.5 4.930E-02 1.477E-06 1.913E-13 4.930E-02 2.997E-02 1.275E-01 11.3120.0 4.564E-02 1.085E-06 9.550E-14 4.564E-02 2.775E-02 1.232E-01 10.9720.5 4.225E-02 7.967E-07 4.768E-14 4.225E-02 2.569E-02 1.191E-01 10.6421.0 3.911E-02 5.851E-07 2.381E-14 3.911E-02 2.378E-02 1.154E-01 10.3421.5 3.621E-02 4.297E-07 1.189E-14 3.621E-02 2.201E-02 1.119E-01 10.0722.0 3.352E-02 3.156E-07 5.935E-15 3.352E-02 2.038E-02 1.087E-01 9.80

t (hour)


Appendices

130

T=35oC u=1.0m/s

1 2 30.5 9.667E-01 2.183E-01 8.192E-02 1.267E+00 7.702E-01 1.580E+00 61.241.0 9.345E-01 1.907E-01 6.041E-02 1.186E+00 7.208E-01 1.485E+00 59.761.5 9.034E-01 1.665E-01 4.454E-02 1.114E+00 6.775E-01 1.402E+00 58.372.0 8.733E-01 1.454E-01 3.284E-02 1.052E+00 6.393E-01 1.328E+00 57.052.5 8.443E-01 1.270E-01 2.421E-02 9.955E-01 6.052E-01 1.263E+00 55.813.0 8.162E-01 1.109E-01 1.785E-02 9.449E-01 5.744E-01 1.204E+00 54.623.5 7.890E-01 9.687E-02 1.316E-02 8.990E-01 5.465E-01 1.150E+00 53.494.0 7.627E-01 8.460E-02 9.706E-03 8.570E-01 5.210E-01 1.101E+00 52.404.5 7.373E-01 7.389E-02 7.156E-03 8.184E-01 4.975E-01 1.056E+00 51.365.0 7.128E-01 6.453E-02 5.276E-03 7.826E-01 4.758E-01 1.014E+00 50.355.5 6.890E-01 5.636E-02 3.890E-03 7.493E-01 4.555E-01 9.750E-01 49.376.0 6.661E-01 4.922E-02 2.869E-03 7.182E-01 4.366E-01 9.386E-01 48.426.5 6.439E-01 4.298E-02 2.115E-03 6.890E-01 4.189E-01 9.045E-01 47.497.0 6.225E-01 3.754E-02 1.559E-03 6.616E-01 4.022E-01 8.725E-01 46.597.5 6.018E-01 3.278E-02 1.150E-03 6.357E-01 3.865E-01 8.422E-01 45.728.0 5.817E-01 2.863E-02 8.478E-04 6.112E-01 3.716E-01 8.136E-01 44.868.5 5.624E-01 2.500E-02 6.251E-04 5.880E-01 3.575E-01 7.864E-01 44.029.0 5.436E-01 2.184E-02 4.609E-04 5.659E-01 3.441E-01 7.606E-01 43.209.5 5.255E-01 1.907E-02 3.398E-04 5.450E-01 3.313E-01 7.361E-01 42.4010.0 5.081E-01 1.666E-02 2.506E-04 5.250E-01 3.191E-01 7.127E-01 41.6110.5 4.911E-01 1.455E-02 1.847E-04 5.059E-01 3.075E-01 6.904E-01 40.8411.0 4.748E-01 1.270E-02 1.362E-04 4.876E-01 2.964E-01 6.691E-01 40.0911.5 4.590E-01 1.109E-02 1.004E-04 4.702E-01 2.858E-01 6.487E-01 39.3512.0 4.437E-01 9.689E-03 7.406E-05 4.535E-01 2.757E-01 6.291E-01 38.6212.5 4.289E-01 8.462E-03 5.460E-05 4.374E-01 2.659E-01 6.104E-01 37.9013.0 4.146E-01 7.390E-03 4.026E-05 4.221E-01 2.566E-01 5.924E-01 37.2013.5 4.008E-01 6.454E-03 2.968E-05 4.073E-01 2.476E-01 5.752E-01 36.5214.0 3.875E-01 5.637E-03 2.189E-05 3.932E-01 2.390E-01 5.586E-01 35.8414.5 3.746E-01 4.923E-03 1.614E-05 3.795E-01 2.307E-01 5.427E-01 35.1815.0 3.621E-01 4.299E-03 1.190E-05 3.664E-01 2.228E-01 5.274E-01 34.5315.5 3.501E-01 3.755E-03 8.773E-06 3.538E-01 2.151E-01 5.127E-01 33.8916.0 3.384E-01 3.279E-03 6.469E-06 3.417E-01 2.077E-01 4.985E-01 33.2716.5 3.272E-01 2.864E-03 4.770E-06 3.300E-01 2.006E-01 4.848E-01 32.6517.0 3.163E-01 2.501E-03 3.517E-06 3.188E-01 1.938E-01 4.717E-01 32.0517.5 3.057E-01 2.184E-03 2.593E-06 3.079E-01 1.872E-01 4.590E-01 31.4618.0 2.956E-01 1.908E-03 1.912E-06 2.975E-01 1.808E-01 4.468E-01 30.88

t (hour)


Appendices

131


t (hour)


Appendices

132

1 2 336.5 8.444E-02 1.271E-05 2.426E-11 8.446E-02 5.134E-02 1.977E-01 16.5137.0 8.163E-02 1.110E-05 1.788E-11 8.164E-02 4.963E-02 1.944E-01 16.2837.5 7.891E-02 9.695E-06 1.319E-11 7.892E-02 4.798E-02 1.913E-01 16.0638.0 7.629E-02 8.467E-06 9.723E-12 7.629E-02 4.638E-02 1.882E-01 15.8438.5 7.375E-02 7.395E-06 7.169E-12 7.375E-02 4.484E-02 1.852E-01 15.6339.0 7.129E-02 6.458E-06 5.286E-12 7.130E-02 4.334E-02 1.824E-01 15.4239.5 6.892E-02 5.640E-06 3.897E-12 6.892E-02 4.190E-02 1.796E-01 15.2240.0 6.662E-02 4.926E-06 2.874E-12 6.663E-02 4.051E-02 1.769E-01 15.0340.5 6.441E-02 4.302E-06 2.119E-12 6.441E-02 3.916E-02 1.743E-01 14.8441.0 6.226E-02 3.757E-06 1.562E-12 6.227E-02 3.785E-02 1.718E-01 14.6641.5 6.019E-02 3.281E-06 1.152E-12 6.019E-02 3.659E-02 1.694E-01 14.4842.0 5.818E-02 2.865E-06 8.493E-13 5.819E-02 3.537E-02 1.670E-01 14.3142.5 5.625E-02 2.502E-06 6.262E-13 5.625E-02 3.420E-02 1.648E-01 14.1543.0 5.438E-02 2.185E-06 4.617E-13 5.438E-02 3.306E-02 1.626E-01 13.9843.5 5.257E-02 1.909E-06 3.404E-13 5.257E-02 3.196E-02 1.605E-01 13.8344.0 5.082E-02 1.667E-06 2.510E-13 5.082E-02 3.089E-02 1.584E-01 13.6744.5 4.912E-02 1.456E-06 1.851E-13 4.912E-02 2.986E-02 1.564E-01 13.5345.0 4.749E-02 1.271E-06 1.365E-13 4.749E-02 2.887E-02 1.545E-01 13.3845.5 4.591E-02 1.110E-06 1.006E-13 4.591E-02 2.791E-02 1.527E-01 13.2546.0 4.438E-02 9.697E-07 7.419E-14 4.438E-02 2.698E-02 1.509E-01 13.1146.5 4.290E-02 8.469E-07 5.470E-14 4.290E-02 2.608E-02 1.492E-01 12.9847.0 4.147E-02 7.396E-07 4.033E-14 4.147E-02 2.521E-02 1.475E-01 12.8547.5 4.009E-02 6.459E-07 2.974E-14 4.009E-02 2.437E-02 1.459E-01 12.7348.0 3.876E-02 5.641E-07 2.193E-14 3.876E-02 2.356E-02 1.443E-01 12.6148.5 3.747E-02 4.927E-07 1.617E-14 3.747E-02 2.278E-02 1.428E-01 12.5049.0 3.622E-02 4.303E-07 1.192E-14 3.622E-02 2.202E-02 1.413E-01 12.3849.5 3.501E-02 3.758E-07 8.789E-15 3.501E-02 2.129E-02 1.399E-01 12.2850.0 3.385E-02 3.282E-07 6.480E-15 3.385E-02 2.058E-02 1.386E-01 12.1750.5 3.272E-02 2.866E-07 4.778E-15 3.272E-02 1.989E-02 1.373E-01 12.07

t (hour)


Appendices

133

APPENDIX 6B: CALCULATION OF PIPERINE CONTENTIN PIPER NIGRUM

L. BERRIES WITH TIME FOR FORCED CONVECTION

TRIALS VIA THE ANALYTIC SOLUTION

T=55oC u=0.5m/s

1 2 30.5 9.946E-01 2.446E-01 1.058E-01 1.345E+00 8.177E-01 4.852E-02 4.631.0 9.892E-01 2.394E-01 1.008E-01 1.329E+00 8.082E-01 4.842E-02 4.621.5 9.839E-01 2.343E-01 9.601E-02 1.314E+00 7.989E-01 4.832E-02 4.612.0 9.786E-01 2.293E-01 9.144E-02 1.299E+00 7.899E-01 4.823E-02 4.602.5 9.733E-01 2.244E-01 8.710E-02 1.285E+00 7.810E-01 4.814E-02 4.593.0 9.681E-01 2.196E-01 8.296E-02 1.271E+00 7.724E-01 4.805E-02 4.583.5 9.628E-01 2.148E-01 7.901E-02 1.257E+00 7.640E-01 4.796E-02 4.584.0 9.576E-01 2.102E-01 7.526E-02 1.243E+00 7.557E-01 4.787E-02 4.574.5 9.525E-01 2.057E-01 7.168E-02 1.230E+00 7.477E-01 4.779E-02 4.565.0 9.473E-01 2.013E-01 6.827E-02 1.217E+00 7.398E-01 4.771E-02 4.555.5 9.422E-01 1.970E-01 6.503E-02 1.204E+00 7.321E-01 4.763E-02 4.556.0 9.371E-01 1.928E-01 6.193E-02 1.192E+00 7.246E-01 4.755E-02 4.546.5 9.321E-01 1.887E-01 5.899E-02 1.180E+00 7.172E-01 4.747E-02 4.537.0 9.270E-01 1.846E-01 5.619E-02 1.168E+00 7.100E-01 4.740E-02 4.537.5 9.220E-01 1.807E-01 5.352E-02 1.156E+00 7.029E-01 4.732E-02 4.528.0 9.171E-01 1.768E-01 5.097E-02 1.145E+00 6.960E-01 4.725E-02 4.518.5 9.121E-01 1.730E-01 4.855E-02 1.134E+00 6.892E-01 4.718E-02 4.519.0 9.072E-01 1.693E-01 4.624E-02 1.123E+00 6.825E-01 4.711E-02 4.509.5 9.023E-01 1.657E-01 4.404E-02 1.112E+00 6.760E-01 4.704E-02 4.4910.0 8.974E-01 1.622E-01 4.195E-02 1.102E+00 6.696E-01 4.698E-02 4.4910.5 8.926E-01 1.587E-01 3.995E-02 1.091E+00 6.634E-01 4.691E-02 4.4811.0 8.878E-01 1.553E-01 3.805E-02 1.081E+00 6.572E-01 4.685E-02 4.4811.5 8.830E-01 1.520E-01 3.625E-02 1.071E+00 6.512E-01 4.679E-02 4.4712.0 8.782E-01 1.487E-01 3.452E-02 1.061E+00 6.453E-01 4.672E-02 4.4612.5 8.735E-01 1.455E-01 3.288E-02 1.052E+00 6.395E-01 4.666E-02 4.4613.0 8.687E-01 1.424E-01 3.132E-02 1.042E+00 6.337E-01 4.660E-02 4.4513.5 8.641E-01 1.394E-01 2.983E-02 1.033E+00 6.281E-01 4.655E-02 4.4514.0 8.594E-01 1.364E-01 2.841E-02 1.024E+00 6.226E-01 4.649E-02 4.4414.5 8.548E-01 1.334E-01 2.706E-02 1.015E+00 6.172E-01 4.643E-02 4.4415.0 8.501E-01 1.306E-01 2.577E-02 1.007E+00 6.119E-01 4.638E-02 4.4315.5 8.456E-01 1.278E-01 2.455E-02 9.979E-01 6.066E-01 4.632E-02 4.4316.0 8.410E-01 1.251E-01 2.338E-02 9.894E-01 6.015E-01 4.627E-02 4.4216.5 8.365E-01 1.224E-01 2.227E-02 9.811E-01 5.964E-01 4.621E-02 4.4217.0 8.319E-01 1.198E-01 2.121E-02 9.729E-01 5.915E-01 4.616E-02 4.4117.5 8.275E-01 1.172E-01 2.020E-02 9.648E-01 5.866E-01 4.611E-02 4.4118.0 8.230E-01 1.147E-01 1.924E-02 9.569E-01 5.817E-01 4.606E-02 4.40

t (hour)


Appendices

134

T=45oC u=0.5m/s

1 2 30.5 9.962E-01 2.462E-01 1.073E-01 1.350E+00 8.205E-01 4.909E-02 4.681.0 9.923E-01 2.424E-01 1.037E-01 1.338E+00 8.137E-01 4.902E-02 4.671.5 9.885E-01 2.387E-01 1.002E-01 1.327E+00 8.070E-01 4.894E-02 4.672.0 9.847E-01 2.351E-01 9.675E-02 1.317E+00 8.004E-01 4.887E-02 4.662.5 9.810E-01 2.315E-01 9.345E-02 1.306E+00 7.939E-01 4.880E-02 4.653.0 9.772E-01 2.280E-01 9.027E-02 1.295E+00 7.875E-01 4.873E-02 4.653.5 9.734E-01 2.245E-01 8.720E-02 1.285E+00 7.813E-01 4.866E-02 4.644.0 9.697E-01 2.211E-01 8.424E-02 1.275E+00 7.751E-01 4.859E-02 4.634.5 9.660E-01 2.177E-01 8.137E-02 1.265E+00 7.690E-01 4.852E-02 4.635.0 9.623E-01 2.144E-01 7.860E-02 1.255E+00 7.631E-01 4.846E-02 4.625.5 9.586E-01 2.111E-01 7.593E-02 1.246E+00 7.572E-01 4.839E-02 4.626.0 9.549E-01 2.079E-01 7.335E-02 1.236E+00 7.515E-01 4.833E-02 4.616.5 9.512E-01 2.047E-01 7.085E-02 1.227E+00 7.458E-01 4.827E-02 4.607.0 9.476E-01 2.016E-01 6.844E-02 1.218E+00 7.402E-01 4.820E-02 4.607.5 9.439E-01 1.985E-01 6.611E-02 1.209E+00 7.347E-01 4.814E-02 4.598.0 9.403E-01 1.955E-01 6.386E-02 1.200E+00 7.293E-01 4.808E-02 4.598.5 9.367E-01 1.925E-01 6.169E-02 1.191E+00 7.240E-01 4.802E-02 4.589.0 9.331E-01 1.895E-01 5.959E-02 1.182E+00 7.187E-01 4.797E-02 4.589.5 9.295E-01 1.866E-01 5.756E-02 1.174E+00 7.135E-01 4.791E-02 4.5710.0 9.260E-01 1.838E-01 5.561E-02 1.165E+00 7.085E-01 4.785E-02 4.5710.5 9.224E-01 1.810E-01 5.371E-02 1.157E+00 7.034E-01 4.780E-02 4.5611.0 9.189E-01 1.782E-01 5.189E-02 1.149E+00 6.985E-01 4.774E-02 4.5611.5 9.153E-01 1.755E-01 5.012E-02 1.141E+00 6.936E-01 4.769E-02 4.5512.0 9.118E-01 1.728E-01 4.842E-02 1.133E+00 6.888E-01 4.763E-02 4.5512.5 9.083E-01 1.702E-01 4.677E-02 1.125E+00 6.841E-01 4.758E-02 4.5413.0 9.048E-01 1.676E-01 4.518E-02 1.118E+00 6.794E-01 4.753E-02 4.5413.5 9.014E-01 1.650E-01 4.364E-02 1.110E+00 6.748E-01 4.748E-02 4.5314.0 8.979E-01 1.625E-01 4.216E-02 1.103E+00 6.703E-01 4.743E-02 4.5314.5 8.945E-01 1.600E-01 4.072E-02 1.095E+00 6.658E-01 4.738E-02 4.5215.0 8.910E-01 1.576E-01 3.934E-02 1.088E+00 6.614E-01 4.733E-02 4.5215.5 8.876E-01 1.552E-01 3.800E-02 1.081E+00 6.570E-01 4.728E-02 4.5116.0 8.842E-01 1.528E-01 3.671E-02 1.074E+00 6.527E-01 4.723E-02 4.5116.5 8.808E-01 1.505E-01 3.546E-02 1.067E+00 6.485E-01 4.719E-02 4.5117.0 8.774E-01 1.482E-01 3.425E-02 1.060E+00 6.443E-01 4.714E-02 4.5017.5 8.741E-01 1.459E-01 3.309E-02 1.053E+00 6.402E-01 4.709E-02 4.50

t (hour)


Appendices

135

1 2 318.0 8.707E-01 1.437E-01 3.196E-02 1.046E+00 6.361E-01 4.705E-02 4.4918.5 8.674E-01 1.415E-01 3.087E-02 1.040E+00 6.321E-01 4.701E-02 4.4919.0 8.640E-01 1.393E-01 2.982E-02 1.033E+00 6.281E-01 4.696E-02 4.4919.5 8.607E-01 1.372E-01 2.881E-02 1.027E+00 6.242E-01 4.692E-02 4.4820.0 8.574E-01 1.351E-01 2.783E-02 1.020E+00 6.203E-01 4.687E-02 4.4820.5 8.541E-01 1.331E-01 2.688E-02 1.014E+00 6.165E-01 4.683E-02 4.4721.0 8.508E-01 1.310E-01 2.597E-02 1.008E+00 6.127E-01 4.679E-02 4.4721.5 8.476E-01 1.290E-01 2.508E-02 1.002E+00 6.089E-01 4.675E-02 4.4722.0 8.443E-01 1.271E-01 2.423E-02 9.956E-01 6.053E-01 4.671E-02 4.4622.5 8.411E-01 1.251E-01 2.341E-02 9.896E-01 6.016E-01 4.667E-02 4.4623.0 8.379E-01 1.232E-01 2.261E-02 9.837E-01 5.980E-01 4.663E-02 4.4623.5 8.346E-01 1.213E-01 2.184E-02 9.778E-01 5.944E-01 4.659E-02 4.4524.0 8.314E-01 1.195E-01 2.110E-02 9.720E-01 5.909E-01 4.655E-02 4.4524.5 8.282E-01 1.176E-01 2.038E-02 9.663E-01 5.874E-01 4.651E-02 4.4425.0 8.251E-01 1.158E-01 1.969E-02 9.606E-01 5.840E-01 4.647E-02 4.4425.5 8.219E-01 1.141E-01 1.902E-02 9.550E-01 5.806E-01 4.643E-02 4.4426.0 8.187E-01 1.123E-01 1.837E-02 9.495E-01 5.772E-01 4.640E-02 4.4326.5 8.156E-01 1.106E-01 1.774E-02 9.440E-01 5.739E-01 4.636E-02 4.4327.0 8.125E-01 1.089E-01 1.714E-02 9.385E-01 5.706E-01 4.632E-02 4.4327.5 8.094E-01 1.073E-01 1.656E-02 9.332E-01 5.673E-01 4.629E-02 4.4228.0 8.062E-01 1.056E-01 1.599E-02 9.279E-01 5.641E-01 4.625E-02 4.4228.5 8.032E-01 1.040E-01 1.545E-02 9.226E-01 5.609E-01 4.622E-02 4.4229.0 8.001E-01 1.024E-01 1.492E-02 9.174E-01 5.577E-01 4.618E-02 4.4129.5 7.970E-01 1.009E-01 1.442E-02 9.123E-01 5.546E-01 4.615E-02 4.4130.0 7.939E-01 9.933E-02 1.393E-02 9.072E-01 5.515E-01 4.611E-02 4.4130.5 7.909E-01 9.781E-02 1.345E-02 9.022E-01 5.484E-01 4.608E-02 4.4031.0 7.879E-01 9.632E-02 1.299E-02 8.972E-01 5.454E-01 4.604E-02 4.4031.5 7.848E-01 9.485E-02 1.255E-02 8.922E-01 5.424E-01 4.601E-02 4.4032.0 7.818E-01 9.340E-02 1.213E-02 8.873E-01 5.394E-01 4.598E-02 4.4032.5 7.788E-01 9.198E-02 1.171E-02 8.825E-01 5.365E-01 4.595E-02 4.3933.0 7.758E-01 9.057E-02 1.131E-02 8.777E-01 5.336E-01 4.591E-02 4.3933.5 7.728E-01 8.919E-02 1.093E-02 8.730E-01 5.307E-01 4.588E-02 4.3934.0 7.699E-01 8.783E-02 1.056E-02 8.683E-01 5.278E-01 4.585E-02 4.38

t (hour)


