thermal properties of selected materials for thermal insulation

THERMAL PROPERTIES OFSELECTED MATERIALS FOR

THERMAL INSULATION AVAILABLEIN UGANDA

BY

AYUGI GERTRUDE (B Sc. Ed, Mak)

Department of Physics

Makerere University

REG.NO:2009/HD13/15595U

A DISSERTATION SUBMITTED TO THE DIRECTORATE OF

RESEARCH AND GRADUATE TRAINING IN PARTIAL

FULFILLMENT FOR THE AWARD OF A DEGREE OF

MASTER OF SCIENCE (PHYSICS) OF MAKERERE

UNIVERSITY

DECEMBER 2011

Declaration

I certify that this dissertation which I now submit for examination for the award of Masters

of Science in Physics, is entirely my own work and has not been taken from the work of others

and to the extent that where such work has been cited, it has been acknowledged within the

text of my work.

Signature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ayugi Gertrude

2009/HD13/15595U

Supervisors

Signature:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Prof. E. J. K. B. Banda


Makerere University,

P.O Box 7062,

Kampala.

Signature:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Dr. Florence Mutonyi D'ujanga


Makerere University,

P.O Box 7062,

Kampala.

i

Dedication

This work is dedicated to my parents Mr. and Mrs Ogwal for their in-put in my education,

my late sister Diana Angwech, may her soul rest in eternal peace and my nephew Favor

Lubanga.

ii

Acknowledgments

I would like to express my deep appreciation and gratitude to the following people for helping

me complete this dissertation.

My �rst supervisor Prof. Eldad J.K.B. Banda at the Department of Physics Makerere Uni-

versity for his endless help, guidance and support throughout out the course of study.

My second supervisor Dr. Florence Mutonyi D'ujanga, the Head of Department of Physics

for her invaluable support and advice throughout the duration of this research.

All the Lecturers and Professors in the Department of Physics who taught me the �rst year

courses.

Mr. Benon Fred Twinamasiko, Assistant lecturer in the Department of Physics who allowed

me to access the keys to the project Laboratory anytime.

Mr. Dennis Okello , Assistant lecturer and a PhD. student at the Department of Physics

who helped me in various ways.

Mr. Micheal Okiror, the technician in charge of the project laboratory where the experiments

were carried out, Mr. Micheal Musoke , a technician in charge of the second year laboratory

and Mr. Ronald Nteziyaremye the technician in charge of the of the departmental workshop

for all their help during the time I was carrying out the experiments.

My brothers Robert Odong , Julius Elai, William Okello, Steven Ongwen and Geofrey Okulla

and sisters Teopista Akullo and Hellen Amongi for their support during the course of my

study as a postgraduate student.

I would also like to thank the sponsors of Millennium Science Initiative Project for having

iii

iv

provided some of the apparatus that was used during the experimental study.

Lastly, but most importantly, I extend my sincere appreciations to my sponsors NUFU project

`Small Scale Concentrating Solar Energy Systems ' for all the �nancial support without

which this work would have never become possible.

Contents

Declaration i

Dedication ii

Acknowledgments iii

Table of contents v

List of Figures viii

List of Tables x

Abstract xi

1 INTRODUCTION 1

1.1 Background of study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Statement of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Specif�ic objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.6 Signif�icance of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.7 Justif�ication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

v

CONTENTS vi

2 LITERATURE REVIEW 5

2.1 Thermal insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Benef�its of thermal insulation . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Types and Application . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Major thermal insulation materials used in thermal heat storage . . . . . . . 9

2.2.1 Calcium silicate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Mineral f�iber (rock and slag wool) . . . . . . . . . . . . . . . . . . . 9

2.2.3 F�ibre glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.4 Expanded silica, or perlite . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.5 Refractories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.6 Foamed plastic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.7 Insulating cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.8 Cotton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Thermal insulators available in Uganda . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.2 Ash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 Bagasse (Sugarcane f�ibres) . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.4 Banana f�ibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.5 Sawdust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.6 Charcoal dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Important thermal properties of an insulating material . . . . . . . . . . . . 20

2.4.1 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.3 Thermal dif�fusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.4 Other pertinent physical properties . . . . . . . . . . . . . . . . . . . 27

2.5 Measurement of thermal conductivity of insulators . . . . . . . . . . . . . . . 28

2.5.1 Steady state methods for measurement of thermal conductivity . . . . 28

CONTENTS vii

2.5.2 Transient state methods for measurement of thermal conductivity . . 31

2.6 Measurement of specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . 34

3 METHODS AND MATERIALS 39

3.1 Sample collection and preparation . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Measurement of thermal conductivity . . . . . . . . . . . . . . . . . . . . . 43

3.3 Measurement of thermal dif�fusivity . . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Determination of specif�ic heat capacity . . . . . . . . . . . . . . . . . . . . . 48

4 RESULTS AND DISCUSSION 49

4.1 Thermal conductivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1.1 Ef�fect of particle/f�ibre size on thermal conductivity . . . . . . . . . . 49

4.1.2 Ef�fect of compaction pressure on thermal conductivity . . . . . . . . 55

4.2 Thermal di�f�fusivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3 Specif�ic heat capacity determination . . . . . . . . . . . . . . . . . . . . . . 69

5 CONCLUSIONS AND RECOMMENDATIONS 74

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2 Recommendation for future work . . . . . . . . . . . . . . . . . . . . . . . . 75

Bibliography 76

Appendix I: Temperature response of the samples to a heat 84

List of Figures

2.1 Increase in thermal conductivity of polyurethane insulation material in the

f�irst 15 years of manufacture [26]. . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 The thermal conductivity of a mineral f�iber insulation versus packing density

[53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Variation of Thermal conductivity with porosity of refractory bricks[54]. . . . 23

2.4 Variation of thermal conductivity with temperature for selected insulation

materials [55]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Distribution and geometry of embedded material in continous phase. . . . . 25

2.6 Schematic diagram of the guarded hot plate apparatus . . . . . . . . . . . . 29

2.7 Lees' disk apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.8 Schematic representation of the dual-needle heat-pulse (DNHP) sensor . . . 36