Appendices

136

T=35oC u=0.5m/s



t (hour)


Appendices

137


t (hour)


Appendices

138


t (hour)


Appendices

139


t (hour)


Appendices

140

T=55oC u=1.0m/s


10.0 8.474E-01 1.289E-01 2.502E-02 1.001E+00 6.087E-01 4.634E-02 4.4310.5 8.404E-01 1.247E-01 2.323E-02 9.883E-01 6.008E-01 4.626E-02 4.4211.0 8.334E-01 1.206E-01 2.156E-02 9.756E-01 5.931E-01 4.618E-02 4.4111.5 8.266E-01 1.167E-01 2.001E-02 9.633E-01 5.856E-01 4.610E-02 4.4112.0 8.197E-01 1.129E-01 1.857E-02 9.512E-01 5.783E-01 4.603E-02 4.4012.5 8.130E-01 1.092E-01 1.724E-02 9.394E-01 5.711E-01 4.595E-02 4.3913.0 8.063E-01 1.057E-01 1.600E-02 9.279E-01 5.641E-01 4.588E-02 4.3913.5 7.996E-01 1.022E-01 1.485E-02 9.167E-01 5.573E-01 4.581E-02 4.3814.0 7.930E-01 9.888E-02 1.378E-02 9.057E-01 5.506E-01 4.574E-02 4.3714.5 7.865E-01 9.566E-02 1.279E-02 8.949E-01 5.441E-01 4.567E-02 4.37

t (hour)


Appendices

141

T=45oC u=1.0m/s


10.0 8.536E-01 1.327E-01 2.674E-02 1.013E+00 6.159E-01 4.608E-02 4.4010.5 8.469E-01 1.286E-01 2.490E-02 1.000E+00 6.082E-01 4.600E-02 4.4011.0 8.402E-01 1.246E-01 2.319E-02 9.880E-01 6.006E-01 4.593E-02 4.3911.5 8.336E-01 1.207E-01 2.159E-02 9.759E-01 5.933E-01 4.585E-02 4.3812.0 8.270E-01 1.169E-01 2.011E-02 9.641E-01 5.861E-01 4.578E-02 4.3812.5 8.205E-01 1.133E-01 1.873E-02 9.525E-01 5.791E-01 4.571E-02 4.3713.0 8.140E-01 1.098E-01 1.744E-02 9.412E-01 5.722E-01 4.565E-02 4.3713.5 8.076E-01 1.064E-01 1.624E-02 9.302E-01 5.655E-01 4.558E-02 4.3614.0 8.012E-01 1.030E-01 1.512E-02 9.194E-01 5.589E-01 4.552E-02 4.3514.5 7.949E-01 9.983E-02 1.408E-02 9.088E-01 5.525E-01 4.545E-02 4.3515.0 7.887E-01 9.672E-02 1.312E-02 8.985E-01 5.462E-01 4.539E-02 4.3415.5 7.824E-01 9.371E-02 1.221E-02 8.884E-01 5.401E-01 4.533E-02 4.3416.0 7.763E-01 9.079E-02 1.137E-02 8.784E-01 5.340E-01 4.527E-02 4.3316.5 7.702E-01 8.796E-02 1.059E-02 8.687E-01 5.281E-01 4.521E-02 4.3317.0 7.641E-01 8.522E-02 9.864E-03 8.592E-01 5.223E-01 4.515E-02 4.3217.5 7.581E-01 8.256E-02 9.186E-03 8.498E-01 5.166E-01 4.510E-02 4.32

t (hour)


Appendices

142

1 2 318.0 7.521E-01 7.999E-02 8.555E-03 8.406E-01 5.110E-01 4.504E-02 4.3118.5 7.462E-01 7.750E-02 7.967E-03 8.316E-01 5.056E-01 4.499E-02 4.3119.0 7.403E-01 7.508E-02 7.419E-03 8.228E-01 5.002E-01 4.494E-02 4.3019.5 7.344E-01 7.274E-02 6.909E-03 8.141E-01 4.949E-01 4.488E-02 4.3020.0 7.287E-01 7.048E-02 6.434E-03 8.056E-01 4.897E-01 4.483E-02 4.2920.5 7.229E-01 6.828E-02 5.992E-03 7.972E-01 4.846E-01 4.478E-02 4.2921.0 7.172E-01 6.615E-02 5.580E-03 7.889E-01 4.796E-01 4.473E-02 4.2821.5 7.116E-01 6.409E-02 5.196E-03 7.808E-01 4.747E-01 4.468E-02 4.2822.0 7.060E-01 6.209E-02 4.839E-03 7.729E-01 4.699E-01 4.464E-02 4.27

t (hour)


Appendices

143

T=35oC u=1.0m/s


t (hour)


Appendices

144

1 2 318.5 8.992E-01 1.634E-01 4.271E-02 1.105E+00 6.720E-01 5.313E-02 5.0519.0 8.966E-01 1.616E-01 4.162E-02 1.100E+00 6.686E-01 5.307E-02 5.0419.5 8.941E-01 1.597E-01 4.056E-02 1.094E+00 6.653E-01 5.300E-02 5.0320.0 8.915E-01 1.579E-01 3.952E-02 1.089E+00 6.620E-01 5.294E-02 5.0320.5 8.889E-01 1.561E-01 3.851E-02 1.084E+00 6.587E-01 5.288E-02 5.0221.0 8.864E-01 1.543E-01 3.753E-02 1.078E+00 6.555E-01 5.281E-02 5.0221.5 8.838E-01 1.526E-01 3.657E-02 1.073E+00 6.523E-01 5.275E-02 5.0122.0 8.813E-01 1.508E-01 3.564E-02 1.068E+00 6.491E-01 5.269E-02 5.0122.5 8.788E-01 1.491E-01 3.473E-02 1.063E+00 6.460E-01 5.263E-02 5.0023.0 8.763E-01 1.474E-01 3.384E-02 1.058E+00 6.429E-01 5.257E-02 4.9923.5 8.738E-01 1.457E-01 3.298E-02 1.052E+00 6.398E-01 5.251E-02 4.9924.0 8.712E-01 1.440E-01 3.214E-02 1.047E+00 6.368E-01 5.245E-02 4.9824.5 8.688E-01 1.424E-01 3.132E-02 1.042E+00 6.337E-01 5.239E-02 4.9825.0 8.663E-01 1.408E-01 3.052E-02 1.038E+00 6.308E-01 5.233E-02 4.9725.5 8.638E-01 1.392E-01 2.974E-02 1.033E+00 6.278E-01 5.227E-02 4.9726.0 8.613E-01 1.376E-01 2.898E-02 1.028E+00 6.249E-01 5.221E-02 4.9626.5 8.588E-01 1.360E-01 2.824E-02 1.023E+00 6.220E-01 5.216E-02 4.9627.0 8.564E-01 1.345E-01 2.752E-02 1.018E+00 6.191E-01 5.210E-02 4.9527.5 8.539E-01 1.329E-01 2.682E-02 1.014E+00 6.162E-01 5.205E-02 4.9528.0 8.515E-01 1.314E-01 2.614E-02 1.009E+00 6.134E-01 5.199E-02 4.9428.5 8.490E-01 1.299E-01 2.547E-02 1.004E+00 6.106E-01 5.193E-02 4.9429.0 8.466E-01 1.284E-01 2.482E-02 9.998E-01 6.078E-01 5.188E-02 4.9329.5 8.442E-01 1.270E-01 2.419E-02 9.953E-01 6.051E-01 5.183E-02 4.9330.0 8.417E-01 1.255E-01 2.357E-02 9.908E-01 6.023E-01 5.177E-02 4.9230.5 8.393E-01 1.241E-01 2.297E-02 9.864E-01 5.996E-01 5.172E-02 4.9231.0 8.369E-01 1.227E-01 2.238E-02 9.820E-01 5.970E-01 5.167E-02 4.9131.5 8.345E-01 1.213E-01 2.181E-02 9.776E-01 5.943E-01 5.162E-02 4.9132.0 8.321E-01 1.199E-01 2.125E-02 9.732E-01 5.917E-01 5.156E-02 4.9032.5 8.297E-01 1.185E-01 2.071E-02 9.690E-01 5.890E-01 5.151E-02 4.9033.0 8.274E-01 1.171E-01 2.018E-02 9.647E-01 5.865E-01 5.146E-02 4.8933.5 8.250E-01 1.158E-01 1.967E-02 9.605E-01 5.839E-01 5.141E-02 4.8934.0 8.226E-01 1.145E-01 1.917E-02 9.563E-01 5.813E-01 5.136E-02 4.8934.5 8.203E-01 1.132E-01 1.868E-02 9.521E-01 5.788E-01 5.131E-02 4.8835.0 8.179E-01 1.119E-01 1.820E-02 9.480E-01 5.763E-01 5.126E-02 4.8835.5 8.156E-01 1.106E-01 1.774E-02 9.439E-01 5.738E-01 5.122E-02 4.8736.0 8.132E-01 1.093E-01 1.729E-02 9.399E-01 5.714E-01 5.117E-02 4.87

t (hour)


Appendices

145

1 2 336.5 8.109E-01 1.081E-01 1.684E-02 9.358E-01 5.689E-01 5.112E-02 4.8637.0 8.086E-01 1.069E-01 1.641E-02 9.318E-01 5.665E-01 5.107E-02 4.8637.5 8.063E-01 1.056E-01 1.600E-02 9.279E-01 5.641E-01 5.103E-02 4.8538.0 8.039E-01 1.044E-01 1.559E-02 9.240E-01 5.617E-01 5.098E-02 4.8538.5 8.016E-01 1.032E-01 1.519E-02 9.201E-01 5.593E-01 5.093E-02 4.8539.0 7.993E-01 1.021E-01 1.480E-02 9.162E-01 5.570E-01 5.089E-02 4.8439.5 7.970E-01 1.009E-01 1.442E-02 9.124E-01 5.547E-01 5.084E-02 4.8440.0 7.948E-01 9.974E-02 1.406E-02 9.086E-01 5.523E-01 5.080E-02 4.8340.5 7.925E-01 9.860E-02 1.370E-02 9.048E-01 5.500E-01 5.075E-02 4.8341.0 7.902E-01 9.748E-02 1.335E-02 9.010E-01 5.478E-01 5.071E-02 4.8341.5 7.879E-01 9.637E-02 1.301E-02 8.973E-01 5.455E-01 5.066E-02 4.8242.0 7.857E-01 9.526E-02 1.268E-02 8.936E-01 5.433E-01 5.062E-02 4.8242.5 7.834E-01 9.418E-02 1.235E-02 8.900E-01 5.410E-01 5.058E-02 4.8143.0 7.812E-01 9.310E-02 1.204E-02 8.863E-01 5.388E-01 5.053E-02 4.8143.5 7.789E-01 9.204E-02 1.173E-02 8.827E-01 5.366E-01 5.049E-02 4.8144.0 7.767E-01 9.099E-02 1.143E-02 8.791E-01 5.344E-01 5.045E-02 4.8044.5 7.745E-01 8.995E-02 1.114E-02 8.756E-01 5.323E-01 5.040E-02 4.8045.0 7.723E-01 8.892E-02 1.086E-02 8.720E-01 5.301E-01 5.036E-02 4.7945.5 7.701E-01 8.791E-02 1.058E-02 8.685E-01 5.280E-01 5.032E-02 4.7946.0 7.678E-01 8.690E-02 1.031E-02 8.651E-01 5.259E-01 5.028E-02 4.7946.5 7.656E-01 8.591E-02 1.005E-02 8.616E-01 5.238E-01 5.024E-02 4.7847.0 7.634E-01 8.493E-02 9.789E-03 8.582E-01 5.217E-01 5.020E-02 4.7847.5 7.613E-01 8.396E-02 9.540E-03 8.548E-01 5.196E-01 5.016E-02 4.7848.0 7.591E-01 8.300E-02 9.296E-03 8.514E-01 5.176E-01 5.012E-02 4.7748.5 7.569E-01 8.205E-02 9.059E-03 8.480E-01 5.155E-01 5.008E-02 4.7749.0 7.547E-01 8.111E-02 8.828E-03 8.447E-01 5.135E-01 5.004E-02 4.7749.5 7.526E-01 8.019E-02 8.603E-03 8.414E-01 5.115E-01 5.000E-02 4.7650.0 7.504E-01 7.927E-02 8.383E-03 8.381E-01 5.095E-01 4.996E-02 4.7650.5 7.483E-01 7.837E-02 8.169E-03 8.348E-01 5.075E-01 4.992E-02 4.75

t (hour)


Appendices

146

APPENDIX 7A: MOISTURE PROFILE OF A PIPER NIGRUM L. BERRY

(Mi, j+1 ,Mn, j+1, Ms, j+1)

The following shows calculation done to compute the local moisture contentMi, j+1 , Mn, j+1, Ms, j+1 in a PiperNigrum L. berry:

T=55oC u=0.5m/s

j

t (hours)

1 2 3 4

0.0 2.077E+00 2.077E+00 2.077E+00 2.077E+00 1.154E-010.5 2.077E+00 2.077E+00 2.077E+00 1.046E+00 8.199E-021.0 2.077E+00 2.077E+00 1.767E+00 7.117E-01 7.115E-021.5 2.077E+00 1.956E+00 1.501E+00 5.514E-01 6.596E-022.0 1.976E+00 1.799E+00 1.291E+00 4.550E-01 6.283E-022.5 1.828E+00 1.630E+00 1.124E+00 3.887E-01 6.068E-023.0 1.662E+00 1.466E+00 9.875E-01 3.393E-01 5.908E-023.5 1.498E+00 1.312E+00 8.723E-01 3.004E-01 5.782E-024.0 1.342E+00 1.172E+00 7.737E-01 2.685E-01 5.678E-024.5 1.200E+00 1.045E+00 6.882E-01 2.417E-01 5.591E-025.0 1.070E+00 9.315E-01 6.134E-01 2.187E-01 5.517E-025.5 9.542E-01 8.306E-01 5.478E-01 1.988E-01 5.452E-026.0 8.508E-01 7.409E-01 4.900E-01 1.813E-01 5.395E-026.5 7.589E-01 6.614E-01 4.390E-01 1.660E-01 5.346E-027.0 6.774E-01 5.909E-01 3.940E-01 1.525E-01 5.302E-027.5 6.051E-01 5.285E-01 3.543E-01 1.406E-01 5.263E-028.0 5.411E-01 4.733E-01 3.191E-01 1.301E-01 5.229E-028.5 4.844E-01 4.245E-01 2.880E-01 1.208E-01 5.199E-029.0 4.343E-01 3.812E-01 2.605E-01 1.126E-01 5.173E-029.5 3.899E-01 3.430E-01 2.362E-01 1.053E-01 5.149E-02

10.0 3.507E-01 3.091E-01 2.146E-01 9.891E-02 5.128E-0210.5 3.159E-01 2.792E-01 1.956E-01 9.323E-02 5.110E-0211.0 2.852E-01 2.527E-01 1.788E-01 8.821E-02 5.093E-0211.5 2.581E-01 2.293E-01 1.639E-01 8.376E-02 5.079E-0212.0 2.340E-01 2.086E-01 1.507E-01 7.983E-02 5.066E-0212.5 2.127E-01 1.902E-01 1.390E-01 7.635E-02 5.055E-0213.0 1.939E-01 1.740E-01 1.287E-01 7.327E-02 5.045E-0213.5 1.773E-01 1.597E-01 1.196E-01 7.055E-02 5.036E-0214.0 1.626E-01 1.470E-01 1.115E-01 6.815E-02 5.028E-0214.5 1.495E-01 1.358E-01 1.044E-01 6.602E-02 5.022E-0215.0 1.380E-01 1.258E-01 9.809E-02 6.413E-02 5.015E-0215.5 1.278E-01 1.170E-01 9.251E-02 6.246E-02 5.010E-0216.0 1.188E-01 1.093E-01 8.757E-02 6.099E-02 5.005E-0216.5 1.108E-01 1.024E-01 8.320E-02 5.969E-02 5.001E-0217.0 1.038E-01 9.632E-02 7.933E-02 5.853E-02 4.997E-0217.5 9.754E-02 9.094E-02 7.591E-02 5.751E-02 4.994E-0218.0 9.202E-02 8.618E-02 7.288E-02 5.661E-02 4.991E-02

is

Appendices

147

T=45oC u=0.5m/s

j

t (hours)

1 2 3 4

0.0 1.986E+00 1.986E+00 1.986E+00 1.986E+00 1.125E-010.5 1.986E+00 1.986E+00 1.986E+00 1.510E+00 1.055E-011.0 1.986E+00 1.986E+00 1.916E+00 1.191E+00 9.735E-021.5 1.986E+00 1.973E+00 1.816E+00 9.709E-01 9.175E-022.0 1.981E+00 1.944E+00 1.706E+00 8.155E-01 8.778E-022.5 1.966E+00 1.902E+00 1.595E+00 7.022E-01 8.489E-023.0 1.940E+00 1.849E+00 1.490E+00 6.173E-01 8.273E-023.5 1.903E+00 1.789E+00 1.391E+00 5.518E-01 8.106E-024.0 1.857E+00 1.723E+00 1.301E+00 4.999E-01 7.974E-024.5 1.802E+00 1.654E+00 1.218E+00 4.578E-01 7.866E-025.0 1.742E+00 1.583E+00 1.143E+00 4.229E-01 7.777E-025.5 1.678E+00 1.513E+00 1.073E+00 3.933E-01 7.702E-026.0 1.611E+00 1.443E+00 1.010E+00 3.679E-01 7.637E-026.5 1.543E+00 1.375E+00 9.513E-01 3.456E-01 7.580E-027.0 1.475E+00 1.308E+00 8.972E-01 3.260E-01 7.530E-027.5 1.407E+00 1.244E+00 8.472E-01 3.084E-01 7.485E-028.0 1.341E+00 1.182E+00 8.007E-01 2.926E-01 7.445E-028.5 1.277E+00 1.123E+00 7.575E-01 2.782E-01 7.408E-029.0 1.214E+00 1.066E+00 7.172E-01 2.650E-01 7.374E-029.5 1.154E+00 1.012E+00 6.795E-01 2.530E-01 7.344E-02

10.0 1.097E+00 9.608E-01 6.442E-01 2.418E-01 7.315E-0210.5 1.042E+00 9.120E-01 6.112E-01 2.315E-01 7.289E-0211.0 9.891E-01 8.656E-01 5.802E-01 2.218E-01 7.264E-0211.5 9.390E-01 8.216E-01 5.510E-01 2.129E-01 7.241E-0212.0 8.914E-01 7.799E-01 5.236E-01 2.045E-01 7.220E-0212.5 8.462E-01 7.405E-01 4.978E-01 1.967E-01 7.200E-0213.0 8.034E-01 7.031E-01 4.735E-01 1.893E-01 7.181E-0213.5 7.627E-01 6.678E-01 4.507E-01 1.824E-01 7.164E-0214.0 7.243E-01 6.345E-01 4.291E-01 1.759E-01 7.147E-0214.5 6.879E-01 6.029E-01 4.088E-01 1.698E-01 7.132E-0215.0 6.534E-01 5.731E-01 3.897E-01 1.641E-01 7.117E-0215.5 6.209E-01 5.449E-01 3.716E-01 1.587E-01 7.103E-0216.0 5.901E-01 5.183E-01 3.546E-01 1.536E-01 7.090E-0216.5 5.610E-01 4.931E-01 3.386E-01 1.489E-01 7.078E-0217.0 5.335E-01 4.694E-01 3.234E-01 1.443E-01 7.066E-02

is

Appendices

148

j

t (hours)

1 2 3 4

17.5 5.075E-01 4.470E-01 3.091E-01 1.401E-01 7.056E-0218.0 4.830E-01 4.258E-01 2.956E-01 1.361E-01 7.045E-0218.5 4.598E-01 4.058E-01 2.829E-01 1.323E-01 7.036E-0219.0 4.379E-01 3.869E-01 2.709E-01 1.287E-01 7.027E-0219.5 4.172E-01 3.691E-01 2.595E-01 1.254E-01 7.018E-0220.0 3.977E-01 3.523E-01 2.488E-01 1.222E-01 7.010E-0220.5 3.793E-01 3.364E-01 2.387E-01 1.192E-01 7.002E-0221.0 3.619E-01 3.214E-01 2.292E-01 1.163E-01 6.995E-0221.5 3.455E-01 3.073E-01 2.202E-01 1.137E-01 6.988E-0222.0 3.300E-01 2.939E-01 2.117E-01 1.112E-01 6.982E-0222.5 3.154E-01 2.813E-01 2.037E-01 1.088E-01 6.976E-0223.0 3.015E-01 2.694E-01 1.961E-01 1.065E-01 6.970E-0223.5 2.885E-01 2.581E-01 1.890E-01 1.044E-01 6.965E-0224.0 2.762E-01 2.475E-01 1.823E-01 1.024E-01 6.960E-0224.5 2.646E-01 2.375E-01 1.759E-01 1.005E-01 6.955E-0225.0 2.536E-01 2.280E-01 1.699E-01 9.874E-02 6.950E-0225.5 2.432E-01 2.191E-01 1.642E-01 9.706E-02 6.946E-0226.0 2.335E-01 2.107E-01 1.589E-01 9.547E-02 6.942E-0226.5 2.242E-01 2.027E-01 1.538E-01 9.397E-02 6.938E-0227.0 2.155E-01 1.952E-01 1.491E-01 9.256E-02 6.934E-0227.5 2.073E-01 1.881E-01 1.446E-01 9.122E-02 6.931E-0228.0 1.995E-01 1.814E-01 1.403E-01 8.996E-02 6.928E-0228.5 1.922E-01 1.751E-01 1.363E-01 8.877E-02 6.925E-0229.0 1.853E-01 1.692E-01 1.325E-01 8.765E-02 6.922E-0229.5 1.787E-01 1.635E-01 1.289E-01 8.659E-02 6.919E-0230.0 1.726E-01 1.582E-01 1.256E-01 8.559E-02 6.917E-0230.5 1.668E-01 1.532E-01 1.224E-01 8.465E-02 6.914E-0231.0 1.613E-01 1.485E-01 1.194E-01 8.375E-02 6.912E-0231.5 1.561E-01 1.440E-01 1.165E-01 8.291E-02 6.910E-0232.0 1.512E-01 1.398E-01 1.139E-01 8.212E-02 6.908E-0232.5 1.466E-01 1.358E-01 1.113E-01 8.137E-02 6.906E-0233.0 1.422E-01 1.320E-01 1.089E-01 8.066E-02 6.904E-0233.5 1.381E-01 1.285E-01 1.067E-01 7.999E-02 6.902E-0234.0 1.342E-01 1.251E-01 1.046E-01 7.936E-02 6.901E-02

is

Appendices

149

T=35oC u=0.5m/s

j

t (hours)

1 2 3 4

0.0 1.986E+00 1.986E+00 1.986E+00 1.986E+00 1.125E-010.5 1.986E+00 1.986E+00 1.986E+00 1.762E+00 1.321E-011.0 1.986E+00 1.986E+00 1.970E+00 1.573E+00 1.284E-011.5 1.986E+00 1.985E+00 1.943E+00 1.414E+00 1.252E-012.0 1.986E+00 1.981E+00 1.908E+00 1.278E+00 1.225E-012.5 1.985E+00 1.975E+00 1.867E+00 1.162E+00 1.202E-013.0 1.983E+00 1.965E+00 1.823E+00 1.063E+00 1.182E-013.5 1.979E+00 1.953E+00 1.775E+00 9.781E-01 1.165E-014.0 1.974E+00 1.938E+00 1.727E+00 9.045E-01 1.150E-014.5 1.967E+00 1.921E+00 1.678E+00 8.406E-01 1.138E-015.0 1.958E+00 1.901E+00 1.629E+00 7.849E-01 1.127E-015.5 1.947E+00 1.878E+00 1.581E+00 7.360E-01 1.117E-016.0 1.934E+00 1.854E+00 1.534E+00 6.930E-01 1.108E-016.5 1.919E+00 1.829E+00 1.488E+00 6.549E-01 1.101E-017.0 1.901E+00 1.802E+00 1.443E+00 6.210E-01 1.094E-017.5 1.882E+00 1.773E+00 1.400E+00 5.907E-01 1.088E-018.0 1.861E+00 1.744E+00 1.358E+00 5.636E-01 1.083E-018.5 1.839E+00 1.714E+00 1.318E+00 5.391E-01 1.078E-019.0 1.814E+00 1.683E+00 1.279E+00 5.169E-01 1.073E-019.5 1.789E+00 1.652E+00 1.242E+00 4.966E-01 1.069E-0110.0 1.763E+00 1.620E+00 1.206E+00 4.782E-01 1.066E-0110.5 1.735E+00 1.588E+00 1.172E+00 4.612E-01 1.062E-0111.0 1.707E+00 1.557E+00 1.138E+00 4.456E-01 1.059E-0111.5 1.678E+00 1.525E+00 1.106E+00 4.312E-01 1.056E-0112.0 1.648E+00 1.493E+00 1.076E+00 4.178E-01 1.053E-0112.5 1.619E+00 1.462E+00 1.046E+00 4.053E-01 1.051E-0113.0 1.588E+00 1.430E+00 1.018E+00 3.936E-01 1.049E-0113.5 1.558E+00 1.399E+00 9.903E-01 3.827E-01 1.047E-0114.0 1.527E+00 1.369E+00 9.640E-01 3.724E-01 1.044E-0114.5 1.497E+00 1.338E+00 9.385E-01 3.628E-01 1.043E-0115.0 1.466E+00 1.309E+00 9.140E-01 3.537E-01 1.041E-0115.5 1.436E+00 1.279E+00 8.903E-01 3.450E-01 1.039E-0116.0 1.406E+00 1.250E+00 8.675E-01 3.368E-01 1.037E-0116.5 1.376E+00 1.222E+00 8.454E-01 3.291E-01 1.036E-0117.0 1.346E+00 1.194E+00 8.241E-01 3.217E-01 1.034E-0117.5 1.317E+00 1.167E+00 8.035E-01 3.146E-01 1.033E-01

is

Appendices

150

j

t (hours)

1 2 3 4

18.0 1.288E+00 1.140E+00 7.836E-01 3.078E-01 1.032E-0118.5 1.259E+00 1.113E+00 7.643E-01 3.014E-01 1.030E-0119.0 1.231E+00 1.088E+00 7.457E-01 2.952E-01 1.029E-0119.5 1.204E+00 1.062E+00 7.276E-01 2.893E-01 1.028E-0120.0 1.176E+00 1.038E+00 7.101E-01 2.836E-01 1.027E-0120.5 1.150E+00 1.014E+00 6.931E-01 2.781E-01 1.026E-0121.0 1.123E+00 9.900E-01 6.767E-01 2.728E-01 1.025E-0121.5 1.098E+00 9.670E-01 6.608E-01 2.678E-01 1.024E-0122.0 1.073E+00 9.445E-01 6.453E-01 2.629E-01 1.023E-0122.5 1.048E+00 9.226E-01 6.303E-01 2.582E-01 1.022E-0123.0 1.024E+00 9.011E-01 6.158E-01 2.536E-01 1.021E-0123.5 1.000E+00 8.802E-01 6.016E-01 2.492E-01 1.020E-0124.0 9.770E-01 8.598E-01 5.879E-01 2.450E-01 1.019E-0124.5 9.544E-01 8.398E-01 5.746E-01 2.409E-01 1.018E-0125.0 9.323E-01 8.204E-01 5.617E-01 2.369E-01 1.017E-0125.5 9.108E-01 8.015E-01 5.491E-01 2.330E-01 1.017E-0126.0 8.897E-01 7.830E-01 5.369E-01 2.293E-01 1.016E-0126.5 8.692E-01 7.650E-01 5.251E-01 2.257E-01 1.015E-0127.0 8.491E-01 7.474E-01 5.136E-01 2.222E-01 1.015E-0127.5 8.295E-01 7.303E-01 5.024E-01 2.188E-01 1.014E-0128.0 8.104E-01 7.137E-01 4.915E-01 2.155E-01 1.013E-0128.5 7.918E-01 6.974E-01 4.809E-01 2.123E-01 1.013E-0129.0 7.736E-01 6.816E-01 4.706E-01 2.092E-01 1.012E-0129.5 7.559E-01 6.662E-01 4.606E-01 2.062E-01 1.011E-0130.0 7.386E-01 6.511E-01 4.509E-01 2.033E-01 1.011E-0130.5 7.217E-01 6.365E-01 4.414E-01 2.004E-01 1.010E-0131.0 7.053E-01 6.222E-01 4.322E-01 1.977E-01 1.010E-0131.5 6.893E-01 6.084E-01 4.233E-01 1.950E-01 1.009E-0132.0 6.737E-01 5.948E-01 4.146E-01 1.924E-01 1.009E-0132.5 6.585E-01 5.817E-01 4.061E-01 1.899E-01 1.008E-0133.0 6.437E-01 5.689E-01 3.979E-01 1.874E-01 1.008E-0133.5 6.293E-01 5.564E-01 3.899E-01 1.850E-01 1.007E-0134.0 6.152E-01 5.442E-01 3.821E-01 1.827E-01 1.007E-0134.5 6.016E-01 5.324E-01 3.745E-01 1.805E-01 1.006E-0135.0 5.882E-01 5.208E-01 3.671E-01 1.783E-01 1.006E-0135.5 5.753E-01 5.096E-01 3.600E-01 1.761E-01 1.005E-01

si

Appendices

151

j

t (hours)

1 2 3 4

36.0 5.626E-01 4.987E-01 3.530E-01 1.741E-01 1.005E-0136.5 5.503E-01 4.881E-01 3.462E-01 1.721E-01 1.005E-0137.0 5.383E-01 4.777E-01 3.396E-01 1.701E-01 1.004E-0137.5 5.266E-01 4.676E-01 3.331E-01 1.682E-01 1.004E-0138.0 5.153E-01 4.578E-01 3.269E-01 1.663E-01 1.003E-0138.5 5.042E-01 4.483E-01 3.208E-01 1.645E-01 1.003E-0139.0 4.934E-01 4.389E-01 3.149E-01 1.628E-01 1.003E-0139.5 4.829E-01 4.299E-01 3.091E-01 1.611E-01 1.002E-0140.0 4.727E-01 4.211E-01 3.035E-01 1.594E-01 1.002E-0140.5 4.628E-01 4.125E-01 2.980E-01 1.578E-01 1.002E-0141.0 4.531E-01 4.041E-01 2.927E-01 1.562E-01 1.001E-0141.5 4.436E-01 3.960E-01 2.875E-01 1.547E-01 1.001E-0142.0 4.345E-01 3.881E-01 2.825E-01 1.532E-01 1.001E-0142.5 4.255E-01 3.804E-01 2.776E-01 1.517E-01 1.001E-0143.0 4.168E-01 3.729E-01 2.728E-01 1.503E-01 1.000E-0143.5 4.084E-01 3.656E-01 2.682E-01 1.490E-01 1.000E-0144.0 4.001E-01 3.585E-01 2.637E-01 1.476E-01 9.997E-0244.5 3.921E-01 3.516E-01 2.593E-01 1.463E-01 9.994E-0245.0 3.843E-01 3.448E-01 2.550E-01 1.451E-01 9.992E-0245.5 3.767E-01 3.383E-01 2.508E-01 1.438E-01 9.989E-0246.0 3.693E-01 3.319E-01 2.468E-01 1.426E-01 9.987E-0246.5 3.621E-01 3.257E-01 2.428E-01 1.415E-01 9.985E-0247.0 3.551E-01 3.196E-01 2.390E-01 1.403E-01 9.982E-0247.5 3.482E-01 3.138E-01 2.353E-01 1.392E-01 9.980E-0248.0 3.416E-01 3.080E-01 2.316E-01 1.382E-01 9.978E-0248.5 3.351E-01 3.024E-01 2.281E-01 1.371E-01 9.976E-0249.0 3.288E-01 2.970E-01 2.246E-01 1.361E-01 9.974E-0249.5 3.227E-01 2.917E-01 2.213E-01 1.351E-01 9.972E-0250.0 3.167E-01 2.866E-01 2.180E-01 1.341E-01 9.970E-0250.5 3.109E-01 2.816E-01 2.149E-01 1.332E-01 9.968E-0251.0 3.053E-01 2.767E-01 2.118E-01 1.323E-01 9.966E-0251.5 2.998E-01 2.720E-01 2.088E-01 1.314E-01 9.965E-0252.0 2.944E-01 2.674E-01 2.058E-01 1.305E-01 9.963E-0252.5 2.892E-01 2.629E-01 2.030E-01 1.297E-01 9.961E-0253.0 2.841E-01 2.585E-01 2.002E-01 1.289E-01 9.960E-0253.5 2.792E-01 2.543E-01 1.975E-01 1.281E-01 9.958E-02

is

Appendices

152

j

t (hours)

1 2 3 4

54.0 2.744E-01 2.501E-01 1.949E-01 1.273E-01 9.957E-0254.5 2.697E-01 2.461E-01 1.923E-01 1.265E-01 9.955E-0255.0 2.652E-01 2.422E-01 1.898E-01 1.258E-01 9.954E-0255.5 2.607E-01 2.383E-01 1.874E-01 1.251E-01 9.952E-0256.0 2.564E-01 2.346E-01 1.850E-01 1.244E-01 9.951E-0256.5 2.522E-01 2.310E-01 1.827E-01 1.237E-01 9.949E-0257.0 2.481E-01 2.275E-01 1.805E-01 1.231E-01 9.948E-0257.5 2.442E-01 2.241E-01 1.783E-01 1.224E-01 9.947E-0258.0 2.403E-01 2.207E-01 1.762E-01 1.218E-01 9.946E-0258.5 2.365E-01 2.175E-01 1.742E-01 1.212E-01 9.944E-0259.0 2.328E-01 2.143E-01 1.722E-01 1.206E-01 9.943E-0259.5 2.293E-01 2.112E-01 1.702E-01 1.200E-01 9.942E-0260.0 2.258E-01 2.082E-01 1.683E-01 1.195E-01 9.941E-0260.5 2.224E-01 2.053E-01 1.665E-01 1.189E-01 9.940E-0261.0 2.191E-01 2.025E-01 1.647E-01 1.184E-01 9.939E-0261.5 2.159E-01 1.997E-01 1.629E-01 1.179E-01 9.938E-0262.0 2.128E-01 1.970E-01 1.612E-01 1.174E-01 9.937E-0262.5 2.098E-01 1.944E-01 1.595E-01 1.169E-01 9.936E-0263.0 2.068E-01 1.919E-01 1.579E-01 1.164E-01 9.935E-0263.5 2.039E-01 1.894E-01 1.564E-01 1.159E-01 9.934E-0264.0 2.011E-01 1.870E-01 1.548E-01 1.155E-01 9.933E-0264.5 1.984E-01 1.846E-01 1.533E-01 1.150E-01 9.932E-0265.0 1.958E-01 1.824E-01 1.519E-01 1.146E-01 9.931E-0265.5 1.932E-01 1.801E-01 1.505E-01 1.142E-01 9.930E-0266.0 1.907E-01 1.780E-01 1.491E-01 1.138E-01 9.930E-0266.5 1.882E-01 1.759E-01 1.478E-01 1.134E-01 9.929E-0267.0 1.858E-01 1.738E-01 1.465E-01 1.130E-01 9.928E-0267.5 1.835E-01 1.718E-01 1.452E-01 1.126E-01 9.927E-0268.0 1.813E-01 1.699E-01 1.440E-01 1.123E-01 9.927E-0268.5 1.791E-01 1.680E-01 1.428E-01 1.119E-01 9.926E-0269.0 1.769E-01 1.661E-01 1.416E-01 1.116E-01 9.925E-0269.5 1.749E-01 1.644E-01 1.405E-01 1.112E-01 9.925E-0270.0 1.728E-01 1.626E-01 1.394E-01 1.109E-01 9.924E-0270.5 1.709E-01 1.609E-01 1.383E-01 1.106E-01 9.923E-0271.0 1.690E-01 1.593E-01 1.372E-01 1.103E-01 9.923E-0271.5 1.671E-01 1.577E-01 1.362E-01 1.100E-01 9.922E-0272.0 1.653E-01 1.561E-01 1.352E-01 1.097E-01 9.921E-02

is

Appendices

153

T=55oC u=1.0m/s

j

t (hours)