2.9 Temperature response measured for a sample. . . . . . . . . . . . . . . . . . 37

2.10 A plot of the linearisation ln (δT ) against 1t. . . . . . . . . . . . . . . . . . . 38

3.1 Nested sieves on a mechanical vibrator . . . . . . . . . . . . . . . . . . . . . 41

3.2 Arrangement of a metal plate and a hollow rigid metal frame. . . . . . . . . 42

3.3 Hydraulic manual press type PW40 with die between its upper and lower plates. 43

3.4 Experimental set up for thermal conductivity measurement . . . . . . . . . . 44

3.5 Typical curves displayed on QTM-500 for small and large thermal conductivities 45

3.6 Display of the QTM-500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

viii

LIST OF FIGURES ix

3.7 Experimental set up for measurement of temperature response of a sample to

a heat pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Thermal conductivity against f�ibre size at various compaction pressures . . . 51

4.2 Thermal conductivity against particle size at various compaction pressures . 54

4.3 Variation of thermal conductivity with compaction pressure for di�f�ferent f�ibre

sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4 Variation of thermal conductivity with compaction pressure for di�f�ferent par-

ticle sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.5 Temperature response of the �brous samples to a heat pulse . . . . . . . . . 62

4.6 Temperature response of the particulate sample to a heat pulse . . . . . . . 66

4.7 Graphs of ln(δT ) versus 1/t for �brous samples . . . . . . . . . . . . . . . . . 68

4.8 Graphs of ln(δT ) versus 1/t for particulate samples . . . . . . . . . . . . . . . 72

List of Tables

2.1 Energy lost using mineral wool insulation [12] . . . . . . . . . . . . . . . . . 5

2.2 Thermal conductivity of insulating refractories [23]. . . . . . . . . . . . . . . 12

2.3 Thermal conductivity of gases used as blowing agents in foam plastic insula-

tion[24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Types of foamed plastics [19]. . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Average Bagasse Composition [41]. . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Thermal conductivity of the samples at di�f�ferent compaction pressures and

particle/f�ibre sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 RMSE values for the di�erent �ts for thermal conductivity variation with

particle/�bre size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3 Values of ε and β for dif�ferent particle/f�ibre sizes . . . . . . . . . . . . . . . 55

4.4 RMSE values for the di�erent �ts of thermal conductivity variation with com-

paction pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.5 Values of ξ and γ for the di�f�ferent samples and particle/ f�ibre sizes . . . . . . 61

4.6 Constants ai, bi, ci for the di�erent samples . . . . . . . . . . . . . . . . . . . 67

4.7 Thermal dif�fussivities of the samples . . . . . . . . . . . . . . . . . . . . . . 69

4.8 Specif�ic heat capacity of the samples . . . . . . . . . . . . . . . . . . . . . . 69

x

Abstract

The use of thermal insulators is one of the most important aspect in thermal energy storage

systems. This dissertation presents investigations of thermal properties of selected materials

available in Uganda which can be used for thermal insulation. Thermal properties of seven

di�erent materials were measured. The materials studied were: sugar cane �bres, ash, banana

�bres, sawdust, clay, kaolin, and charcoal dust.The thermal properties investigated were,

thermal conductivity, thermal di�f�fusivity and speci��c heat capacity.

The Quick thermal conductivity meter which uses the hot wire method was used in the

measurement of thermal conductivity at room temperature (approximately 25oC). Thermal

di�f�fusivity was determined using the transient heat pulse technique and the speci�f�ic heat

capacity was calculated using the thermal conductivity, thermal dif�fusivity and density of

the samples.

The samples were prepared by sieving the dry materials to obtain smaller particles/ �bre sizes

in the ranges of 90-125, 125-150, 150-180, and 180-355µm. The powders were compacted at

pressures of 18.2, 36.4, 54.6, and 72.9MPa and dried in the oven at 100oC for 48h.

Graphical analysis using MATlab showed that the thermal conductivity:

(i) Increased with compaction pressure,P, for the di�erent particle sizes according to the

power law,κ = ξP γ. The values for γ were approximately 0.13 for ash, 0.08 for sawdust,

0.18 for clay and 0.08 for kaolin.

xi

ABSTRACT xii

(ii) Decreased with increasing particle size ,S, according to the equation κ = εSβ . The

values for β were approximately 0.04 for sugarcane �bres,0.26 for ash, 0.06 for sawdust,

0.20 for clay, 0.15 for kaolin and 0.25 for charcoal dust.

However, there was no clear variation of thermal conductivity with compaction pressure and

�bre diameter or length for the sugar cane and banana �bres.An attempt to �t the results

to a power law yielded values for γ of approximately 0.05 for sugarcane �bres and 0.04 for

banana �bres.

Particle/�bre sizes of ≤ 180µm were used in the determination of thermal di�usivity of

the samples. Using MATLab the graphs of temperature response to a heat pulse were �t-

ted using a Gaussian distribution and linerlisation of (δT )vs 1twas used to determine the

thermal di�usivity. The values for thermal di�usivity were 5.05x10−7m2s for sugarcane �bres,

3.67x10−7m2s for ash, 8.13x10−7m2s for banana �bres, 1.12x10−7m2s for sawdust,1.58x10−7m2s

for clay, 4.27x10−7m2s for kaolin and 6.90x10−7m2s for charcoal dust.

In the study the speci�c heat capacity was obtained from the relation, c = κρα .

From the samples studied, sugarcane �bres/ bagasse was the best insulating material with a

thermal conductivity ranging from 0.0840 to 0.1125Wm−1K−1, a thermal di�usivity 5.05×10−7m2s

of and a speci�c heat capacity of 1125 Jkg−1K−1at about 25oC.