1 2 3 4

0.0 2.077E+00 2.077E+00 2.077E+00 2.077E+00 9.964E-020.5 2.077E+00 2.077E+00 2.077E+00 8.194E-01 6.865E-021.0 2.077E+00 2.077E+00 1.619E+00 5.964E-01 6.316E-021.5 2.077E+00 1.861E+00 1.339E+00 4.642E-01 5.990E-022.0 1.858E+00 1.658E+00 1.126E+00 3.841E-01 5.793E-022.5 1.656E+00 1.447E+00 9.635E-01 3.268E-01 5.651E-023.0 1.445E+00 1.261E+00 8.295E-01 2.837E-01 5.545E-023.5 1.259E+00 1.094E+00 7.180E-01 2.490E-01 5.460E-024.0 1.093E+00 9.500E-01 6.234E-01 2.203E-01 5.389E-024.5 9.483E-01 8.246E-01 5.426E-01 1.960E-01 5.329E-025.0 8.232E-01 7.165E-01 4.735E-01 1.754E-01 5.278E-025.5 7.153E-01 6.233E-01 4.141E-01 1.577E-01 5.235E-026.0 6.222E-01 5.431E-01 3.630E-01 1.426E-01 5.197E-026.5 5.422E-01 4.741E-01 3.192E-01 1.296E-01 5.165E-027.0 4.733E-01 4.147E-01 2.815E-01 1.184E-01 5.138E-027.5 4.140E-01 3.637E-01 2.490E-01 1.088E-01 5.114E-028.0 3.631E-01 3.197E-01 2.211E-01 1.005E-01 5.094E-028.5 3.192E-01 2.820E-01 1.972E-01 9.339E-02 5.076E-029.0 2.815E-01 2.495E-01 1.765E-01 8.728E-02 5.061E-029.5 2.491E-01 2.215E-01 1.588E-01 8.202E-02 5.048E-02

10.0 2.212E-01 1.975E-01 1.435E-01 7.749E-02 5.037E-0210.5 1.972E-01 1.768E-01 1.304E-01 7.360E-02 5.027E-0211.0 1.765E-01 1.590E-01 1.191E-01 7.026E-02 5.019E-0211.5 1.588E-01 1.437E-01 1.094E-01 6.738E-02 5.012E-0212.0 1.435E-01 1.306E-01 1.010E-01 6.490E-02 5.006E-0212.5 1.304E-01 1.192E-01 9.384E-02 6.277E-02 5.001E-0213.0 1.191E-01 1.095E-01 8.767E-02 6.094E-02 4.996E-0213.5 1.094E-01 1.011E-01 8.235E-02 5.937E-02 4.992E-0214.0 1.010E-01 9.394E-02 7.778E-02 5.801E-02 4.989E-0214.5 9.386E-02 8.775E-02 7.385E-02 5.685E-02 4.986E-02

is

Appendices

154

T=45oC u=1.0m/s

j

t (hours)

1 2 3 4

0.0 2.030E+00 2.030E+00 2.030E+00 2.030E+00 8.527E-020.5 2.030E+00 2.030E+00 2.030E+00 1.275E+00 9.398E-021.0 2.030E+00 2.030E+00 1.860E+00 9.052E-01 8.624E-021.5 2.030E+00 1.981E+00 1.666E+00 7.027E-01 8.200E-022.0 1.999E+00 1.895E+00 1.489E+00 5.792E-01 7.942E-022.5 1.934E+00 1.790E+00 1.335E+00 4.965E-01 7.769E-023.0 1.844E+00 1.675E+00 1.203E+00 4.367E-01 7.644E-023.5 1.738E+00 1.558E+00 1.089E+00 3.909E-01 7.548E-024.0 1.626E+00 1.444E+00 9.907E-01 3.543E-01 7.471E-024.5 1.512E+00 1.334E+00 9.041E-01 3.240E-01 7.408E-025.0 1.401E+00 1.231E+00 8.273E-01 2.983E-01 7.354E-025.5 1.295E+00 1.134E+00 7.587E-01 2.761E-01 7.308E-026.0 1.194E+00 1.045E+00 6.970E-01 2.566E-01 7.267E-026.5 1.101E+00 9.619E-01 6.413E-01 2.394E-01 7.231E-027.0 1.014E+00 8.857E-01 5.909E-01 2.240E-01 7.198E-027.5 9.337E-01 8.157E-01 5.452E-01 2.101E-01 7.169E-028.0 8.599E-01 7.515E-01 5.036E-01 1.976E-01 7.143E-028.5 7.921E-01 6.927E-01 4.657E-01 1.863E-01 7.120E-029.0 7.299E-01 6.388E-01 4.312E-01 1.760E-01 7.098E-029.5 6.729E-01 5.896E-01 3.997E-01 1.666E-01 7.078E-0210.0 6.208E-01 5.446E-01 3.710E-01 1.581E-01 7.061E-0210.5 5.731E-01 5.034E-01 3.447E-01 1.503E-01 7.044E-0211.0 5.295E-01 4.658E-01 3.208E-01 1.432E-01 7.030E-0211.5 4.897E-01 4.315E-01 2.990E-01 1.368E-01 7.016E-0212.0 4.533E-01 4.001E-01 2.790E-01 1.309E-01 7.004E-0212.5 4.200E-01 3.714E-01 2.608E-01 1.255E-01 6.992E-0213.0 3.896E-01 3.452E-01 2.442E-01 1.206E-01 6.982E-0213.5 3.618E-01 3.213E-01 2.290E-01 1.161E-01 6.973E-0214.0 3.364E-01 2.994E-01 2.151E-01 1.120E-01 6.964E-0214.5 3.133E-01 2.794E-01 2.024E-01 1.082E-01 6.956E-02

is

Appendices

155

j

t (hours)

1 2 3 4

15.0 2.921E-01 2.612E-01 1.908E-01 1.048E-01 6.949E-0215.5 2.728E-01 2.445E-01 1.803E-01 1.017E-01 6.943E-0216.0 2.551E-01 2.293E-01 1.706E-01 9.883E-02 6.937E-0216.5 2.390E-01 2.154E-01 1.618E-01 9.623E-02 6.931E-0217.0 2.242E-01 2.027E-01 1.537E-01 9.385E-02 6.926E-0217.5 2.107E-01 1.911E-01 1.464E-01 9.167E-02 6.922E-0218.0 1.985E-01 1.805E-01 1.396E-01 8.969E-02 6.917E-0218.5 1.872E-01 1.708E-01 1.335E-01 8.787E-02 6.914E-0219.0 1.770E-01 1.620E-01 1.279E-01 8.621E-02 6.910E-0219.5 1.676E-01 1.539E-01 1.228E-01 8.470E-02 6.907E-0220.0 1.590E-01 1.465E-01 1.181E-01 8.332E-02 6.904E-0220.5 1.512E-01 1.398E-01 1.138E-01 8.206E-02 6.902E-0221.0 1.441E-01 1.336E-01 1.099E-01 8.090E-02 6.899E-0221.5 1.375E-01 1.280E-01 1.063E-01 7.985E-02 6.897E-0222.0 1.316E-01 1.229E-01 1.031E-01 7.889E-02 6.895E-02

is

Appendices

156

T=35oC u=1.0m/s

j

t (hours)

1 2 3 4

0.0 2.022E+00 2.022E+00 2.022E+00 2.022E+00 8.512E-020.5 2.022E+00 2.022E+00 2.022E+00 1.696E+00 1.244E-011.0 2.022E+00 2.022E+00 1.990E+00 1.442E+00 1.204E-011.5 2.022E+00 2.018E+00 1.937E+00 1.244E+00 1.172E-012.0 2.021E+00 2.008E+00 1.873E+00 1.088E+00 1.147E-012.5 2.017E+00 1.991E+00 1.803E+00 9.632E-01 1.127E-013.0 2.010E+00 1.969E+00 1.731E+00 8.626E-01 1.111E-013.5 1.999E+00 1.940E+00 1.658E+00 7.806E-01 1.098E-014.0 1.983E+00 1.907E+00 1.587E+00 7.131E-01 1.088E-014.5 1.962E+00 1.871E+00 1.518E+00 6.568E-01 1.079E-015.0 1.937E+00 1.830E+00 1.452E+00 6.093E-01 1.071E-015.5 1.908E+00 1.788E+00 1.390E+00 5.690E-01 1.065E-016.0 1.875E+00 1.743E+00 1.330E+00 5.342E-01 1.059E-016.5 1.839E+00 1.698E+00 1.274E+00 5.041E-01 1.054E-017.0 1.800E+00 1.651E+00 1.222E+00 4.776E-01 1.050E-017.5 1.759E+00 1.604E+00 1.172E+00 4.541E-01 1.046E-018.0 1.717E+00 1.557E+00 1.125E+00 4.332E-01 1.043E-018.5 1.673E+00 1.511E+00 1.080E+00 4.144E-01 1.040E-019.0 1.629E+00 1.465E+00 1.038E+00 3.974E-01 1.037E-019.5 1.583E+00 1.419E+00 9.980E-01 3.819E-01 1.035E-01

10.0 1.538E+00 1.374E+00 9.603E-01 3.677E-01 1.033E-0110.5 1.493E+00 1.330E+00 9.244E-01 3.546E-01 1.031E-0111.0 1.448E+00 1.287E+00 8.904E-01 3.425E-01 1.029E-0111.5 1.404E+00 1.245E+00 8.580E-01 3.312E-01 1.027E-0112.0 1.360E+00 1.204E+00 8.272E-01 3.207E-01 1.025E-0112.5 1.318E+00 1.165E+00 7.979E-01 3.109E-01 1.024E-0113.0 1.276E+00 1.126E+00 7.699E-01 3.016E-01 1.022E-0113.5 1.235E+00 1.089E+00 7.432E-01 2.929E-01 1.021E-0114.0 1.194E+00 1.052E+00 7.176E-01 2.847E-01 1.020E-0114.5 1.155E+00 1.017E+00 6.932E-01 2.770E-01 1.018E-0115.0 1.118E+00 9.834E-01 6.699E-01 2.696E-01 1.017E-0115.5 1.081E+00 9.506E-01 6.476E-01 2.626E-01 1.016E-0116.0 1.045E+00 9.189E-01 6.262E-01 2.560E-01 1.015E-0116.5 1.010E+00 8.884E-01 6.057E-01 2.496E-01 1.014E-0117.0 9.769E-01 8.588E-01 5.860E-01 2.436E-01 1.013E-0117.5 9.445E-01 8.304E-01 5.671E-01 2.379E-01 1.012E-01

is

Appendices

157

j

t (hours)

1 2 3 4


is

Appendices

158

j

t (hours)

1 2 3 4

36.0 3.020E-01 2.739E-01 2.099E-01 1.316E-01 9.952E-0236.5 2.943E-01 2.672E-01 2.057E-01 1.304E-01 9.950E-0237.0 2.869E-01 2.608E-01 2.016E-01 1.292E-01 9.948E-0237.5 2.797E-01 2.547E-01 1.977E-01 1.280E-01 9.946E-0238.0 2.729E-01 2.488E-01 1.939E-01 1.269E-01 9.945E-0238.5 2.662E-01 2.431E-01 1.903E-01 1.259E-01 9.943E-0239.0 2.599E-01 2.376E-01 1.869E-01 1.248E-01 9.941E-0239.5 2.538E-01 2.323E-01 1.835E-01 1.239E-01 9.940E-0240.0 2.479E-01 2.272E-01 1.803E-01 1.229E-01 9.938E-0240.5 2.422E-01 2.224E-01 1.772E-01 1.220E-01 9.937E-0241.0 2.368E-01 2.177E-01 1.742E-01 1.211E-01 9.935E-0241.5 2.315E-01 2.132E-01 1.714E-01 1.203E-01 9.934E-0242.0 2.265E-01 2.088E-01 1.686E-01 1.195E-01 9.933E-0242.5 2.216E-01 2.046E-01 1.660E-01 1.187E-01 9.931E-0243.0 2.170E-01 2.006E-01 1.634E-01 1.179E-01 9.930E-0243.5 2.125E-01 1.967E-01 1.610E-01 1.172E-01 9.929E-0244.0 2.082E-01 1.930E-01 1.586E-01 1.165E-01 9.928E-0244.5 2.040E-01 1.894E-01 1.563E-01 1.159E-01 9.927E-0245.0 2.000E-01 1.860E-01 1.542E-01 1.152E-01 9.926E-0245.5 1.962E-01 1.827E-01 1.521E-01 1.146E-01 9.925E-0246.0 1.925E-01 1.795E-01 1.500E-01 1.140E-01 9.924E-0246.5 1.889E-01 1.765E-01 1.481E-01 1.134E-01 9.923E-0247.0 1.855E-01 1.735E-01 1.462E-01 1.129E-01 9.922E-0247.5 1.822E-01 1.707E-01 1.444E-01 1.124E-01 9.921E-0248.0 1.790E-01 1.679E-01 1.427E-01 1.119E-01 9.921E-0248.5 1.760E-01 1.653E-01 1.410E-01 1.114E-01 9.920E-0249.0 1.731E-01 1.628E-01 1.394E-01 1.109E-01 9.919E-0249.5 1.702E-01 1.604E-01 1.379E-01 1.104E-01 9.918E-0250.0 1.675E-01 1.580E-01 1.364E-01 1.100E-01 9.918E-0250.5 1.649E-01 1.558E-01 1.350E-01 1.096E-01 9.917E-02

is

Appendices

159

APPENDIX 7B: PIPERINE PROFILE OF A PIPER NIGRUM L. BERRY

(Pi, j+1 ,Pn, j+1, Ps, j+1)

T=55oC u=0.5m/s

j

t (hours)

1 2 3 4

0.0 5.042E-02 5.042E-02 5.042E-02 5.042E-02 4.002E-020.5 5.042E-02 5.042E-02 5.042E-02 5.013E-02 4.002E-021.0 5.042E-02 5.042E-02 5.042E-02 4.986E-02 4.002E-021.5 5.042E-02 5.042E-02 5.041E-02 4.959E-02 4.002E-022.0 5.042E-02 5.042E-02 5.039E-02 4.933E-02 4.002E-022.5 5.042E-02 5.042E-02 5.038E-02 4.909E-02 4.002E-023.0 5.042E-02 5.042E-02 5.036E-02 4.885E-02 4.002E-023.5 5.042E-02 5.042E-02 5.033E-02 4.862E-02 4.002E-024.0 5.042E-02 5.042E-02 5.031E-02 4.840E-02 4.001E-024.5 5.042E-02 5.041E-02 5.028E-02 4.818E-02 4.001E-025.0 5.042E-02 5.041E-02 5.025E-02 4.797E-02 4.001E-025.5 5.042E-02 5.041E-02 5.021E-02 4.777E-02 4.001E-026.0 5.042E-02 5.040E-02 5.018E-02 4.758E-02 4.001E-026.5 5.042E-02 5.040E-02 5.014E-02 4.740E-02 4.001E-027.0 5.042E-02 5.039E-02 5.010E-02 4.722E-02 4.001E-027.5 5.042E-02 5.039E-02 5.005E-02 4.704E-02 4.001E-028.0 5.041E-02 5.038E-02 5.001E-02 4.688E-02 4.001E-028.5 5.041E-02 5.037E-02 4.996E-02 4.671E-02 4.001E-029.0 5.041E-02 5.037E-02 4.991E-02 4.656E-02 4.001E-029.5 5.041E-02 5.036E-02 4.987E-02 4.641E-02 4.001E-02

10.0 5.041E-02 5.035E-02 4.981E-02 4.626E-02 4.001E-0210.5 5.040E-02 5.034E-02 4.976E-02 4.612E-02 4.001E-0211.0 5.040E-02 5.033E-02 4.971E-02 4.598E-02 4.001E-0211.5 5.040E-02 5.031E-02 4.966E-02 4.585E-02 4.001E-0212.0 5.039E-02 5.030E-02 4.960E-02 4.572E-02 4.001E-0212.5 5.039E-02 5.029E-02 4.955E-02 4.560E-02 4.001E-0213.0 5.039E-02 5.027E-02 4.949E-02 4.548E-02 4.001E-0213.5 5.038E-02 5.026E-02 4.944E-02 4.536E-02 4.001E-0214.0 5.038E-02 5.024E-02 4.938E-02 4.525E-02 4.001E-0214.5 5.037E-02 5.023E-02 4.932E-02 4.514E-02 4.001E-0215.0 5.036E-02 5.021E-02 4.926E-02 4.504E-02 4.001E-0215.5 5.036E-02 5.019E-02 4.920E-02 4.494E-02 4.001E-0216.0 5.035E-02 5.017E-02 4.915E-02 4.484E-02 4.001E-0216.5 5.034E-02 5.015E-02 4.909E-02 4.474E-02 4.001E-0217.0 5.033E-02 5.013E-02 4.903E-02 4.465E-02 4.001E-0217.5 5.032E-02 5.011E-02 4.897E-02 4.456E-02 4.001E-0218.0 5.032E-02 5.009E-02 4.891E-02 4.447E-02 4.001E-02

is

Appendices

160

T=45oC u=0.5m/s

j

t (hours)

1 2 3 4



is

Appendices

161

j

t (hours)

1 2 3 4

17.5 5.105E-02 5.094E-02 5.016E-02 4.599E-02 4.001E-0218.0 5.105E-02 5.093E-02 5.012E-02 4.590E-02 4.001E-0218.5 5.104E-02 5.092E-02 5.008E-02 4.581E-02 4.001E-0219.0 5.104E-02 5.091E-02 5.003E-02 4.572E-02 4.001E-0219.5 5.104E-02 5.090E-02 4.999E-02 4.564E-02 4.001E-0220.0 5.103E-02 5.088E-02 4.995E-02 4.555E-02 4.001E-0220.5 5.103E-02 5.087E-02 4.990E-02 4.547E-02 4.001E-0221.0 5.102E-02 5.086E-02 4.986E-02 4.539E-02 4.001E-0221.5 5.102E-02 5.084E-02 4.982E-02 4.531E-02 4.001E-0222.0 5.101E-02 5.083E-02 4.977E-02 4.524E-02 4.001E-0222.5 5.101E-02 5.082E-02 4.973E-02 4.516E-02 4.001E-0223.0 5.100E-02 5.080E-02 4.968E-02 4.509E-02 4.001E-0223.5 5.099E-02 5.079E-02 4.964E-02 4.502E-02 4.001E-0224.0 5.099E-02 5.077E-02 4.959E-02 4.495E-02 4.001E-0224.5 5.098E-02 5.075E-02 4.955E-02 4.488E-02 4.001E-0225.0 5.097E-02 5.074E-02 4.950E-02 4.482E-02 4.001E-0225.5 5.097E-02 5.072E-02 4.946E-02 4.475E-02 4.001E-0226.0 5.096E-02 5.071E-02 4.941E-02 4.469E-02 4.001E-0226.5 5.095E-02 5.069E-02 4.937E-02 4.463E-02 4.001E-0227.0 5.094E-02 5.067E-02 4.932E-02 4.457E-02 4.001E-0227.5 5.093E-02 5.065E-02 4.928E-02 4.451E-02 4.001E-0228.0 5.092E-02 5.063E-02 4.923E-02 4.445E-02 4.001E-0228.5 5.092E-02 5.062E-02 4.919E-02 4.439E-02 4.001E-0229.0 5.091E-02 5.060E-02 4.914E-02 4.433E-02 4.001E-0229.5 5.090E-02 5.058E-02 4.910E-02 4.428E-02 4.001E-0230.0 5.089E-02 5.056E-02 4.905E-02 4.423E-02 4.001E-0230.5 5.088E-02 5.054E-02 4.901E-02 4.417E-02 4.001E-0231.0 5.087E-02 5.052E-02 4.896E-02 4.412E-02 4.001E-0231.5 5.086E-02 5.050E-02 4.892E-02 4.407E-02 4.001E-0232.0 5.084E-02 5.048E-02 4.888E-02 4.402E-02 4.001E-0232.5 5.083E-02 5.046E-02 4.883E-02 4.397E-02 4.001E-0233.0 5.082E-02 5.043E-02 4.879E-02 4.393E-02 4.001E-0233.5 5.081E-02 5.041E-02 4.874E-02 4.388E-02 4.001E-0234.0 5.080E-02 5.039E-02 4.870E-02 4.383E-02 4.001E-02

is

Appendices

162

T=35oC u=0.5m/s

j

t (hours)

1 2 3 4


is

Appendices

163

j

t (hours)

1 2 3 4


is

Appendices

164

j

t (hours)

1 2 3 4


is

Appendices

165

j

t (hours)

1 2 3 4

54.0 5.108E-02 5.108E-02 5.104E-02 4.989E-02 4.000E-0254.5 5.108E-02 5.108E-02 5.104E-02 4.988E-02 4.000E-0255.0 5.108E-02 5.108E-02 5.104E-02 4.987E-02 4.000E-0255.5 5.108E-02 5.108E-02 5.104E-02 4.986E-02 4.000E-0256.0 5.108E-02 5.108E-02 5.104E-02 4.985E-02 4.000E-0256.5 5.108E-02 5.108E-02 5.104E-02 4.984E-02 4.000E-0257.0 5.108E-02 5.108E-02 5.104E-02 4.983E-02 4.000E-0257.5 5.108E-02 5.108E-02 5.104E-02 4.982E-02 4.000E-0258.0 5.108E-02 5.108E-02 5.104E-02 4.981E-02 4.000E-0258.5 5.108E-02 5.108E-02 5.104E-02 4.980E-02 4.000E-0259.0 5.108E-02 5.108E-02 5.104E-02 4.979E-02 4.000E-0259.5 5.108E-02 5.108E-02 5.104E-02 4.978E-02 4.000E-0260.0 5.108E-02 5.108E-02 5.103E-02 4.977E-02 4.000E-0260.5 5.108E-02 5.108E-02 5.103E-02 4.976E-02 4.000E-0261.0 5.108E-02 5.108E-02 5.103E-02 4.975E-02 4.000E-0261.5 5.108E-02 5.108E-02 5.103E-02 4.974E-02 4.000E-0262.0 5.108E-02 5.108E-02 5.103E-02 4.973E-02 4.000E-0262.5 5.108E-02 5.108E-02 5.103E-02 4.972E-02 4.000E-0263.0 5.108E-02 5.108E-02 5.103E-02 4.971E-02 4.000E-0263.5 5.108E-02 5.108E-02 5.103E-02 4.970E-02 4.000E-0264.0 5.108E-02 5.108E-02 5.103E-02 4.969E-02 4.000E-0264.5 5.108E-02 5.108E-02 5.103E-02 4.968E-02 4.000E-0265.0 5.108E-02 5.108E-02 5.103E-02 4.967E-02 4.000E-0265.5 5.108E-02 5.108E-02 5.103E-02 4.966E-02 4.000E-0266.0 5.108E-02 5.108E-02 5.103E-02 4.965E-02 4.000E-0266.5 5.108E-02 5.108E-02 5.102E-02 4.964E-02 4.000E-0267.0 5.108E-02 5.108E-02 5.102E-02 4.963E-02 4.000E-0267.5 5.108E-02 5.108E-02 5.102E-02 4.962E-02 4.000E-0268.0 5.108E-02 5.108E-02 5.102E-02 4.961E-02 4.000E-0268.5 5.108E-02 5.108E-02 5.102E-02 4.960E-02 4.000E-0269.0 5.108E-02 5.108E-02 5.102E-02 4.959E-02 4.000E-0269.5 5.108E-02 5.108E-02 5.102E-02 4.958E-02 4.000E-0270.0 5.108E-02 5.108E-02 5.102E-02 4.957E-02 4.000E-0270.5 5.108E-02 5.108E-02 5.102E-02 4.956E-02 4.000E-0271.0 5.108E-02 5.108E-02 5.102E-02 4.955E-02 4.000E-0271.5 5.108E-02 5.108E-02 5.102E-02 4.954E-02 4.000E-0272.0 5.108E-02 5.108E-02 5.101E-02 4.953E-02 4.000E-02

is

Appendices

166

T=55oC u=1.0m/s

j

t (hours)

1 2 3 4


is

Appendices

167

T=45oC u=1.0m/s

j

t (hours)

1 2 3 4


10.0 4.982E-02 4.969E-02 4.882E-02 4.482E-02 4.001E-0210.5 4.981E-02 4.966E-02 4.874E-02 4.468E-02 4.001E-0211.0 4.980E-02 4.964E-02 4.865E-02 4.455E-02 4.001E-0211.5 4.979E-02 4.961E-02 4.857E-02 4.442E-02 4.001E-0212.0 4.978E-02 4.958E-02 4.849E-02 4.429E-02 4.001E-0212.5 4.977E-02 4.955E-02 4.841E-02 4.417E-02 4.001E-0213.0 4.975E-02 4.952E-02 4.832E-02 4.406E-02 4.001E-0213.5 4.974E-02 4.949E-02 4.824E-02 4.395E-02 4.001E-0214.0 4.972E-02 4.945E-02 4.816E-02 4.385E-02 4.001E-0214.5 4.971E-02 4.942E-02 4.807E-02 4.375E-02 4.001E-02

is

Appendices

168

j

t (hours)

1 2 3 4


is

Appendices

169

T=35oC u=1.0m/s

j

t (hours)

1 2 3 4


10.0 5.954E-02 5.952E-02 5.917E-02 5.476E-02 4.002E-0210.5 5.954E-02 5.952E-02 5.914E-02 5.456E-02 4.002E-0211.0 5.954E-02 5.951E-02 5.910E-02 5.437E-02 4.002E-0211.5 5.954E-02 5.951E-02 5.906E-02 5.419E-02 4.002E-0212.0 5.954E-02 5.951E-02 5.902E-02 5.400E-02 4.002E-0212.5 5.954E-02 5.950E-02 5.898E-02 5.382E-02 4.002E-0213.0 5.954E-02 5.949E-02 5.894E-02 5.364E-02 4.002E-0213.5 5.954E-02 5.949E-02 5.890E-02 5.347E-02 4.002E-0214.0 5.954E-02 5.948E-02 5.886E-02 5.330E-02 4.002E-0214.5 5.954E-02 5.948E-02 5.881E-02 5.313E-02 4.002E-0215.0 5.954E-02 5.947E-02 5.877E-02 5.296E-02 4.002E-0215.5 5.953E-02 5.946E-02 5.872E-02 5.280E-02 4.002E-0216.0 5.953E-02 5.945E-02 5.868E-02 5.264E-02 4.002E-0216.5 5.953E-02 5.945E-02 5.863E-02 5.248E-02 4.002E-0217.0 5.953E-02 5.944E-02 5.858E-02 5.233E-02 4.002E-0217.5 5.953E-02 5.943E-02 5.853E-02 5.218E-02 4.002E-02

is

Appendices

170

j

t (hours)

1 2 3 4


is

Appendices

171

j

t (hours)

1 2 3 4


is

Appendices

172

APPENDIX 8: CALCULATION OF THE AVERAGE MOISTURE CONTENT BASED ON THE MOISTURE PROFILE OF A BERRY T=55oC u=0.5m/s

(decimal)dry basis

(%)wet basis

0.0 1.038E+00 8.931E+01 1.778E+01 2.534E+00 71.710.5 1.038E+00 7.281E+01 9.197E+00 1.946E+00 66.061.0 1.038E+00 6.188E+01 6.414E+00 1.625E+00 61.901.5 1.038E+00 5.356E+01 5.079E+00 1.399E+00 58.312.0 9.878E-01 4.688E+01 4.276E+00 1.222E+00 55.002.5 9.138E-01 4.133E+01 3.724E+00 1.077E+00 51.863.0 8.312E-01 3.659E+01 3.313E+00 9.547E-01 48.843.5 7.490E-01 3.250E+01 2.989E+00 8.494E-01 45.934.0 6.712E-01 2.894E+01 2.723E+00 7.578E-01 43.114.5 5.998E-01 2.581E+01 2.500E+00 6.776E-01 40.395.0 5.351E-01 2.306E+01 2.308E+00 6.072E-01 37.785.5 4.771E-01 2.064E+01 2.142E+00 5.451E-01 35.286.0 4.254E-01 1.850E+01 1.997E+00 4.904E-01 32.906.5 3.795E-01 1.661E+01 1.869E+00 4.420E-01 30.657.0 3.387E-01 1.494E+01 1.757E+00 3.992E-01 28.537.5 3.025E-01 1.346E+01 1.658E+00 3.614E-01 26.558.0 2.705E-01 1.215E+01 1.570E+00 3.280E-01 24.708.5 2.422E-01 1.100E+01 1.493E+00 2.984E-01 22.989.0 2.171E-01 9.974E+00 1.424E+00 2.723E-01 21.409.5 1.950E-01 9.070E+00 1.364E+00 2.491E-01 19.9410.0 1.753E-01 8.270E+00 1.311E+00 2.287E-01 18.6110.5 1.580E-01 7.562E+00 1.263E+00 2.105E-01 17.3911.0 1.426E-01 6.936E+00 1.221E+00 1.945E-01 16.2911.5 1.290E-01 6.382E+00 1.184E+00 1.804E-01 15.2812.0 1.170E-01 5.893E+00 1.152E+00 1.678E-01 14.3712.5 1.064E-01 5.459E+00 1.123E+00 1.568E-01 13.5513.0 9.696E-02 5.076E+00 1.097E+00 1.469E-01 12.8113.5 8.864E-02 4.737E+00 1.074E+00 1.383E-01 12.1514.0 8.128E-02 4.437E+00 1.054E+00 1.306E-01 11.5514.5 7.477E-02 4.171E+00 1.037E+00 1.238E-01 11.0215.0 6.901E-02 3.936E+00 1.021E+00 1.178E-01 10.5415.5 6.391E-02 3.729E+00 1.007E+00 1.125E-01 10.1116.0 5.941E-02 3.545E+00 9.947E-01 1.078E-01 9.7316.5 5.542E-02 3.383E+00 9.838E-01 1.036E-01 9.3917.0 5.189E-02 3.239E+00 9.742E-01 9.996E-02 9.0917.5 4.877E-02 3.112E+00 9.657E-01 9.670E-02 8.8218.0 4.601E-02 2.999E+00 9.582E-01 9.383E-02 8.58

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

173

T=45oC u=0.5m/s

(decimal)dry basis

(%)wet basis

0.0 9.930E-01 8.540E+01 1.703E+01 2.424E+00 70.790.5 9.930E-01 7.778E+01 1.315E+01 2.154E+00 68.301.0 9.930E-01 7.142E+01 1.051E+01 1.944E+00 66.031.5 9.930E-01 6.600E+01 8.697E+00 1.774E+00 63.952.0 9.903E-01 6.128E+01 7.412E+00 1.633E+00 62.022.5 9.829E-01 5.713E+01 6.477E+00 1.514E+00 60.223.0 9.700E-01 5.342E+01 5.776E+00 1.410E+00 58.513.5 9.516E-01 5.009E+01 5.235E+00 1.319E+00 56.884.0 9.284E-01 4.706E+01 4.807E+00 1.237E+00 55.304.5 9.012E-01 4.429E+01 4.459E+00 1.164E+00 53.785.0 8.711E-01 4.174E+01 4.170E+00 1.097E+00 52.305.5 8.389E-01 3.940E+01 3.926E+00 1.035E+00 50.866.0 8.055E-01 3.722E+01 3.716E+00 9.783E-01 49.456.5 7.715E-01 3.519E+01 3.532E+00 9.257E-01 48.077.0 7.374E-01 3.331E+01 3.370E+00 8.769E-01 46.727.5 7.037E-01 3.154E+01 3.225E+00 8.314E-01 45.408.0 6.706E-01 2.989E+01 3.094E+00 7.889E-01 44.108.5 6.384E-01 2.835E+01 2.976E+00 7.491E-01 42.839.0 6.072E-01 2.689E+01 2.867E+00 7.118E-01 41.589.5 5.772E-01 2.553E+01 2.767E+00 6.768E-01 40.3610.0 5.484E-01 2.425E+01 2.675E+00 6.439E-01 39.1710.5 5.208E-01 2.304E+01 2.590E+00 6.129E-01 38.0011.0 4.945E-01 2.191E+01 2.510E+00 5.838E-01 36.8611.5 4.695E-01 2.084E+01 2.436E+00 5.564E-01 35.7512.0 4.457E-01 1.983E+01 2.367E+00 5.306E-01 34.6712.5 4.231E-01 1.888E+01 2.302E+00 5.063E-01 33.6113.0 4.017E-01 1.798E+01 2.242E+00 4.834E-01 32.5913.5 3.814E-01 1.714E+01 2.185E+00 4.618E-01 31.5914.0 3.621E-01 1.634E+01 2.131E+00 4.414E-01 30.6214.5 3.439E-01 1.559E+01 2.081E+00 4.222E-01 29.6815.0 3.267E-01 1.488E+01 2.034E+00 4.040E-01 28.7815.5 3.104E-01 1.421E+01 1.989E+00 3.869E-01 27.9016.0 2.950E-01 1.358E+01 1.947E+00 3.708E-01 27.0516.5 2.805E-01 1.298E+01 1.907E+00 3.555E-01 26.2317.0 2.667E-01 1.242E+01 1.870E+00 3.412E-01 25.4417.5 2.537E-01 1.189E+01 1.835E+00 3.276E-01 24.68

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

174

(decimal)dry basis

(%)wet basis

18.0 2.415E-01 1.139E+01 1.802E+00 3.148E-01 23.9418.5 2.299E-01 1.091E+01 1.771E+00 3.027E-01 23.2419.0 2.190E-01 1.047E+01 1.741E+00 2.913E-01 22.5619.5 2.086E-01 1.005E+01 1.713E+00 2.805E-01 21.9120.0 1.989E-01 9.650E+00 1.687E+00 2.704E-01 21.2820.5 1.897E-01 9.275E+00 1.662E+00 2.608E-01 20.6821.0 1.810E-01 8.921E+00 1.639E+00 2.517E-01 20.1121.5 1.727E-01 8.586E+00 1.617E+00 2.432E-01 19.5622.0 1.650E-01 8.271E+00 1.596E+00 2.351E-01 19.0422.5 1.577E-01 7.973E+00 1.577E+00 2.275E-01 18.5323.0 1.508E-01 7.692E+00 1.558E+00 2.203E-01 18.0523.5 1.443E-01 7.426E+00 1.540E+00 2.135E-01 17.6024.0 1.381E-01 7.176E+00 1.524E+00 2.071E-01 17.1624.5 1.323E-01 6.939E+00 1.508E+00 2.011E-01 16.7425.0 1.268E-01 6.716E+00 1.494E+00 1.954E-01 16.3425.5 1.216E-01 6.505E+00 1.480E+00 1.900E-01 15.9726.0 1.167E-01 6.306E+00 1.467E+00 1.849E-01 15.6126.5 1.121E-01 6.118E+00 1.454E+00 1.801E-01 15.2627.0 1.078E-01 5.941E+00 1.443E+00 1.756E-01 14.9427.5 1.036E-01 5.774E+00 1.432E+00 1.713E-01 14.6328.0 9.976E-02 5.616E+00 1.421E+00 1.673E-01 14.3328.5 9.610E-02 5.467E+00 1.411E+00 1.635E-01 14.0529.0 9.264E-02 5.326E+00 1.402E+00 1.599E-01 13.7829.5 8.937E-02 5.193E+00 1.393E+00 1.565E-01 13.5330.0 8.629E-02 5.068E+00 1.385E+00 1.533E-01 13.2930.5 8.338E-02 4.949E+00 1.377E+00 1.502E-01 13.0631.0 8.063E-02 4.838E+00 1.370E+00 1.474E-01 12.8531.5 7.804E-02 4.732E+00 1.363E+00 1.447E-01 12.6432.0 7.559E-02 4.633E+00 1.356E+00 1.421E-01 12.4532.5 7.328E-02 4.539E+00 1.350E+00 1.397E-01 12.2633.0 7.110E-02 4.450E+00 1.344E+00 1.375E-01 12.0933.5 6.904E-02 4.366E+00 1.339E+00 1.353E-01 11.9234.0 6.710E-02 4.287E+00 1.334E+00 1.333E-01 11.76

TotalM bar 2

M bar 3

t (hours)

M bar1

Appendices

175

T=35oC u=0.5m/s

(decimal)dry basis

(%)wet basis

0.0 9.930E-01 8.540E+01 1.703E+01 2.424E+00 70.790.5 9.930E-01 8.181E+01 1.543E+01 2.303E+00 69.721.0 9.930E-01 7.851E+01 1.389E+01 2.189E+00 68.641.5 9.930E-01 7.546E+01 1.258E+01 2.087E+00 67.602.0 9.928E-01 7.263E+01 1.146E+01 1.994E+00 66.602.5 9.924E-01 6.999E+01 1.052E+01 1.910E+00 65.643.0 9.914E-01 6.753E+01 9.703E+00 1.833E+00 64.713.5 9.897E-01 6.521E+01 9.005E+00 1.763E+00 63.804.0 9.872E-01 6.304E+01 8.401E+00 1.698E+00 62.934.5 9.837E-01 6.099E+01 7.877E+00 1.637E+00 62.085.0 9.792E-01 5.905E+01 7.420E+00 1.581E+00 61.255.5 9.736E-01 5.721E+01 7.019E+00 1.528E+00 60.456.0 9.670E-01 5.547E+01 6.666E+00 1.479E+00 59.666.5 9.593E-01 5.381E+01 6.354E+00 1.433E+00 58.897.0 9.507E-01 5.223E+01 6.076E+00 1.389E+00 58.147.5 9.411E-01 5.072E+01 5.828E+00 1.347E+00 57.408.0 9.306E-01 4.928E+01 5.605E+00 1.308E+00 56.688.5 9.193E-01 4.790E+01 5.404E+00 1.271E+00 55.969.0 9.072E-01 4.658E+01 5.221E+00 1.235E+00 55.269.5 8.946E-01 4.531E+01 5.056E+00 1.201E+00 54.57

10.0 8.813E-01 4.409E+01 4.904E+00 1.169E+00 53.8910.5 8.676E-01 4.291E+01 4.765E+00 1.138E+00 53.2211.0 8.535E-01 4.178E+01 4.637E+00 1.108E+00 52.5611.5 8.390E-01 4.069E+01 4.519E+00 1.079E+00 51.9112.0 8.242E-01 3.964E+01 4.409E+00 1.052E+00 51.2612.5 8.093E-01 3.863E+01 4.306E+00 1.025E+00 50.6213.0 7.942E-01 3.765E+01 4.211E+00 9.997E-01 49.9913.5 7.789E-01 3.670E+01 4.121E+00 9.750E-01 49.3714.0 7.637E-01 3.579E+01 4.037E+00 9.513E-01 48.7514.5 7.484E-01 3.490E+01 3.958E+00 9.283E-01 48.1415.0 7.331E-01 3.405E+01 3.883E+00 9.061E-01 47.5415.5 7.179E-01 3.322E+01 3.812E+00 8.847E-01 46.9416.0 7.028E-01 3.241E+01 3.745E+00 8.639E-01 46.3516.5 6.879E-01 3.163E+01 3.681E+00 8.438E-01 45.7617.0 6.730E-01 3.088E+01 3.620E+00 8.243E-01 45.1917.5 6.584E-01 3.015E+01 3.563E+00 8.055E-01 44.6118.0 6.439E-01 2.944E+01 3.507E+00 7.872E-01 44.0518.5 6.296E-01 2.875E+01 3.454E+00 7.695E-01 43.4919.0 6.156E-01 2.808E+01 3.404E+00 7.523E-01 42.9319.5 6.018E-01 2.743E+01 3.355E+00 7.356E-01 42.3820.0 5.882E-01 2.680E+01 3.308E+00 7.194E-01 41.8420.5 5.748E-01 2.618E+01 3.263E+00 7.037E-01 41.3021.0 5.617E-01 2.559E+01 3.220E+00 6.884E-01 40.7721.5 5.489E-01 2.501E+01 3.179E+00 6.736E-01 40.2522.0 5.363E-01 2.445E+01 3.139E+00 6.592E-01 39.7322.5 5.239E-01 2.390E+01 3.100E+00 6.452E-01 39.2223.0 5.119E-01 2.337E+01 3.063E+00 6.316E-01 38.7123.5 5.001E-01 2.286E+01 3.026E+00 6.184E-01 38.2124.0 4.885E-01 2.236E+01 2.992E+00 6.056E-01 37.72