Chapter 1

INTRODUCTION

1.1 Background of study

Solar energy is abundant and inexhaustible. This energy can be converted to thermal or

electrical energy. One of the most promising application of solar energy involves using solar

collectors, to heat water or air for domestic and industrial applications [1]. The production

of hot water is particularly an important application of solar energy using plane collectors

to heat water. In addition to its inexhaustible nature, solar energy has the advantage that

it is non polluting. However, solar energy utilisation is often inf�luenced by its intermittent

character and the signif�icant mismatch between the time of availability and that of intended

use. Early heat recovery systems used water as a storage medium [2]. However, solar energy

source and household demands in general, do not match each other at any time. This

necessitates the use of thermal energy storage (TES) systems to address this mismatch so

as to meet energy needs at all times [3]. There is a huge potential for the application of

thermal energy storage systems. TES systems can play an important role, as they provide

great potential for facilitating energy savings and reducing environmental impact [4].Energy

storage systems are not as widely used as they could due to several reasons. Some of these

systems are not yet economically competitive with fossil fuels and their long term reliability

1

INTRODUCTION 2

is not yet proven.

It is necessary to use thermal insulators around such storage systems to maintain high tem-

peratures inside by preventing heat losses to the surroundings [5]. There are varieties of

insulating materials which come in various forms like loose f�ill, rigid boards,pipe and foam.

Proper selection of the insulating material to be used is based on the thermal properties

which include the thermal conductivity, specif�ic heat capacity and thermal dif�fusivity. The

thermal insulation is provided by embedding insulation materials at least on the roof areas

and the vertical walls of the storage systems [6]. Poor thermal insulation of the heat storage

systems leads to high heat losses [7].

Rock wool and f�ibre glass are currently used as thermal insulation materials for the storage

systems. This is mainly due to their low thermal conductivity values leading to good thermal

insulation. However, these thermal insulators are expensive and also risky to human health

as a result of exposure during handling especially those in f�ibrous form [8]. Studies show that

people who manufacture f�ibre glass have 60% more f�ibre glass material in their lungs than

those who had not been exposed [9]. There is a need for f�inding alternative thermal insulating

materials which are cheap, readily available and do not pose a risk to human health and also

cheaply and readily available [10].

1.2 Statement of the problem

Thermal Energy storage systems are usually insulated with glass wool, f�ibre glass or rock

wool. The thickness of insulation used is large and ranges from 10 to 20 cm. Because of this,

the cost of the insulation represents a signif�icant part of the total cost of a thermal storage

system and means to reduce this cost need to be explored. There is need to investigate

thermal properties of cheap and readily available materials in Uganda . The properties

include thermal conductivity, thermal dif�fusivity and specif�ic heat capacity. This will make

INTRODUCTION 3

it possible to identify those materials that can be used as thermal insulators .

1.3 Objective

The main objective was to investigate the thermal properties of selected insulating materials

available in Uganda that can be used for thermal insulation.

1.4 Specif�ic objectives

The specif�ic objectives of this study are to investigate :

1. The thermal conductivity of selected materials available in Uganda.

2. T he thermal dif�fusivity of selected materials available in Uganda.

3. The specif�ic heat capacity of selected materials available in Uganda.

1.5 Scope

The investigation will cover the determination of thermal conductivity, thermal dif�fusivity

and specif�ic heat capacity of the following materials: clay, kaolin, ash, charcoal dust, sugar

cane f�ibre, banana f�ibre and saw dust.

1.6 Signif�icance of the study

This study is focused on identifying suitable materials in Uganda which can be used for ther-

mal insulation in thermal storage. In order to determine which material can best be used for

thermal insulation, their thermal properties, namely specif�ic heat capacity, thermal dif�fusiv-

ity and thermal conductivity will be studied. This investigation will provide an appropriate

INTRODUCTION 4

local material which can be used in thermal energy storage systems for insulation and hence

increase the economic ef�f�iciency of the systems.

1.7 Justif�ication

Materials currently in use for thermal insulation are mainly of synthetic origin. The com-

monly used materials are rock wool, f�ibre glass, polystyrene and the polyurethane. These

materials are expensive, required in large quantities and can sometimes be a health risk to

those handling them in �brous form [11]. The thermal characterization of insulating mate-

rials available in Uganda will allow identif�ication of those materials which can be used as

thermal insulators in place of existing ones therefore leading to reduction in the overall costs

of thermal energy storage systems.

Chapter 2

LITERATURE REVIEW

2.1 Thermal insulators

Thermal insulators are those materials or combinations of materials which retard the f�low of

heat energy. Installation of thermal insulation can signif�icantly reduce the thermal energy

(heat) lost from thermal heat storage system surfaces. The energy lost for an insulating

material depends on the the thermal properties and thicknesses of the insulation. Clausen [12]

calculated the energy lost for dif�ferent thickness of mineral wool insulation used in thermal

energy storage system and the results are shown in table 2.1. The thicker the insulation the

less the amount of heat loss.

Insulation materials can be made in dif�ferent forms including loose-f�ill form, blanket batt

or roll form, rigid form, foamed in place, or ref�lective form. The choice of the type and

Table 2.1: Energy lost using mineral wool insulation [12]

Insulation layer thickness [mm] Heat loss, 50 years [MJ]0 1995880 5424250 1855350 1338500 943

5

LITERATURE REVIEW 6

form of the proper insulation materials depends on where the insulation is to be applied as

well as the desired material's physical and thermal properties [13]. Some typical properties

of insulating materials that are considered as a must in terms of mechanical, physical and

thermal properties are: low thermal conductivity, prevention of water leak, ease of handling

and machining, durability and light weight, f�ire resistance, safety and installation. Identifying

the rate at which thermal energy (heat) is lost from an uninsulated surface provides the need

for installing thermal insulation. The basic requirement for thermal insulation is to provide a

signif�icant resistance path to the f�low of heat through the insulation material. To accomplish

this, the insulation material must reduce the rate of heat transfer by conduction, convection,

radiation, or any combination of these mechanisms.

The heat loss depends on a number of factors, such as the heating system or heat source

temperature, selection and thickness of insulation used, and exposure of insulated surfaces

to ambient conditions.

Heating systems may lose 2% to 5% of the total heat input through insulated surfaces. It

is not feasible or possible to eliminate all insulation-related heat loss, but it is possible to

reduce these losses by 10% to 25% [13]. To achieve this, one must:

(i) Review process requirements

(ii) Know the available and applicable insulation materials

(iii) Select materials to meet the process requirements

(iv) Properly design, install and precondition insulation systems

(v) Properly operate the equipment to avoid damage to the insulation

(vi) Perform periodic maintenance, repairs and replacement of the insulation

LITERATURE REVIEW 7

2.1.1 Benef�its of thermal insulation

Thermal insulation delivers the following benef�its.