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

176

(decimal)dry basis

(%)wet basis

24.5 4.772E-01 2.187E+01 2.958E+00 5.931E-01 37.2325.0 4.662E-01 2.140E+01 2.925E+00 5.810E-01 36.7525.5 4.554E-01 2.094E+01 2.894E+00 5.692E-01 36.2726.0 4.449E-01 2.049E+01 2.863E+00 5.577E-01 35.8026.5 4.346E-01 2.005E+01 2.834E+00 5.466E-01 35.3427.0 4.245E-01 1.963E+01 2.805E+00 5.357E-01 34.8827.5 4.148E-01 1.922E+01 2.777E+00 5.252E-01 34.4328.0 4.052E-01 1.881E+01 2.750E+00 5.149E-01 33.9928.5 3.959E-01 1.842E+01 2.724E+00 5.049E-01 33.5529.0 3.868E-01 1.804E+01 2.698E+00 4.952E-01 33.1229.5 3.779E-01 1.768E+01 2.674E+00 4.858E-01 32.7030.0 3.693E-01 1.732E+01 2.650E+00 4.766E-01 32.2830.5 3.609E-01 1.697E+01 2.626E+00 4.677E-01 31.8631.0 3.527E-01 1.663E+01 2.604E+00 4.590E-01 31.4631.5 3.447E-01 1.630E+01 2.582E+00 4.505E-01 31.0632.0 3.369E-01 1.597E+01 2.561E+00 4.423E-01 30.6732.5 3.293E-01 1.566E+01 2.540E+00 4.343E-01 30.2833.0 3.219E-01 1.536E+01 2.520E+00 4.265E-01 29.9033.5 3.146E-01 1.506E+01 2.500E+00 4.189E-01 29.5234.0 3.076E-01 1.477E+01 2.481E+00 4.115E-01 29.1634.5 3.008E-01 1.449E+01 2.463E+00 4.044E-01 28.7935.0 2.941E-01 1.422E+01 2.445E+00 3.974E-01 28.4435.5 2.876E-01 1.395E+01 2.427E+00 3.906E-01 28.0936.0 2.813E-01 1.369E+01 2.410E+00 3.840E-01 27.7436.5 2.751E-01 1.344E+01 2.394E+00 3.775E-01 27.4137.0 2.692E-01 1.319E+01 2.378E+00 3.713E-01 27.0737.5 2.633E-01 1.296E+01 2.362E+00 3.652E-01 26.7538.0 2.576E-01 1.272E+01 2.347E+00 3.592E-01 26.4338.5 2.521E-01 1.250E+01 2.332E+00 3.535E-01 26.1239.0 2.467E-01 1.228E+01 2.317E+00 3.478E-01 25.8139.5 2.415E-01 1.206E+01 2.303E+00 3.424E-01 25.5040.0 2.364E-01 1.185E+01 2.290E+00 3.370E-01 25.2140.5 2.314E-01 1.165E+01 2.277E+00 3.319E-01 24.9241.0 2.265E-01 1.145E+01 2.264E+00 3.268E-01 24.6341.5 2.218E-01 1.126E+01 2.251E+00 3.219E-01 24.3542.0 2.172E-01 1.108E+01 2.239E+00 3.171E-01 24.0842.5 2.128E-01 1.089E+01 2.227E+00 3.125E-01 23.8143.0 2.084E-01 1.072E+01 2.215E+00 3.080E-01 23.5543.5 2.042E-01 1.054E+01 2.204E+00 3.036E-01 23.2944.0 2.001E-01 1.038E+01 2.193E+00 2.993E-01 23.0344.5 1.961E-01 1.021E+01 2.183E+00 2.951E-01 22.7945.0 1.921E-01 1.005E+01 2.172E+00 2.911E-01 22.5445.5 1.883E-01 9.899E+00 2.162E+00 2.871E-01 22.3146.0 1.846E-01 9.749E+00 2.152E+00 2.833E-01 22.0746.5 1.810E-01 9.602E+00 2.143E+00 2.795E-01 21.8547.0 1.775E-01 9.460E+00 2.133E+00 2.759E-01 21.6247.5 1.741E-01 9.321E+00 2.124E+00 2.723E-01 21.4048.0 1.708E-01 9.186E+00 2.116E+00 2.689E-01 21.19

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

177

(decimal)dry basis

(%)wet basis

48.5 1.676E-01 9.054E+00 2.107E+00 2.655E-01 20.9849.0 1.644E-01 8.926E+00 2.099E+00 2.622E-01 20.7849.5 1.614E-01 8.802E+00 2.090E+00 2.591E-01 20.5850.0 1.584E-01 8.680E+00 2.083E+00 2.560E-01 20.3850.5 1.555E-01 8.562E+00 2.075E+00 2.530E-01 20.1951.0 1.526E-01 8.447E+00 2.067E+00 2.500E-01 20.0051.5 1.499E-01 8.336E+00 2.060E+00 2.472E-01 19.8252.0 1.472E-01 8.227E+00 2.053E+00 2.444E-01 19.6452.5 1.446E-01 8.121E+00 2.046E+00 2.417E-01 19.4653.0 1.421E-01 8.018E+00 2.039E+00 2.390E-01 19.2953.5 1.396E-01 7.918E+00 2.033E+00 2.365E-01 19.1354.0 1.372E-01 7.820E+00 2.027E+00 2.340E-01 18.9654.5 1.349E-01 7.725E+00 2.020E+00 2.316E-01 18.8055.0 1.326E-01 7.632E+00 2.014E+00 2.292E-01 18.6555.5 1.304E-01 7.542E+00 2.008E+00 2.269E-01 18.4956.0 1.282E-01 7.455E+00 2.003E+00 2.247E-01 18.3456.5 1.261E-01 7.369E+00 1.997E+00 2.225E-01 18.2057.0 1.241E-01 7.286E+00 1.992E+00 2.204E-01 18.0657.5 1.221E-01 7.205E+00 1.986E+00 2.183E-01 17.9258.0 1.201E-01 7.127E+00 1.981E+00 2.163E-01 17.7858.5 1.183E-01 7.050E+00 1.976E+00 2.143E-01 17.6559.0 1.164E-01 6.976E+00 1.972E+00 2.124E-01 17.5259.5 1.146E-01 6.903E+00 1.967E+00 2.106E-01 17.3960.0 1.129E-01 6.833E+00 1.962E+00 2.088E-01 17.2760.5 1.112E-01 6.764E+00 1.958E+00 2.070E-01 17.1561.0 1.096E-01 6.697E+00 1.953E+00 2.053E-01 17.0361.5 1.080E-01 6.632E+00 1.949E+00 2.036E-01 16.9262.0 1.064E-01 6.569E+00 1.945E+00 2.020E-01 16.8162.5 1.049E-01 6.507E+00 1.941E+00 2.005E-01 16.7063.0 1.034E-01 6.447E+00 1.937E+00 1.989E-01 16.5963.5 1.020E-01 6.388E+00 1.933E+00 1.974E-01 16.4964.0 1.006E-01 6.332E+00 1.930E+00 1.960E-01 16.3964.5 9.921E-02 6.276E+00 1.926E+00 1.946E-01 16.2965.0 9.788E-02 6.222E+00 1.922E+00 1.932E-01 16.1965.5 9.659E-02 6.170E+00 1.919E+00 1.918E-01 16.1066.0 9.533E-02 6.119E+00 1.916E+00 1.905E-01 16.0066.5 9.411E-02 6.069E+00 1.912E+00 1.893E-01 15.9267.0 9.292E-02 6.021E+00 1.909E+00 1.880E-01 15.8367.5 9.176E-02 5.974E+00 1.906E+00 1.868E-01 15.7468.0 9.064E-02 5.928E+00 1.903E+00 1.857E-01 15.6668.5 8.954E-02 5.884E+00 1.900E+00 1.845E-01 15.5869.0 8.847E-02 5.840E+00 1.898E+00 1.834E-01 15.5069.5 8.743E-02 5.798E+00 1.895E+00 1.823E-01 15.4270.0 8.642E-02 5.757E+00 1.892E+00 1.813E-01 15.3570.5 8.543E-02 5.717E+00 1.889E+00 1.803E-01 15.2771.0 8.448E-02 5.678E+00 1.887E+00 1.793E-01 15.2071.5 8.354E-02 5.640E+00 1.884E+00 1.783E-01 15.1372.0 8.263E-02 5.603E+00 1.882E+00 1.774E-01 15.06

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

178

T=55oC u=1.0m/s

(decimal)dry basis

(%)wet basis

0.0 1.038.E+00 8.931E+01 1.762.E+01 2.531E+00 71.680.5 1.038.E+00 6.919E+01 7.251.E+00 1.816E+00 64.491.0 1.038.E+00 5.738E+01 5.411.E+00 1.496E+00 59.931.5 1.038.E+00 4.849E+01 4.320.E+00 1.262E+00 55.792.0 9.291.E-01 4.154E+01 3.660.E+00 1.081E+00 51.952.5 8.279.E-01 3.581E+01 3.187.E+00 9.333E-01 48.273.0 7.225.E-01 3.100E+01 2.831.E+00 8.099E-01 44.753.5 6.295.E-01 2.692E+01 2.545.E+00 7.054E-01 41.364.0 5.463.E-01 2.344E+01 2.308.E+00 6.162E-01 38.134.5 4.742.E-01 2.045E+01 2.108.E+00 5.398E-01 35.065.0 4.116.E-01 1.788E+01 1.938.E+00 4.742E-01 32.175.5 3.576.E-01 1.568E+01 1.792.E+00 4.179E-01 29.476.0 3.111.E-01 1.378E+01 1.667.E+00 3.694E-01 26.986.5 2.711.E-01 1.215E+01 1.560.E+00 3.278E-01 24.687.0 2.367.E-01 1.075E+01 1.467.E+00 2.919E-01 22.607.5 2.070.E-01 9.546E+00 1.388.E+00 2.611E-01 20.718.0 1.815.E-01 8.510E+00 1.320.E+00 2.346E-01 19.008.5 1.596.E-01 7.618E+00 1.261.E+00 2.118E-01 17.489.0 1.408.E-01 6.851E+00 1.211.E+00 1.922E-01 16.129.5 1.245.E-01 6.191E+00 1.167.E+00 1.754E-01 14.9210.0 1.106.E-01 5.624E+00 1.130.E+00 1.609E-01 13.8610.5 9.859.E-02 5.136E+00 1.098.E+00 1.484E-01 12.9211.0 8.827.E-02 4.716E+00 1.070.E+00 1.377E-01 12.1011.5 7.940.E-02 4.355E+00 1.047.E+00 1.285E-01 11.3812.0 7.177.E-02 4.045E+00 1.026.E+00 1.205E-01 10.7612.5 6.520.E-02 3.778E+00 1.009.E+00 1.137E-01 10.2113.0 5.955.E-02 3.548E+00 9.934.E-01 1.078E-01 9.7313.5 5.470.E-02 3.351E+00 9.804.E-01 1.028E-01 9.3214.0 5.052.E-02 3.181E+00 9.692.E-01 9.845E-02 8.9614.5 4.693.E-02 3.035E+00 9.596.E-01 9.472E-02 8.65

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

179

T=45oC u=1.0m/s

T=35oC

(decimal)dry basis

(%)wet basis

0.0 1.015E+00 8.730E+01 1.711E+01 2.471E+00 71.190.5 1.015E+00 7.522E+01 1.115E+01 2.048E+00 67.191.0 1.015E+00 6.624E+01 8.115E+00 1.766E+00 63.851.5 1.015E+00 5.911E+01 6.452E+00 1.560E+00 60.952.0 9.996E-01 5.322E+01 5.438E+00 1.398E+00 58.302.5 9.671E-01 4.822E+01 4.758E+00 1.264E+00 55.843.0 9.218E-01 4.388E+01 4.267E+00 1.150E+00 53.493.5 8.690E-01 4.007E+01 3.891E+00 1.051E+00 51.234.0 8.128E-01 3.668E+01 3.591E+00 9.628E-01 49.054.5 7.559E-01 3.364E+01 3.342E+00 8.846E-01 46.945.0 7.004E-01 3.091E+01 3.131E+00 8.143E-01 44.885.5 6.473E-01 2.844E+01 2.949E+00 7.509E-01 42.896.0 5.972E-01 2.620E+01 2.789E+00 6.935E-01 40.956.5 5.504E-01 2.417E+01 2.647E+00 6.414E-01 39.087.0 5.070E-01 2.232E+01 2.521E+00 5.941E-01 37.277.5 4.669E-01 2.063E+01 2.407E+00 5.510E-01 35.528.0 4.299E-01 1.910E+01 2.304E+00 5.117E-01 33.858.5 3.960E-01 1.770E+01 2.211E+00 4.759E-01 32.249.0 3.649E-01 1.642E+01 2.127E+00 4.432E-01 30.719.5 3.365E-01 1.525E+01 2.050E+00 4.133E-01 29.25

10.0 3.104E-01 1.418E+01 1.980E+00 3.861E-01 27.8610.5 2.866E-01 1.321E+01 1.916E+00 3.613E-01 26.5411.0 2.648E-01 1.232E+01 1.858E+00 3.386E-01 25.2911.5 2.448E-01 1.151E+01 1.805E+00 3.178E-01 24.1212.0 2.266E-01 1.077E+01 1.756E+00 2.989E-01 23.0112.5 2.100E-01 1.009E+01 1.712E+00 2.816E-01 21.9713.0 1.948E-01 9.475E+00 1.671E+00 2.658E-01 21.0013.5 1.809E-01 8.911E+00 1.635E+00 2.514E-01 20.0914.0 1.682E-01 8.395E+00 1.601E+00 2.382E-01 19.2414.5 1.566E-01 7.924E+00 1.570E+00 2.262E-01 18.4515.0 1.460E-01 7.494E+00 1.542E+00 2.152E-01 17.7115.5 1.364E-01 7.101E+00 1.516E+00 2.052E-01 17.0216.0 1.275E-01 6.742E+00 1.493E+00 1.960E-01 16.3916.5 1.195E-01 6.414E+00 1.472E+00 1.876E-01 15.8017.0 1.121E-01 6.114E+00 1.452E+00 1.800E-01 15.2517.5 1.054E-01 5.841E+00 1.434E+00 1.730E-01 14.7518.0 9.923E-02 5.591E+00 1.418E+00 1.666E-01 14.2818.5 9.361E-02 5.363E+00 1.403E+00 1.608E-01 13.8519.0 8.848E-02 5.154E+00 1.389E+00 1.554E-01 13.4519.5 8.379E-02 4.964E+00 1.377E+00 1.506E-01 13.0920.0 7.951E-02 4.790E+00 1.366E+00 1.461E-01 12.7520.5 7.560E-02 4.631E+00 1.355E+00 1.421E-01 12.4421.0 7.203E-02 4.486E+00 1.346E+00 1.384E-01 12.1621.5 6.877E-02 4.354E+00 1.337E+00 1.350E-01 11.8922.0 6.579E-02 4.233E+00 1.329E+00 1.319E-01 11.65

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

180

u=1.0m/s

(decimal)dry basis

(%)wet basis

0.0 1.011E+00 8.695E+01 1.704E+01 2.461E+00 71.110.5 1.011E+00 8.173E+01 1.482E+01 2.287E+00 69.571.0 1.011E+00 7.709E+01 1.276E+01 2.130E+00 68.051.5 1.011E+00 7.295E+01 1.114E+01 1.995E+00 66.612.0 1.010E+00 6.921E+01 9.866E+00 1.877E+00 65.242.5 1.009E+00 6.582E+01 8.847E+00 1.774E+00 63.953.0 1.005E+00 6.271E+01 8.026E+00 1.681E+00 62.713.5 9.994E-01 5.985E+01 7.357E+00 1.599E+00 61.524.0 9.914E-01 5.721E+01 6.806E+00 1.524E+00 60.374.5 9.811E-01 5.476E+01 6.346E+00 1.455E+00 59.275.0 9.685E-01 5.247E+01 5.959E+00 1.392E+00 58.205.5 9.539E-01 5.033E+01 5.630E+00 1.334E+00 57.156.0 9.374E-01 4.832E+01 5.346E+00 1.280E+00 56.146.5 9.194E-01 4.643E+01 5.100E+00 1.229E+00 55.147.0 9.000E-01 4.464E+01 4.884E+00 1.182E+00 54.177.5 8.796E-01 4.295E+01 4.693E+00 1.137E+00 53.218.0 8.584E-01 4.135E+01 4.522E+00 1.095E+00 52.278.5 8.365E-01 3.983E+01 4.369E+00 1.056E+00 51.359.0 8.143E-01 3.839E+01 4.230E+00 1.018E+00 50.449.5 7.917E-01 3.701E+01 4.103E+00 9.821E-01 49.5510.0 7.692E-01 3.570E+01 3.987E+00 9.482E-01 48.6710.5 7.466E-01 3.445E+01 3.880E+00 9.158E-01 47.8011.0 7.242E-01 3.325E+01 3.782E+00 8.849E-01 46.9511.5 7.021E-01 3.211E+01 3.690E+00 8.555E-01 46.1112.0 6.802E-01 3.102E+01 3.604E+00 8.274E-01 45.2812.5 6.588E-01 2.997E+01 3.524E+00 8.004E-01 44.4613.0 6.378E-01 2.897E+01 3.448E+00 7.747E-01 43.6513.5 6.173E-01 2.801E+01 3.377E+00 7.500E-01 42.8614.0 5.972E-01 2.709E+01 3.310E+00 7.264E-01 42.0814.5 5.777E-01 2.620E+01 3.247E+00 7.038E-01 41.3115.0 5.588E-01 2.536E+01 3.187E+00 6.821E-01 40.5515.5 5.404E-01 2.454E+01 3.130E+00 6.613E-01 39.8016.0 5.225E-01 2.376E+01 3.075E+00 6.413E-01 39.0716.5 5.052E-01 2.301E+01 3.024E+00 6.221E-01 38.3517.0 4.885E-01 2.229E+01 2.975E+00 6.037E-01 37.6417.5 4.723E-01 2.160E+01 2.928E+00 5.860E-01 36.9518.0 4.566E-01 2.094E+01 2.883E+00 5.690E-01 36.2618.5 4.415E-01 2.030E+01 2.840E+00 5.527E-01 35.5919.0 4.269E-01 1.969E+01 2.799E+00 5.370E-01 34.9419.5 4.128E-01 1.910E+01 2.760E+00 5.219E-01 34.2920.0 3.992E-01 1.853E+01 2.722E+00 5.074E-01 33.6620.5 3.860E-01 1.798E+01 2.686E+00 4.935E-01 33.0421.0 3.734E-01 1.746E+01 2.651E+00 4.801E-01 32.4421.5 3.612E-01 1.696E+01 2.618E+00 4.672E-01 31.8422.0 3.495E-01 1.647E+01 2.586E+00 4.549E-01 31.2722.5 3.381E-01 1.601E+01 2.556E+00 4.430E-01 30.7023.0 3.272E-01 1.556E+01 2.527E+00 4.315E-01 30.1423.5 3.167E-01 1.513E+01 2.498E+00 4.205E-01 29.6024.0 3.066E-01 1.471E+01 2.471E+00 4.100E-01 29.0824.5 2.969E-01 1.431E+01 2.445E+00 3.998E-01 28.5625.0 2.875E-01 1.393E+01 2.420E+00 3.900E-01 28.06