Conservation of energy

Substantial quantities of heat energy are wasted daily in thermal energy storage plants be-

cause of under insulated and uninsulated heated and cooled surfaces. Properly designed and

installed insulation systems will immediately reduce the energy loss by the system. Insulation

helps in reducing heat loss or gain and maintaining process temperature to a pre-determined

value or within a predetermined range. The insulation thickness must be suf�f�icient to limit

the heat transfer in a dynamic system or limit the temperature change, with time, in a static

system.The benef�its to industry include enormous cost savings, improved productivity, and

enhanced environmental quality.

Protection of personnel

Thermal insulation is one of the most ef�fective means of protecting workers from second

and third degree burns resulting from skin contact for more than 5 seconds with surfaces of

hot piping and equipment operating at high temperatures. Insulation reduces the surface

temperature of piping or equipment to a safer level as required by Occupational Safety and

Health Administration (OSHA), resulting in increased worker safety [14].

Protection from f�ire

Insulation is used in combination with other materials in f�ire stop systems designed to pro-

vide an ef�fective barrier against the spread of f�lame, smoke, and gases at penetrations of f�ire

resistance rated assemblies by ducts, pipes, and cable [15].

LITERATURE REVIEW 8

Insulation materials fall into two broad categories: organic foams and inorganic materials.

Organic insulation are based on hydrocarbon polymers, which can be expanded to obtain

high void structures. The organic foams include materials such as polystyrene,

polyurethane, phenolic foam and polyethylene foam. Inorganic insulation is based on

siliceous/aluminous/calcium materials in f�ibrous, granular or powder forms. The inorganic

materials include mineral wool, calcium silicate, cellular glass, microporous silica, magnesia,

ceramic f�ibre, vermiculite, perlite and others. The materials selected for this study are

inorganic materials.

2.1.2 Types and Application

The insulation can be classif�ied into three groups according to the temperature ranges for

which they are used.

Low Temperature Insulators (up to 90oC)

This range covers insulating materials for refrigerators, cold and hot water systems, storage

tanks, etc. The commonly used materials are cork, wood, 85% magnesia, mineral f�ibers,

polyurethane and polystyrene .

Medium Temperature Insulators (90 - 325oC)

Insulators in this range are used in low temperature, heating and steam producing equipment,

steam lines, f�lue ducts etc. The types of materials used in this temperatures range include

85% magnesia, asbestos, calcium Silicate and Mineral f�ibers .

High Temperature Insulators (325oC and above)

These are used in systems like super-heated steam systems, oven dryers and furnaces. The

most extensively used materials in this range are asbestos, calcium silicate, mineral f�ibre,

mica and vermiculite based insulation, f�ireclay or silica based insulation and ceramic f�ibre.

LITERATURE REVIEW 9

2.2 Major thermal insulation materials used in thermal

heat storage

Many types of insulation materials are available which dif�fer with regard to thermal properties

and mechanical properties as well as cost. The following are major insulation materials used

in commercial and industrial installations.

2.2.1 Calcium silicate

In recent years, a variety of low-density calcium silicate-based material products have been

developed for high-temperature insulation and f�ire resistive material (FRM) applications [16].

Calcium silicate is one of the best inorganic light weight thermal insulation materials for high

temperatures [17]. It is a granular insulation made of lime and silica, reinforced with organic

and inorganic f�ibers and molded into rigid forms. Service temperature range covered is 400

to 9500C and the material is not deformed within this temperature range. Calcium silicate

is water absorbent, noncombustible, has high strength and is used primarily on hot piping

and surfaces.

Inhalation of excessive amounts of dust of calcium silicate may cause temporary upper respi-

ratory irritation [18] hence the product is harmful to human beings. Its thermal conductivity

is about 0.0462Wm−1K−1 at room temperature [17].

2.2.2 Mineral f�iber (rock and slag wool)

Rock and slag f�ibers are bonded together with a heat resistant binder to produce mineral

f�iber. The use of rock wool insulation provides a practical and cost ef�fective means of reducing

energy losses in TES. Rock wool derives its excellent thermal properties entirely from the air

trapped between the structures of the wool. As a result, the thermal qualities of rock wool

do not diminish over time and will continue to perform well through out.

LITERATURE REVIEW 10

Rock wool insulation is safe to manufacture and use, when proper guidelines are followed.

Decades of research have shown that it poses little to no health risk to humans, including

that of respiratory and other cancers. When mineral wool insulation is handled, the f�ibres

can cause skin irritations. These are caused by coarser f�ibres (with a diameter over 5µm),

which can pierce the skin owing to their rigidity and cause unpleasant itching.

F�ibrous dust is released during processing. Like any other mineral dust, the f�ibrous dust

from the mineral wool insulation can cause eye irritation. The material has a practically

neutral pH, is noncombustible, and has good sound control qualities. Rock and slag wool

insulation resists the growth of mould, fungi and bacteria because it is inorganic. The thermal

conductivity of rock wool is approximately 0.042Wm−1K−1 at room temperature [19].

2.2.3 F�ibre glass

F�ibre glass contains extremely f�ine f�ibres of glass. It is used as a reinforcing agent for many

polymer products; the resulting composite material is properly known as f�ibre reinforced

polymer (FRP) or glass-reinforced plastic (GRP). It is available as f�lexible blanket, rigid

board, pipe insulation and other pre-moulded shapes. By trapping air within, blocks of glass

f�ibre make good thermal insulation. The glass strands themselves are very poor conductors

of heat. In order for heat to be transferred through the f�ibre glass, then, it must be carried

convectively through the tiny air pockets. But the randomness of the strands means there

is no direct path through the material, so the heated air must take a very circuitous route

through [20]. The insulating properties of f�iberglass depend on this random path. If the

f�iberglass is compressed, the path becomes shorter, and the heat gets through quicker. That

is why the material is not tightly packed insulation.

Useful properties of f�iberglass insulation

The properties of f�iberglass insulation are as follows.


Moisture Absorption

F�iberglass does not absorb any moisture at all. The absorption of moisture by insulating

materials a�ects their thermal properties, which degrades their performance. Since f�iberglass

does not absorb moisture, it is benef�icial for use in moisture laden atmosphere.

Loss of Energy

F�iberglass insulation prevents air inf�iltration to a larger extent. Air inf�iltration refers to the

ability of an insulator to prevent the leakage of air, heat or energy through the walls

Corrosion Resistant

F�iberglass insulation is resistant to corrosion and it does not contain any chemicals that can

cause corrosion problem to wires or pipes.

Weight Issues

F�iberglass insulation is light in weight. It is easy to install in thermal energy storage systems.

F�ire Resistant

F�iberglass is non-combustible, that is, it does not support combustion. It does not need any

extra f�ire deterrent chemicals to be added to it.

Thermal conductivity

The thermal conductivity of f�ibre glass is of the order of 0.05Wm−1K−1[21] at room temper-

ature.

2.2.4 Expanded silica, or perlite

Perlite is a material that can be used for insulation. It is a very important material for

insulation due to its low heat conductivity of about 0.054Wm−1K−1 [19]. Perlite is made

from an inert siliceous volcanic rock combined with water. It is a vitreous substance that

contains 2-6% water. Binding materials such as cement, gypsum, lime, bitumen and clay are


needed for manufacturing perlite brick. Perlite/ clay bricks are some of the lightest ceramic

materials.

Perlite has low shrinkage and high resistance to substrate corrosion. Perlite is noncombustible

and operates in the temperature ranges 325oC and above. The product is available in rigid

pre-formed shapes and blocks. In addition to low thermal conductivity, perlite insulation is

relatively cheap and easy to handle and install.

2.2.5 Refractories

Refractory f�iber insulations are mineral or ceramic f�ibers, including alumina and silica, bound

with extremely high temperature binders. Low density ceramic materials, ceramic composites

and f�ibres are widely used in many high temperature applications. The materials provide low

thermal conductivity and high resistance to chemical attack. Refractories are manufactured

in blanket or rigid form. They are noncombustible and can withstand high temperatures of

3500C and above [22]. Refractory materials are made in varying combinations and shapes

and for dif�ferent applications. F�irebrick is the most common form of refractory material.

It is used extensively for thermal insulation in furnaces or kilns. Thermal conductivity

of refractories depends upon the chemical and mineralogical compositions as well as the

glassy phase contained in the refractory and the application temperature. The thermal

conductivities of some refractories are shown in Table 2.2 [23]

Table 2.2: Thermal conductivity of insulating refractories [23].

Type Thermal conductivity at 400 oC/Wm−1K−1

Diatomite solid grade 0.025Diatomite porous grade 0.014Clay 0.030High alumina 0.028Silica 0.040


2.2.6 Foamed plastic

These insulating materials are formed by blowing a gas of low thermal conductivity and the

type of gas blown inf�luences the thermal properties of the plastic. Table 2.3 [24] shows the

thermal conductivity of gases used as blowing agents in foam plastic insulation materials.

Foam plastics are composed of millions of tiny cells or bubbles. When the cells are completely

intact with no holes or spaces between the cells the material is called closed cell foam. When

the cells have holes connecting one cell to another the material is called open cell foam.

Foamed plastics are light weight with excellent moisture resistance. Foam plastic insulation

materials are considered to be inert materials with no recognized health ef�fects and have

not been linked to any respiratory problems or skin irritations as have some f�iber-based

insulations.

Table 2.3: Thermal conductivity of gases used as blowing agents in foam plastic insulation[24]

Type Gas thermal conductivityat 25oC W m−1 K−1

Air 0.0259Carbon dioxide 0.0162Cyclopentane 0.0130Hydro-chloro-�uoro-carbon (HCFC)-141b 0.0100

The common types of foam plastic insulation include, polyurethane and polystyrene .

Polyurethane

The high mechanical strength, high thermal resistance, ability to f�ill narrow cavities, low

water absorption and the excellent thermal insulation property of polyurethane makes it a

good material for thermal insulation. The insulation performance however will deteriorate

during the service life of a TES, due to gas dif�fusion processes leading to changes in the cell

gas composition. This is referred to as thermal conductivity aging and results in an increased

energy loss during transport of thermal energy which may reduce the prof�itability of a TES.


Long-term tests conducted on rigid polyurethane foam insulation boards showed that thermal

conductivity increases with time [25]. The thermal conductivity and cell gas composition

were determined periodically. F�igure 2.1 shows the change in thermal conductivity of rigid

polyurethane foam boards blown with pentane over a storage period of 15 years at room

temperature[26].

Figure 2.1: Increase in thermal conductivity of polyurethane insulation material in the f�irst15 years of manufacture [26].

Polystyrene

There are dif�ferent forms of polystyrene used for thermal insulation. The most common

type used is extruded polystyrene (XPS) foam plastic insulation which uses highly ef�f�icient

blowing agents specif�ically selected for low thermal conductivity and dif�fusivity. This helps

the insulation retain its properties. The durability of XPS foam plastic insulation is perhaps

the most important environmental consideration. The closed-cell structure and lack of voids

in extruded polystyrene foam plastic insulation not only impart the material's durability and

strength, but also help the foam resist moisture penetration.

Other types of polystyrene include molded polystyrene and injected polystyrene. The thermal


conductivities of foam plastics used for thermal insulation at room temperature are given in

table 2.4[19]

Table 2.4: Types of foamed plastics [19].

Foamed plastic Thermal conductivity/W m−1 K −1

1 Extruded polystyrene 0.0322 Molded polystyrene 0.0363 Injected polystyrene 0.0344 Polyurethane 0.024

2.2.7 Insulating cement

Insulating cement is a mixture of dry granular, f�ibrous or powdery material that develop

plasticity when mixed with water and when dried forms a coherent covering that produces

substantial resistance to heat transmission. It is used in insulation applications to f�ill voids,

joints and also as a f�inish to other insulation applications. According to the ASTM [27] the

thermal conductivity of insulating cements is 1.3Wm−1K−1 at 200oC.