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

181

(decimal)dry basis

(%)wet basis

25.5 2.785E-01 1.356E+01 2.397E+00 3.806E-01 27.5726.0 2.698E-01 1.321E+01 2.373E+00 3.715E-01 27.0926.5 2.615E-01 1.287E+01 2.351E+00 3.628E-01 26.6227.0 2.534E-01 1.254E+01 2.330E+00 3.545E-01 26.1727.5 2.457E-01 1.222E+01 2.310E+00 3.464E-01 25.7328.0 2.382E-01 1.192E+01 2.290E+00 3.387E-01 25.3028.5 2.311E-01 1.163E+01 2.271E+00 3.312E-01 24.8829.0 2.242E-01 1.135E+01 2.253E+00 3.241E-01 24.4729.5 2.175E-01 1.108E+01 2.235E+00 3.172E-01 24.0830.0 2.111E-01 1.082E+01 2.219E+00 3.105E-01 23.7030.5 2.050E-01 1.057E+01 2.202E+00 3.042E-01 23.3231.0 1.991E-01 1.033E+01 2.187E+00 2.980E-01 22.9631.5 1.934E-01 1.010E+01 2.172E+00 2.921E-01 22.6132.0 1.879E-01 9.876E+00 2.158E+00 2.864E-01 22.2732.5 1.827E-01 9.662E+00 2.144E+00 2.810E-01 21.9433.0 1.776E-01 9.457E+00 2.130E+00 2.757E-01 21.6133.5 1.727E-01 9.259E+00 2.118E+00 2.707E-01 21.3034.0 1.680E-01 9.069E+00 2.105E+00 2.658E-01 21.0034.5 1.635E-01 8.885E+00 2.093E+00 2.612E-01 20.7135.0 1.592E-01 8.709E+00 2.082E+00 2.567E-01 20.4235.5 1.550E-01 8.540E+00 2.071E+00 2.523E-01 20.1536.0 1.510E-01 8.377E+00 2.061E+00 2.482E-01 19.8836.5 1.472E-01 8.220E+00 2.050E+00 2.442E-01 19.6337.0 1.434E-01 8.069E+00 2.041E+00 2.403E-01 19.3837.5 1.399E-01 7.924E+00 2.031E+00 2.366E-01 19.1338.0 1.364E-01 7.785E+00 2.022E+00 2.331E-01 18.9038.5 1.331E-01 7.651E+00 2.014E+00 2.296E-01 18.6739.0 1.299E-01 7.521E+00 2.005E+00 2.263E-01 18.4639.5 1.269E-01 7.397E+00 1.997E+00 2.232E-01 18.2440.0 1.239E-01 7.278E+00 1.990E+00 2.201E-01 18.0440.5 1.211E-01 7.163E+00 1.982E+00 2.172E-01 17.8441.0 1.184E-01 7.052E+00 1.975E+00 2.144E-01 17.6541.5 1.158E-01 6.946E+00 1.968E+00 2.116E-01 17.4742.0 1.132E-01 6.844E+00 1.962E+00 2.090E-01 17.2942.5 1.108E-01 6.745E+00 1.955E+00 2.065E-01 17.1243.0 1.085E-01 6.651E+00 1.949E+00 2.041E-01 16.9543.5 1.062E-01 6.560E+00 1.943E+00 2.018E-01 16.7944.0 1.041E-01 6.472E+00 1.937E+00 1.995E-01 16.6344.5 1.020E-01 6.388E+00 1.932E+00 1.974E-01 16.4845.0 1.000E-01 6.307E+00 1.927E+00 1.953E-01 16.3445.5 9.808E-02 6.229E+00 1.922E+00 1.933E-01 16.2046.0 9.624E-02 6.154E+00 1.917E+00 1.914E-01 16.0746.5 9.446E-02 6.081E+00 1.912E+00 1.896E-01 15.9447.0 9.275E-02 6.012E+00 1.908E+00 1.878E-01 15.8147.5 9.110E-02 5.945E+00 1.903E+00 1.861E-01 15.6948.0 8.952E-02 5.881E+00 1.899E+00 1.844E-01 15.5748.5 8.800E-02 5.819E+00 1.895E+00 1.829E-01 15.4649.0 8.653E-02 5.760E+00 1.891E+00 1.814E-01 15.3549.5 8.512E-02 5.703E+00 1.888E+00 1.799E-01 15.2550.0 8.377E-02 5.648E+00 1.884E+00 1.785E-01 15.1550.5 8.246E-02 5.595E+00 1.881E+00 1.771E-01 15.05

Totalt (hours)

M bar1

M bar 2

M bar 3

Appendices

182

APPENDIX 9: CALCULATION OF THE AVERAGE PIPERINE CONTENT

BASED ON THE PIPERINE PROFILE OF A BERRY

T=55oC u=0.5m/s

(decimal)dry basis

(%)wet basis

0.0 2.521E-02 2.168E+00 8.085E-01 7.036E-02 6.570.5 2.521E-02 2.163E+00 8.062E-01 7.019E-02 6.561.0 2.521E-02 2.159E+00 8.040E-01 7.004E-02 6.551.5 2.521E-02 2.155E+00 8.019E-01 6.988E-02 6.532.0 2.521E-02 2.150E+00 7.998E-01 6.973E-02 6.522.5 2.521E-02 2.146E+00 7.979E-01 6.959E-02 6.513.0 2.521E-02 2.142E+00 7.959E-01 6.944E-02 6.493.5 2.521E-02 2.138E+00 7.941E-01 6.930E-02 6.484.0 2.521E-02 2.134E+00 7.923E-01 6.917E-02 6.474.5 2.521E-02 2.130E+00 7.906E-01 6.903E-02 6.465.0 2.521E-02 2.126E+00 7.889E-01 6.890E-02 6.455.5 2.521E-02 2.122E+00 7.873E-01 6.878E-02 6.446.0 2.521E-02 2.118E+00 7.858E-01 6.865E-02 6.426.5 2.521E-02 2.114E+00 7.843E-01 6.853E-02 6.417.0 2.521E-02 2.111E+00 7.829E-01 6.841E-02 6.407.5 2.521E-02 2.107E+00 7.815E-01 6.829E-02 6.398.0 2.521E-02 2.104E+00 7.801E-01 6.818E-02 6.388.5 2.521E-02 2.100E+00 7.788E-01 6.807E-02 6.379.0 2.521E-02 2.097E+00 7.776E-01 6.796E-02 6.369.5 2.520E-02 2.093E+00 7.764E-01 6.785E-02 6.35

10.0 2.520E-02 2.090E+00 7.752E-01 6.774E-02 6.3410.5 2.520E-02 2.087E+00 7.741E-01 6.764E-02 6.3411.0 2.520E-02 2.084E+00 7.730E-01 6.754E-02 6.3311.5 2.520E-02 2.080E+00 7.719E-01 6.744E-02 6.3212.0 2.520E-02 2.077E+00 7.709E-01 6.734E-02 6.3112.5 2.520E-02 2.074E+00 7.699E-01 6.725E-02 6.3013.0 2.519E-02 2.071E+00 7.689E-01 6.715E-02 6.2913.5 2.519E-02 2.068E+00 7.680E-01 6.706E-02 6.2814.0 2.519E-02 2.065E+00 7.671E-01 6.697E-02 6.2814.5 2.518E-02 2.062E+00 7.662E-01 6.688E-02 6.2715.0 2.518E-02 2.059E+00 7.654E-01 6.680E-02 6.2615.5 2.518E-02 2.057E+00 7.646E-01 6.671E-02 6.2516.0 2.517E-02 2.054E+00 7.638E-01 6.663E-02 6.2516.5 2.517E-02 2.051E+00 7.630E-01 6.654E-02 6.2417.0 2.517E-02 2.048E+00 7.623E-01 6.646E-02 6.2317.5 2.516E-02 2.046E+00 7.616E-01 6.638E-02 6.2318.0 2.516E-02 2.043E+00 7.609E-01 6.631E-02 6.22

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

183

T=45oC u=0.5m/s

(decimal)dry basis

(%)wet basis


10.0 2.554E-02 2.135E+00 7.863E-01 6.907E-02 6.4610.5 2.554E-02 2.132E+00 7.853E-01 6.898E-02 6.4511.0 2.554E-02 2.130E+00 7.843E-01 6.889E-02 6.4511.5 2.554E-02 2.127E+00 7.833E-01 6.881E-02 6.4412.0 2.554E-02 2.124E+00 7.823E-01 6.872E-02 6.4312.5 2.554E-02 2.122E+00 7.814E-01 6.864E-02 6.4213.0 2.554E-02 2.119E+00 7.804E-01 6.856E-02 6.4213.5 2.554E-02 2.117E+00 7.795E-01 6.848E-02 6.4114.0 2.553E-02 2.114E+00 7.786E-01 6.840E-02 6.4014.5 2.553E-02 2.112E+00 7.778E-01 6.832E-02 6.3915.0 2.553E-02 2.109E+00 7.769E-01 6.824E-02 6.3915.5 2.553E-02 2.107E+00 7.761E-01 6.816E-02 6.3816.0 2.553E-02 2.104E+00 7.753E-01 6.809E-02 6.3716.5 2.553E-02 2.102E+00 7.745E-01 6.802E-02 6.3717.0 2.553E-02 2.100E+00 7.738E-01 6.794E-02 6.3617.5 2.553E-02 2.097E+00 7.730E-01 6.787E-02 6.36

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

184

(decimal)dry basis

(%)wet basis

18.0 2.552E-02 2.095E+00 7.723E-01 6.780E-02 6.3518.5 2.552E-02 2.093E+00 7.716E-01 6.773E-02 6.3419.0 2.552E-02 2.090E+00 7.709E-01 6.766E-02 6.3419.5 2.552E-02 2.088E+00 7.702E-01 6.759E-02 6.3320.0 2.552E-02 2.086E+00 7.695E-01 6.752E-02 6.3320.5 2.551E-02 2.084E+00 7.689E-01 6.746E-02 6.3221.0 2.551E-02 2.082E+00 7.682E-01 6.739E-02 6.3121.5 2.551E-02 2.079E+00 7.676E-01 6.733E-02 6.3122.0 2.551E-02 2.077E+00 7.670E-01 6.726E-02 6.3022.5 2.550E-02 2.075E+00 7.664E-01 6.720E-02 6.3023.0 2.550E-02 2.073E+00 7.658E-01 6.714E-02 6.2923.5 2.550E-02 2.071E+00 7.653E-01 6.707E-02 6.2924.0 2.549E-02 2.069E+00 7.647E-01 6.701E-02 6.2824.5 2.549E-02 2.067E+00 7.642E-01 6.695E-02 6.2825.0 2.549E-02 2.065E+00 7.636E-01 6.689E-02 6.2725.5 2.548E-02 2.063E+00 7.631E-01 6.684E-02 6.2626.0 2.548E-02 2.061E+00 7.626E-01 6.678E-02 6.2626.5 2.548E-02 2.059E+00 7.621E-01 6.672E-02 6.2527.0 2.547E-02 2.057E+00 7.616E-01 6.666E-02 6.2527.5 2.547E-02 2.055E+00 7.611E-01 6.661E-02 6.2428.0 2.546E-02 2.053E+00 7.607E-01 6.655E-02 6.2428.5 2.546E-02 2.051E+00 7.602E-01 6.650E-02 6.2329.0 2.545E-02 2.050E+00 7.598E-01 6.644E-02 6.2329.5 2.545E-02 2.048E+00 7.593E-01 6.639E-02 6.2330.0 2.544E-02 2.046E+00 7.589E-01 6.633E-02 6.2230.5 2.544E-02 2.044E+00 7.585E-01 6.628E-02 6.2231.0 2.543E-02 2.042E+00 7.581E-01 6.623E-02 6.2131.5 2.543E-02 2.041E+00 7.577E-01 6.618E-02 6.2132.0 2.542E-02 2.039E+00 7.573E-01 6.613E-02 6.2032.5 2.542E-02 2.037E+00 7.569E-01 6.608E-02 6.2033.0 2.541E-02 2.035E+00 7.565E-01 6.603E-02 6.1933.5 2.540E-02 2.034E+00 7.561E-01 6.598E-02 6.1934.0 2.540E-02 2.032E+00 7.557E-01 6.593E-02 6.19

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

185

T=35oC u=0.5m/s

(decimal)dry basis

(%)wet basis

0.0 2.554E-02 2.197E+00 8.139E-01 7.116E-02 6.640.5 2.554E-02 2.196E+00 8.136E-01 7.114E-02 6.641.0 2.554E-02 2.196E+00 8.135E-01 7.114E-02 6.641.5 2.554E-02 2.196E+00 8.134E-01 7.113E-02 6.642.0 2.554E-02 2.196E+00 8.133E-01 7.112E-02 6.642.5 2.554E-02 2.196E+00 8.132E-01 7.112E-02 6.643.0 2.554E-02 2.195E+00 8.131E-01 7.111E-02 6.643.5 2.554E-02 2.195E+00 8.130E-01 7.110E-02 6.644.0 2.554E-02 2.195E+00 8.129E-01 7.110E-02 6.644.5 2.554E-02 2.195E+00 8.128E-01 7.109E-02 6.645.0 2.554E-02 2.195E+00 8.127E-01 7.108E-02 6.645.5 2.554E-02 2.194E+00 8.126E-01 7.108E-02 6.646.0 2.554E-02 2.194E+00 8.125E-01 7.107E-02 6.646.5 2.554E-02 2.194E+00 8.125E-01 7.106E-02 6.637.0 2.554E-02 2.194E+00 8.124E-01 7.106E-02 6.637.5 2.554E-02 2.194E+00 8.123E-01 7.105E-02 6.638.0 2.554E-02 2.194E+00 8.122E-01 7.104E-02 6.638.5 2.554E-02 2.193E+00 8.121E-01 7.104E-02 6.639.0 2.554E-02 2.193E+00 8.120E-01 7.103E-02 6.639.5 2.554E-02 2.193E+00 8.119E-01 7.102E-02 6.6310.0 2.554E-02 2.193E+00 8.118E-01 7.102E-02 6.6310.5 2.554E-02 2.193E+00 8.117E-01 7.101E-02 6.6311.0 2.554E-02 2.192E+00 8.116E-01 7.100E-02 6.6311.5 2.554E-02 2.192E+00 8.115E-01 7.100E-02 6.6312.0 2.554E-02 2.192E+00 8.114E-01 7.099E-02 6.6312.5 2.554E-02 2.192E+00 8.113E-01 7.099E-02 6.6313.0 2.554E-02 2.192E+00 8.112E-01 7.098E-02 6.6313.5 2.554E-02 2.191E+00 8.112E-01 7.097E-02 6.6314.0 2.554E-02 2.191E+00 8.111E-01 7.097E-02 6.6314.5 2.554E-02 2.191E+00 8.110E-01 7.096E-02 6.6315.0 2.554E-02 2.191E+00 8.109E-01 7.095E-02 6.6315.5 2.554E-02 2.191E+00 8.108E-01 7.095E-02 6.6216.0 2.554E-02 2.191E+00 8.107E-01 7.094E-02 6.6216.5 2.554E-02 2.190E+00 8.106E-01 7.093E-02 6.6217.0 2.554E-02 2.190E+00 8.105E-01 7.093E-02 6.6217.5 2.554E-02 2.190E+00 8.104E-01 7.092E-02 6.6218.0 2.554E-02 2.190E+00 8.103E-01 7.091E-02 6.6218.5 2.554E-02 2.190E+00 8.102E-01 7.091E-02 6.6219.0 2.554E-02 2.189E+00 8.101E-01 7.090E-02 6.6219.5 2.554E-02 2.189E+00 8.101E-01 7.089E-02 6.6220.0 2.554E-02 2.189E+00 8.100E-01 7.089E-02 6.6220.5 2.554E-02 2.189E+00 8.099E-01 7.088E-02 6.6221.0 2.554E-02 2.189E+00 8.098E-01 7.087E-02 6.6221.5 2.554E-02 2.188E+00 8.097E-01 7.087E-02 6.6222.0 2.554E-02 2.188E+00 8.096E-01 7.086E-02 6.6222.5 2.554E-02 2.188E+00 8.095E-01 7.086E-02 6.6223.0 2.554E-02 2.188E+00 8.094E-01 7.085E-02 6.6223.5 2.554E-02 2.188E+00 8.093E-01 7.084E-02 6.6224.0 2.554E-02 2.188E+00 8.093E-01 7.084E-02 6.62

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

186

dry basis(decimal)

wet basis(%)

24.5 2.554E-02 2.187E+00 8.092E-01 7.083E-02 6.6125.0 2.554E-02 2.187E+00 8.091E-01 7.082E-02 6.6125.5 2.554E-02 2.187E+00 8.090E-01 7.082E-02 6.6126.0 2.554E-02 2.187E+00 8.089E-01 7.081E-02 6.6126.5 2.554E-02 2.187E+00 8.088E-01 7.080E-02 6.6127.0 2.554E-02 2.186E+00 8.087E-01 7.080E-02 6.6127.5 2.554E-02 2.186E+00 8.086E-01 7.079E-02 6.6128.0 2.554E-02 2.186E+00 8.085E-01 7.079E-02 6.6128.5 2.554E-02 2.186E+00 8.085E-01 7.078E-02 6.6129.0 2.554E-02 2.186E+00 8.084E-01 7.077E-02 6.6129.5 2.554E-02 2.186E+00 8.083E-01 7.077E-02 6.6130.0 2.554E-02 2.185E+00 8.082E-01 7.076E-02 6.6130.5 2.554E-02 2.185E+00 8.081E-01 7.075E-02 6.6131.0 2.554E-02 2.185E+00 8.080E-01 7.075E-02 6.6131.5 2.554E-02 2.185E+00 8.079E-01 7.074E-02 6.6132.0 2.554E-02 2.185E+00 8.078E-01 7.073E-02 6.6132.5 2.554E-02 2.184E+00 8.078E-01 7.073E-02 6.6133.0 2.554E-02 2.184E+00 8.077E-01 7.072E-02 6.6133.5 2.554E-02 2.184E+00 8.076E-01 7.072E-02 6.6034.0 2.554E-02 2.184E+00 8.075E-01 7.071E-02 6.6034.5 2.554E-02 2.184E+00 8.074E-01 7.070E-02 6.6035.0 2.554E-02 2.184E+00 8.073E-01 7.070E-02 6.6035.5 2.554E-02 2.183E+00 8.072E-01 7.069E-02 6.6036.0 2.554E-02 2.183E+00 8.071E-01 7.068E-02 6.6036.5 2.554E-02 2.183E+00 8.071E-01 7.068E-02 6.6037.0 2.554E-02 2.183E+00 8.070E-01 7.067E-02 6.6037.5 2.554E-02 2.183E+00 8.069E-01 7.067E-02 6.6038.0 2.554E-02 2.182E+00 8.068E-01 7.066E-02 6.6038.5 2.554E-02 2.182E+00 8.067E-01 7.065E-02 6.6039.0 2.554E-02 2.182E+00 8.066E-01 7.065E-02 6.6039.5 2.554E-02 2.182E+00 8.065E-01 7.064E-02 6.6040.0 2.554E-02 2.182E+00 8.065E-01 7.063E-02 6.6040.5 2.554E-02 2.182E+00 8.064E-01 7.063E-02 6.6041.0 2.554E-02 2.181E+00 8.063E-01 7.062E-02 6.6041.5 2.554E-02 2.181E+00 8.062E-01 7.062E-02 6.6042.0 2.554E-02 2.181E+00 8.061E-01 7.061E-02 6.6042.5 2.554E-02 2.181E+00 8.060E-01 7.060E-02 6.5943.0 2.554E-02 2.181E+00 8.060E-01 7.060E-02 6.5943.5 2.554E-02 2.180E+00 8.059E-01 7.059E-02 6.5944.0 2.554E-02 2.180E+00 8.058E-01 7.058E-02 6.5944.5 2.554E-02 2.180E+00 8.057E-01 7.058E-02 6.5945.0 2.554E-02 2.180E+00 8.056E-01 7.057E-02 6.5945.5 2.554E-02 2.180E+00 8.055E-01 7.057E-02 6.5946.0 2.554E-02 2.180E+00 8.054E-01 7.056E-02 6.5946.5 2.554E-02 2.179E+00 8.054E-01 7.055E-02 6.5947.0 2.554E-02 2.179E+00 8.053E-01 7.055E-02 6.5947.5 2.554E-02 2.179E+00 8.052E-01 7.054E-02 6.5948.0 2.554E-02 2.179E+00 8.051E-01 7.054E-02 6.59