2.2.8 Cotton

Cotton is one of the oldest �bres under human cultivation. In processing, the f�ibres (cotton

lint) are separated from the seeds by cotton ginning.

Cotton wool has thermal properties similar to those of f�ibre glass. It is environmentally

friendly for insulation and for use in the textile industry [28]. Cotton has disadvantages of

being hard to dry in case excessive moisture leaks into it and it can not seal cavities against

air movement since the material expands.

2.3 Thermal insulators available in Uganda

In Uganda there are many materials available for consideration as thermal insulators. These

materials are either available naturally or are obtained as industrial wastes. Due to the


environment concerns and the need to conserve energy, various research ef�forts have been

directed towards the utilization of waste materials around the world [29]. The potential of

these materials for thermal insulation is based on the following:

(i) Availability of the material

(ii) Thermal and physical properties of the material

(iii) Environmental and health impacts: the impacts from the processes of production of

waste materials into insulation board.

The locally available insulating materials in Uganda include clay, kaolin, ash, banana �bres,

sugarcane �bres, sawdust and charcoal dust.

2.3.1 Clay

Clay is a natural, earthy f�ine grained soil material that develops plasticity when mixed with

limited quantity of water. Clays are grouped into various forms based on the suitability of the

clay to meet user's purpose [30, 31]. The groups are kaolin, ball clay, stone-wave clay and red

earthen wave clays. Classif�ication of clays can be done using the yardsticks of their color and

availability; hence, there are red, gray, white and yellow clays. The variation in their mineral

contents such as kaolinite, montmorillonite, illite, chlorite and attapulgite contributes to the

dif�ferent colours of clays [31]. All refractory materials have a high specif�ic heat capacity,

meaning they can hold a lot of heat within themselves [32].

Thermal conductivities of clays have been previously investigated.

Mukwasibwe [33], using the Lee's Disk method studied the thermal conductivity of f�ired clay

samples from Seeta, Ntawo and Kigombya and the values obtained were in the range of 0.13

-0.30Wm−1K−1 at room temperature.


Owalu [34], used the hot wire method to investigate the thermal conductivity of kaolin

obtained from Buwambo quarry near Kampala. Values in the range of 0.3- 1.5Wm−1K−1

were obtained at room temperature.

No measurement of speci�c heat capacity were done hence there is need to study the specif�ic

heat capacity and thermal dif�fusivity to fully characterise the thermal properties of clay and

hence its insulation property.

2.3.2 Ash

Ash is residue powder left after the combustion of biomass. Properties of biomass di�er

hence the properties of ash will depend on biomass from which it is processed from. The

thermal properties of the ash deposits have a signif�icant inf�luence on the heat transfer rates

in furnace walls, super heater tubes, and other heat transfer surfaces. The in�uence largely

depends on the thickness, thermal conductivity, and emissivity of the deposits [35]. Ash

deposits are a complex, heterogeneous, multiphase, porous material. Like many porous

materials at high temperature, both conduction and radiation can contribute to the overall

heat transfer rate through the deposit. The radiative properties and thermal conductivity

of deposits have signif�icant inf�luence on the boiler performance deposit [36]. The ef�fective

thermal conductivity is used to characterize the overall heat transfer rate.

The thermal properties are strongly inf�luenced by the physical structures of the deposits,

particle size, porosity and sintered condition [37, 38]. Allen et al[35] reported that the

thermal conductivity of ash deposits in situ is 0.14Wm−1K−1.

2.3.3 Bagasse (Sugarcane f�ibres)

Bagasse is a f�ibrous residue left after extraction of sugar from the canes, and contains short

f�ibers.The average sugar content of the sugar canes is 9.3% [39] and the rest is mainly bagasse.


Basically, it is a waste product that causes mills to incur disposal costs. For example, every

metric ton of sugarcane generates about 280 kg of bagasse [40]. It consists of water, f�ibers,

and small amounts of soluble solids. Percent contribution of each of these components varies

according to the variety, maturity, method of harvesting, and the ef�f�iciency of the crushing

plant. In Table 2.5 [41] a typical Bagasse composition is presented.

Table 2.5: Average Bagasse Composition [41].

Item Bagasse % compositionMoisture 49.0f�iber 48.7Soluble solids 2.3

F�ibers in bagasse consist mainly of cellulose, pentosans, and lignin. The resultant sugar cane

f�iber bundles consist of several to hundreds of ultimate f�iber cells, with the width of the

f�iber bundles being dependent on extraction conditions and extraction processes. Nowadays

Bagasse is mainly used as a fuel in the sugar cane mill furnaces. The low caloric power

of bagasse makes this process of low ef�f�iciency . Also, the sugar cane mill management

encounters problems regarding regulations of "clean air" from the Environmental Protection

Agency, due to the quality of the smoke released in the atmosphere. Presently 85% of

Bagasse production is used as fuel in sugar cane mill furnace [42]. Even so, there is an excess

of Bagasse which is left to burn in the open.

Insulation materials containing bagasse have been produced. It is reported that their thermal

conductivity is in the range of 0.046 � 0.051 Wm−1K −1[43]. The thermal conductivity of

bagasse its self was not reported.

2.3.4 Banana f�ibres

Banana f�ibres are a renewable resource but have relatively poor mechanical properties and

have low densities. Matooke the fruit from bananas is one of the major foods in Uganda.

Bananas contribute up to 44.7 % of the total volume of food crops produced in Uganda [44].


Banana f�ibres are usually extracted manually from pseudo stems by peeling them of�f.

Presently banana f�ibres are used for making hand bags, table mats and ropes [45]. One of

the reasons for under utilization of these f�ibres is limited scientif�ic data on them. There have

been some studies of the chemical constituents and mechanical properties of these f�ibres [45].

These materials can also be easily employed for multi-function applications, as the hollow cel-

lular structure of plant f�ibers proved ef�fective in providing insulation against heat and noise.

Paul et al. [46] in their observations on the ef�fect of f�iber loading on banana/polypropylene

(PP) composite found that both the thermal dif�fusivity and thermal conductivity were de-

creasing on increasing f�iber loading (i.e., from 0.24Wm−1 K−1 for neat polypropylene matrix

to 0.217 and 0.157Wm−1 K−1 for 0.10 and 0.50 of volume fraction respectively).

2.3.5 Sawdust

Sawdust is the main by product of wood timber processing. Types of sawdust depend on the

varieties of wood from which it is obtained. Hence their thermal properties will dif�fer from one

to another. Ogunleye and Awogbemi [47] investigated the thermal and physical properties of

eight varieties of sawdust and found that they had dif�ferent thermal conductivity values.

Although many outlets are available for the utilization of this waste, economical disposal of

sawdust remains a problem of growing concern to the wood industry [48]. The saw mill sector

in Uganda currently disposes sawdust by burning which is environmentally inappropriate.

The use of sawmill residues must be carefully analyzed to of�fer the best technical, economic

and environmental alternative [49]. The thermal characterization of the sawdust generated

is essential in order to determine its possible use.


2.3.6 Charcoal dust

Charcoal dust is a residue from charcoal packing. It is a black powdery substance normally

found at the bottom of charcoal sacks, charcoal selling stores or in the charcoal making areas.

It results from the chip of�fs from the charcoal slates.

The properties of charcoal dust are highly dependent on the source and the process conditions

[50].

2.4 Important thermal properties of an insulating mate-

rial

A thermal insulating material must have the appropriate characteristics to retard the trans-

port of heat that occurs by conduction, convection and radiation. In order to decide which

material is best requires an understanding of the following thermal properties: thermal con-

ductivity, specif�ic heat capacity and thermal dif�fusivity.

2.4.1 Thermal conductivity

The thermal conductivity (κ) of a material is a measure of the ef�fectiveness of the material in

conducting heat [51]. Good heat insulators should have low thermal conductivities, in order

to reduce the total coef�f�icient of heat transmission.

The thermal conductivity of a material represents the quantity of heat that passes through

a metre thickness per square metre per second with one degree dif�ference in temperature

between the faces.

In a steady state, that is when the temperature at any point in the material is constant with

time, thermal conductivity is the parameter which controls heat transfer by conduction. The


rate of heat f�low, q, is given by Fourier's law:

q = −κA∂θ∂x

(2.1)

where κ is the thermal conductivity, A is the area of the test piece normal to the heat �ow,

and ∂θ∂x

is the temperature gradient.

Thermal conductivity is regarded as the most important characteristic of a thermal insulator

since it af�fects directly the resistance to transmission of heat that a material of�fers. The

lower the thermal conductivity value, the lower the overall heat transfer.

The thermal conductivity of insulating materials has been found to vary with: density,moisture

content, temperature, direction of heat f�low with respect to grain for f�ibrous materials,the

presence of defects in the material and porosity [52].

F�igures 2.2 [53] and 2.3 [54] show the variation of thermal conductivity with density and

porosity respectively in a mineral f�ibre.

The variation of thermal conductivity with temperature for common heat insulators is shown

in F�igure 2.4 [55]. It is observed that that the thermal conductivity does not vary appreciably

over a temperature range 0oC to 50oC.

Insulation levels are specif�ied by R-value. This is a measure of the resistance to heat f�low as

a result of suppression of conduction, convection and radiation. It depends on the material's

thermal conductivity, density and thickness [51]. It can be calculated from equation .

R =l

κ(2.2)

where l is the thickness and κ is the thermal conductivity of a material.

The higher the R-value the better the thermal performance of an insulator.


Figure 2.2: The thermal conductivity of a mineral f�iber insulation versus packing density[53].

Thermal conductivity of composites

The thermal conductivity of a composite material depends on its component materials and the

arrangement of the materials, It is possible to optimize the property through constitutional

and structural design.

Maxwell and Rayleigh [56] studied the ef�fective thermal conductivity as a function of the con-

stitutional and structural parameters and geometry (F�igure 2.5). Dif�ferent approximations

are used for various geometries.

For heterogeneous solids such as a material made of spheres of thermal conductivity κ0

embedded in a continuous phase of thermal conductivity κ1, the ef�fective thermal conductivity

κeff is given by Maxwell's and Rayleigh's equations 2.3 and 2.4, respectively [57, 58].

Assuming the spheres do not interact thermally (that is, small volume fraction φ as shown

in F�igure2.5a)


Figure 2.3: Variation of Thermal conductivity with porosity of refractory bricks[54].

κeffκ0

= 1 +3φ(

κ1+2κ0κ1−κ0

)− φ

(2.3)

Assuming large volume fraction φ(as shown in F�igure 2.5b)

κeffκ0

= 1 +3φ(

κ1+2κ0κ1−κ0

)− φ+ 1.569

(κ1−κ0

3κ1−4κ0

)φ10/3 + · · ·

(2.4)

For square arrays of long cylinders parallel to z axis(as shown in f�igure 2.5c) the thermal

conductivity is not the same in all directions. E�ective thermal conductivity is given by the

Rayleigh's derivation.

The e�ective thermal conductivity in the z-direction is given by equation 2.5 [59]


Figure 2.4: Variation of thermal conductivity with temperature for selected insulation mate-rials [55].

κeff,zzκ0

= 1 +

(κ1 − κ0κ0

)φ (2.5)

The e�ective thermal conductivity in the y-direction is given by equation 2.6 [59].

κeff,yyκ0

= 1 +2φ(

κ1+κ0κ1−κ0

)− φ+ 1.569

(κ1−κ03κ1+κ0

)(0.30584φ4 + 0.013363φ8 + . . .)

(2.6)

For unconsolidated granular beds as complex non-spherical inclusions in a continuous solid

phase as shown in f�igure 2.5d, the e�ective thermal conductivity is given by the complex

non-spherical approximation 2.7 [59].


(a) Spherical inclusion with a small volume fraction (b) Spherical inclusions with a large volume fraction

(c) Long cylinders parallel to z-axis (d) Complex nonspherical inclusions

Figure 2.5: Distribution and geometry of embedded material in continous phase.

κeffκ0

=(1− φ) + αφ (κ1/κ0)

(1− φ) + αφ(2.7)

where α = 13

∑3

k=1

[1 +

(κ1κ2− 1)gk

]−1and gk are �shape factors� for granules.