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

187

(decimal)dry basis

(%)wet basis

48.5 2.554E-02 2.179E+00 8.050E-01 7.053E-02 6.5949.0 2.554E-02 2.178E+00 8.049E-01 7.052E-02 6.5949.5 2.554E-02 2.178E+00 8.049E-01 7.052E-02 6.5950.0 2.554E-02 2.178E+00 8.048E-01 7.051E-02 6.5950.5 2.554E-02 2.178E+00 8.047E-01 7.050E-02 6.5951.0 2.554E-02 2.178E+00 8.046E-01 7.050E-02 6.5951.5 2.554E-02 2.178E+00 8.045E-01 7.049E-02 6.5952.0 2.554E-02 2.177E+00 8.044E-01 7.049E-02 6.5852.5 2.554E-02 2.177E+00 8.044E-01 7.048E-02 6.5853.0 2.554E-02 2.177E+00 8.043E-01 7.047E-02 6.5853.5 2.554E-02 2.177E+00 8.042E-01 7.047E-02 6.5854.0 2.554E-02 2.177E+00 8.041E-01 7.046E-02 6.5854.5 2.554E-02 2.177E+00 8.040E-01 7.046E-02 6.5855.0 2.554E-02 2.176E+00 8.040E-01 7.045E-02 6.5855.5 2.554E-02 2.176E+00 8.039E-01 7.044E-02 6.5856.0 2.554E-02 2.176E+00 8.038E-01 7.044E-02 6.5856.5 2.554E-02 2.176E+00 8.037E-01 7.043E-02 6.5857.0 2.554E-02 2.176E+00 8.036E-01 7.043E-02 6.5857.5 2.554E-02 2.175E+00 8.035E-01 7.042E-02 6.5858.0 2.554E-02 2.175E+00 8.035E-01 7.041E-02 6.5858.5 2.554E-02 2.175E+00 8.034E-01 7.041E-02 6.5859.0 2.554E-02 2.175E+00 8.033E-01 7.040E-02 6.5859.5 2.554E-02 2.175E+00 8.032E-01 7.040E-02 6.5860.0 2.554E-02 2.175E+00 8.031E-01 7.039E-02 6.5860.5 2.554E-02 2.174E+00 8.031E-01 7.038E-02 6.5861.0 2.554E-02 2.174E+00 8.030E-01 7.038E-02 6.5861.5 2.554E-02 2.174E+00 8.029E-01 7.037E-02 6.5762.0 2.554E-02 2.174E+00 8.028E-01 7.037E-02 6.5762.5 2.554E-02 2.174E+00 8.027E-01 7.036E-02 6.5763.0 2.554E-02 2.174E+00 8.027E-01 7.035E-02 6.5763.5 2.554E-02 2.173E+00 8.026E-01 7.035E-02 6.5764.0 2.554E-02 2.173E+00 8.025E-01 7.034E-02 6.5764.5 2.554E-02 2.173E+00 8.024E-01 7.034E-02 6.5765.0 2.554E-02 2.173E+00 8.023E-01 7.033E-02 6.5765.5 2.554E-02 2.173E+00 8.023E-01 7.032E-02 6.5766.0 2.554E-02 2.173E+00 8.022E-01 7.032E-02 6.5766.5 2.554E-02 2.172E+00 8.021E-01 7.031E-02 6.5767.0 2.554E-02 2.172E+00 8.020E-01 7.031E-02 6.5767.5 2.554E-02 2.172E+00 8.019E-01 7.030E-02 6.5768.0 2.554E-02 2.172E+00 8.019E-01 7.029E-02 6.5768.5 2.554E-02 2.172E+00 8.018E-01 7.029E-02 6.5769.0 2.554E-02 2.171E+00 8.017E-01 7.028E-02 6.5769.5 2.554E-02 2.171E+00 8.016E-01 7.028E-02 6.5770.0 2.554E-02 2.171E+00 8.016E-01 7.027E-02 6.5770.5 2.554E-02 2.171E+00 8.015E-01 7.026E-02 6.5771.0 2.554E-02 2.171E+00 8.014E-01 7.026E-02 6.5671.5 2.554E-02 2.171E+00 8.013E-01 7.025E-02 6.5672.0 2.554E-02 2.170E+00 8.012E-01 7.025E-02 6.56

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

188

T=55oC u=1.0m/s

(decimal)dry basis

(%)wet basis

0.0 2.521E-02 2.168E+00 8.085E-01 7.036E-02 6.570.5 2.521E-02 2.161E+00 8.050E-01 7.011E-02 6.551.0 2.521E-02 2.154E+00 8.017E-01 6.987E-02 6.531.5 2.521E-02 2.148E+00 7.986E-01 6.964E-02 6.512.0 2.521E-02 2.141E+00 7.956E-01 6.942E-02 6.492.5 2.521E-02 2.135E+00 7.928E-01 6.921E-02 6.473.0 2.521E-02 2.129E+00 7.901E-01 6.900E-02 6.453.5 2.521E-02 2.123E+00 7.876E-01 6.880E-02 6.444.0 2.521E-02 2.117E+00 7.852E-01 6.861E-02 6.424.5 2.521E-02 2.111E+00 7.830E-01 6.843E-02 6.405.0 2.521E-02 2.106E+00 7.809E-01 6.825E-02 6.395.5 2.521E-02 2.100E+00 7.788E-01 6.807E-02 6.376.0 2.521E-02 2.095E+00 7.769E-01 6.791E-02 6.366.5 2.520E-02 2.090E+00 7.751E-01 6.774E-02 6.347.0 2.520E-02 2.085E+00 7.734E-01 6.759E-02 6.337.5 2.520E-02 2.080E+00 7.717E-01 6.743E-02 6.328.0 2.520E-02 2.075E+00 7.702E-01 6.728E-02 6.308.5 2.519E-02 2.071E+00 7.687E-01 6.714E-02 6.299.0 2.519E-02 2.066E+00 7.673E-01 6.700E-02 6.289.5 2.519E-02 2.062E+00 7.660E-01 6.686E-02 6.2710.0 2.518E-02 2.057E+00 7.647E-01 6.673E-02 6.2610.5 2.518E-02 2.053E+00 7.635E-01 6.660E-02 6.2411.0 2.517E-02 2.049E+00 7.623E-01 6.648E-02 6.2311.5 2.516E-02 2.045E+00 7.612E-01 6.636E-02 6.2212.0 2.516E-02 2.041E+00 7.602E-01 6.624E-02 6.2112.5 2.515E-02 2.037E+00 7.592E-01 6.612E-02 6.2013.0 2.514E-02 2.033E+00 7.582E-01 6.601E-02 6.1913.5 2.513E-02 2.029E+00 7.573E-01 6.590E-02 6.1814.0 2.512E-02 2.025E+00 7.564E-01 6.579E-02 6.1714.5 2.511E-02 2.022E+00 7.556E-01 6.568E-02 6.16

Totalt (hours)

P bar1

P bar 2

P bar 3

Appendices

189

T=45oC u=1.0m/s

(decimal)dry basis

(%)wet basis


10.0 2.491E-02 2.043E+00 7.637E-01 6.637E-02 6.2210.5 2.491E-02 2.039E+00 7.626E-01 6.625E-02 6.2111.0 2.490E-02 2.035E+00 7.615E-01 6.613E-02 6.2011.5 2.490E-02 2.032E+00 7.604E-01 6.602E-02 6.1912.0 2.489E-02 2.028E+00 7.594E-01 6.591E-02 6.1812.5 2.488E-02 2.024E+00 7.585E-01 6.580E-02 6.1713.0 2.488E-02 2.021E+00 7.576E-01 6.570E-02 6.1613.5 2.487E-02 2.017E+00 7.567E-01 6.559E-02 6.1614.0 2.486E-02 2.014E+00 7.559E-01 6.549E-02 6.1514.5 2.485E-02 2.010E+00 7.551E-01 6.540E-02 6.1415.0 2.484E-02 2.007E+00 7.543E-01 6.530E-02 6.1315.5 2.483E-02 2.004E+00 7.536E-01 6.521E-02 6.1216.0 2.482E-02 2.001E+00 7.529E-01 6.511E-02 6.1116.5 2.481E-02 1.997E+00 7.522E-01 6.502E-02 6.1117.0 2.480E-02 1.994E+00 7.515E-01 6.494E-02 6.1017.5 2.479E-02 1.991E+00 7.509E-01 6.485E-02 6.0918.0 2.478E-02 1.988E+00 7.503E-01 6.477E-02 6.0818.5 2.476E-02 1.985E+00 7.497E-01 6.468E-02 6.0819.0 2.475E-02 1.982E+00 7.492E-01 6.460E-02 6.0719.5 2.473E-02 1.980E+00 7.487E-01 6.452E-02 6.0620.0 2.472E-02 1.977E+00 7.482E-01 6.444E-02 6.0520.5 2.470E-02 1.974E+00 7.477E-01 6.437E-02 6.0521.0 2.469E-02 1.971E+00 7.472E-01 6.429E-02 6.0421.5 2.467E-02 1.969E+00 7.467E-01 6.422E-02 6.0322.0 2.465E-02 1.966E+00 7.463E-01 6.415E-02 6.03

Totalt (hours)

P bar1

P bar 2

P bar 3

Appendices

190

T=35oC u=1.0m/s

(decimal)dry basis

(%)wet basis

0.0 2.977E-02 2.561E+00 8.817E-01 8.137E-02 7.530.5 2.977E-02 2.556E+00 8.794E-01 8.121E-02 7.511.0 2.977E-02 2.551E+00 8.771E-01 8.105E-02 7.501.5 2.977E-02 2.547E+00 8.749E-01 8.090E-02 7.482.0 2.977E-02 2.542E+00 8.728E-01 8.074E-02 7.472.5 2.977E-02 2.538E+00 8.706E-01 8.059E-02 7.463.0 2.977E-02 2.534E+00 8.686E-01 8.044E-02 7.453.5 2.977E-02 2.529E+00 8.665E-01 8.029E-02 7.434.0 2.977E-02 2.525E+00 8.645E-01 8.014E-02 7.424.5 2.977E-02 2.521E+00 8.626E-01 8.000E-02 7.415.0 2.977E-02 2.517E+00 8.606E-01 7.986E-02 7.405.5 2.977E-02 2.513E+00 8.588E-01 7.971E-02 7.386.0 2.977E-02 2.509E+00 8.569E-01 7.957E-02 7.376.5 2.977E-02 2.504E+00 8.551E-01 7.944E-02 7.367.0 2.977E-02 2.500E+00 8.533E-01 7.930E-02 7.357.5 2.977E-02 2.496E+00 8.516E-01 7.917E-02 7.348.0 2.977E-02 2.492E+00 8.498E-01 7.903E-02 7.328.5 2.977E-02 2.489E+00 8.482E-01 7.890E-02 7.319.0 2.977E-02 2.485E+00 8.465E-01 7.877E-02 7.309.5 2.977E-02 2.481E+00 8.449E-01 7.864E-02 7.2910.0 2.977E-02 2.477E+00 8.433E-01 7.852E-02 7.2810.5 2.977E-02 2.473E+00 8.417E-01 7.839E-02 7.2711.0 2.977E-02 2.469E+00 8.402E-01 7.827E-02 7.2611.5 2.977E-02 2.466E+00 8.387E-01 7.814E-02 7.2512.0 2.977E-02 2.462E+00 8.372E-01 7.802E-02 7.2412.5 2.977E-02 2.458E+00 8.358E-01 7.790E-02 7.2313.0 2.977E-02 2.455E+00 8.343E-01 7.778E-02 7.2213.5 2.977E-02 2.451E+00 8.329E-01 7.767E-02 7.2114.0 2.977E-02 2.448E+00 8.316E-01 7.755E-02 7.2014.5 2.977E-02 2.444E+00 8.302E-01 7.744E-02 7.1915.0 2.977E-02 2.441E+00 8.289E-01 7.732E-02 7.1815.5 2.977E-02 2.437E+00 8.276E-01 7.721E-02 7.1716.0 2.977E-02 2.434E+00 8.263E-01 7.710E-02 7.1616.5 2.977E-02 2.430E+00 8.250E-01 7.699E-02 7.1517.0 2.976E-02 2.427E+00 8.238E-01 7.688E-02 7.1417.5 2.976E-02 2.423E+00 8.226E-01 7.678E-02 7.1318.0 2.976E-02 2.420E+00 8.214E-01 7.667E-02 7.1218.5 2.976E-02 2.417E+00 8.202E-01 7.657E-02 7.1119.0 2.976E-02 2.414E+00 8.191E-01 7.646E-02 7.1019.5 2.976E-02 2.410E+00 8.180E-01 7.636E-02 7.0920.0 2.976E-02 2.407E+00 8.169E-01 7.626E-02 7.0920.5 2.975E-02 2.404E+00 8.158E-01 7.616E-02 7.0821.0 2.975E-02 2.401E+00 8.147E-01 7.606E-02 7.0721.5 2.975E-02 2.398E+00 8.137E-01 7.596E-02 7.0622.0 2.975E-02 2.394E+00 8.126E-01 7.586E-02 7.0522.5 2.975E-02 2.391E+00 8.116E-01 7.577E-02 7.0423.0 2.975E-02 2.388E+00 8.106E-01 7.567E-02 7.0323.5 2.974E-02 2.385E+00 8.096E-01 7.558E-02 7.0324.0 2.974E-02 2.382E+00 8.087E-01 7.548E-02 7.0224.5 2.974E-02 2.379E+00 8.077E-01 7.539E-02 7.0125.0 2.974E-02 2.376E+00 8.068E-01 7.530E-02 7.00

t (hours)

P bar1

P bar 2

P bar 3

Total

Appendices

191

(decimal)dry basis

(%)wet basis

25.5 2.973E-02 2.373E+00 8.059E-01 7.521E-02 6.9926.0 2.973E-02 2.370E+00 8.050E-01 7.512E-02 6.9926.5 2.973E-02 2.367E+00 8.041E-01 7.503E-02 6.9827.0 2.973E-02 2.364E+00 8.032E-01 7.494E-02 6.9727.5 2.972E-02 2.362E+00 8.024E-01 7.485E-02 6.9628.0 2.972E-02 2.359E+00 8.015E-01 7.476E-02 6.9628.5 2.972E-02 2.356E+00 8.007E-01 7.468E-02 6.9529.0 2.971E-02 2.353E+00 7.999E-01 7.459E-02 6.9429.5 2.971E-02 2.350E+00 7.991E-01 7.451E-02 6.9330.0 2.970E-02 2.347E+00 7.983E-01 7.443E-02 6.9330.5 2.970E-02 2.345E+00 7.976E-01 7.434E-02 6.9231.0 2.970E-02 2.342E+00 7.968E-01 7.426E-02 6.9131.5 2.969E-02 2.339E+00 7.961E-01 7.418E-02 6.9132.0 2.969E-02 2.337E+00 7.953E-01 7.410E-02 6.9032.5 2.968E-02 2.334E+00 7.946E-01 7.402E-02 6.8933.0 2.968E-02 2.331E+00 7.939E-01 7.394E-02 6.8933.5 2.967E-02 2.329E+00 7.932E-01 7.386E-02 6.8834.0 2.967E-02 2.326E+00 7.925E-01 7.379E-02 6.8734.5 2.966E-02 2.323E+00 7.918E-01 7.371E-02 6.8635.0 2.966E-02 2.321E+00 7.912E-01 7.363E-02 6.8635.5 2.965E-02 2.318E+00 7.905E-01 7.356E-02 6.8536.0 2.965E-02 2.316E+00 7.899E-01 7.348E-02 6.8536.5 2.964E-02 2.313E+00 7.892E-01 7.341E-02 6.8437.0 2.964E-02 2.311E+00 7.886E-01 7.333E-02 6.8337.5 2.963E-02 2.308E+00 7.880E-01 7.326E-02 6.8338.0 2.963E-02 2.306E+00 7.874E-01 7.319E-02 6.8238.5 2.962E-02 2.303E+00 7.868E-01 7.312E-02 6.8139.0 2.961E-02 2.301E+00 7.862E-01 7.304E-02 6.8139.5 2.961E-02 2.298E+00 7.856E-01 7.297E-02 6.8040.0 2.960E-02 2.296E+00 7.850E-01 7.290E-02 6.8040.5 2.959E-02 2.294E+00 7.845E-01 7.283E-02 6.7941.0 2.959E-02 2.291E+00 7.839E-01 7.277E-02 6.7841.5 2.958E-02 2.289E+00 7.834E-01 7.270E-02 6.7842.0 2.957E-02 2.286E+00 7.829E-01 7.263E-02 6.7742.5 2.957E-02 2.284E+00 7.823E-01 7.256E-02 6.7743.0 2.956E-02 2.282E+00 7.818E-01 7.250E-02 6.7643.5 2.955E-02 2.279E+00 7.813E-01 7.243E-02 6.7544.0 2.954E-02 2.277E+00 7.808E-01 7.236E-02 6.7544.5 2.954E-02 2.275E+00 7.803E-01 7.230E-02 6.7445.0 2.953E-02 2.273E+00 7.798E-01 7.223E-02 6.7445.5 2.952E-02 2.270E+00 7.793E-01 7.217E-02 6.7346.0 2.951E-02 2.268E+00 7.789E-01 7.211E-02 6.7346.5 2.950E-02 2.266E+00 7.784E-01 7.204E-02 6.7247.0 2.949E-02 2.264E+00 7.779E-01 7.198E-02 6.7147.5 2.949E-02 2.261E+00 7.775E-01 7.192E-02 6.7148.0 2.948E-02 2.259E+00 7.770E-01 7.186E-02 6.7048.5 2.947E-02 2.257E+00 7.766E-01 7.179E-02 6.7049.0 2.946E-02 2.255E+00 7.762E-01 7.173E-02 6.6949.5 2.945E-02 2.253E+00 7.757E-01 7.167E-02 6.6950.0 2.944E-02 2.251E+00 7.753E-01 7.161E-02 6.6850.5 2.943E-02 2.249E+00 7.749E-01 7.155E-02 6.68

t (hours)

P bar1

P bar 2

P bar 3

Total

Date post:	30-Jul-2021
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Mathematical modelling and experimental investigation of drying … · 2017. 2. 20. · Table 2.1:...

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