The values of gkrange from 0.7-0.98 [60].

For solids containing gas pockets, thermal radiation becomes important. The e�ective ther-

mal conductivity is now given by equation 2.8 [59].

κeffκ0

=1

1− φ+(κ1κ0φ

+ 4σT 3Lκ0

)−1 (2.8)

where σ is the Stefan-Boltzmann constant and L is the total thickness of the material in

direction of heat conduction


2.4.2 Specif�ic heat capacity

Specif�ic heat capacity is one of the important parameters for determining the insulation

property. Specif�ic heat capacity of a material is the amount of heat required to raise the

temperature of one kilogram of a material by one degree Celsius. The principal heat capacities

of a material are those at constant volume and constant pressure. The specif�ic heat capacity

at constant volume Cv, which is impossible to measure for solids , can be calculated from

equation (2.9).

Cp − Cv =TV τ 2

βT(2.9)

where Cp is the specif�ic heat capacity at contant pressure, which is the quantity normally

measured, T is the absolute temperature,τ is the coe�cient of thermal expansion, βT is the

isothermal compressibility and V is the volume.

In solids the volumetric heat capacity, which is the heat capacity per unit volume is the one

which can be determined experimentally.

A high specif�ic heat capacity value means high ability for heat retention and hence good

insulating materials should have a high speci�c heat capacity.

2.4.3 Thermal dif�fusivity

Thermal dif�fusivity, α, is the parameter which determines the temperature distribution in

non steady state or transient conditions. It is given by:

α =κ

ρCp(2.10)

where α is the thermal dif�fusivity, κ is thermal conductivity, Cp is specif�ic heat capacity at

constant pressure and ρ is the density.

Thermal dif�fusivity measures the ability of a material to transmit a thermal disturbance. It


indicates how quickly a material's temperature will change. Thermal dif�fusivity increases

with the ability of a body to conduct heat and decreases with the amount of heat needed to

change the temperature of a body. It is of little interest in many thermal insulation systems

since in these, approximately steady state conditions normally exist.There are few reports

which give direct measurement methods for thermal dif�fusivity of materials. Most of the data

is calculated from equation 2.10 .

Like thermal conductivity, specif�ic heat capacity and thermal dif�fusivity are functions of

temperature, porosity, density and particle sizes.

2.4.4 Other pertinent physical properties

Compression strength

This is the measure of the capacity of a material to withstand axially directed crushing forces.

The importance of this property is for maintaining press alignments. Typically, compression

strength of most insulating materials decreases as temperature increases [61]. In fact, a small

increase in temperature can result in a signif�icant decrease in compression strength in some

insulating materials.

Water absorption

This is def�ined as the amount of water absorbed by a material when immersed in water for

a period of time. Up to 98% of insulation system problems are caused by moisture or water

absorption.The common measure is the percent swell. The disadvantage of water absorption

to insulation is that swelling can cause misalignment and cracking. Also water absorption

causes solidif�ication of insulating materials in high-temperature thermal storage systems.

This leads to accelerated heat loss by a thermal storage system.


2.5 Measurement of thermal conductivity of insulators

The methods of measurement of thermal conductivity can be divided into steady state meth-

ods and transient or non steady state methods. Traditionally, steady state methods were

most widely used as they are mathematically simpler. For materials of low thermal conduc-

tivity, steady state methods can be very time consuming and involve expensive apparatus.

Transient methods have experimental advantages once the much more dif�f�icult mathematical

treatment has been worked out. Methods based on transient heat transfer have the potential

of directly determining thermal dif�fusivity, but they are not as accurate as steady state

methods with dry materials [62].

2.5.1 Steady state methods for measurement of thermal conductiv-

ity

Steady state methods of measuring thermal conductivity apply Fourier's law of heat con-

duction. Underlying all the dif�ferent steady heat f�low methods is the attempt to simplify

the mathematics by reducing the heat transfer problem to a one-dimensional problem. The

calculations use an inf�inite slab, the inf�inite cylinder or a sphere as models.

Guarded Hot Plate

The guarded hot plate is based on the inf�inite slab as the heat transfer model. Since sample

dimensions are f�inite, guard heaters are used to facilitate uni-directional heat f�low. It is

considered the most accurate and most widely used steady state method for the measure-

ment of thermal conductivities of poor conductors of heat [62]. It is most suitable for dry

homogeneous samples that can be formed into a slab.

The sample is sandwiched between a heat source and a heat sink as shown in f�igure 2.6.


Figure 2.6: Schematic diagram of the guarded hot plate apparatus

Thermal guards are kept at the same temperatures as their adjacent surfaces (heat source

and heat sink) to prevent heat leakage from heat source, sample and heat sink, thus ensuring

uni-directional heat f�low. The heat input is monitored. After steady state has developed, as

shown by stable temperatures of the heating and cooling plate, the thermal conductivity can

be calculated from the heat input, the temperature dif�ference across the sample, the sample

thickness and heat transfer area. Since steady state conditions may take several hours to

develop, this method is unsuitable for use with a material in which moisture migration may

take place. Equation (2.1) to determine the thermal conductivity of a material.

Radial Heat F�low Method

Whereas the guarded hot plate is generally used for measuring the thermal conductivity of

samples that can be formed into a slab, radial heat f�low steady state methods are more

commonly used with powdered or granular materials.

A cylindrical test device employs a central line (or cylindrical) heat source. End ef�fects are

assumed negligible due to either the large length or diameter ratio of the test apparatus or

the use of end guard heaters. After steady state has been established, the thermal conduc-

tivity can be calculated from the heating power, the length of the cylinder, the temperature

dif�ference between two internally (to the medium) located sensors and their radial position.


Alternatively, the cylindrical sample can be boardered by the heater on one side and a ref-

erence material on the other side. Temperatures on all surfaces are monitored. The thermal

conductivity of the test material is calculated from the temperatures, the radial position of

the sensors and the thermal conductivity of the reference material. Equation (2.1) is used to

determine the thermal conductivity of a material.

Lees' Disc

This apparatus consists of three copper (or any good conductor) plates (A, B and C) drilled

to accept liquid-in-glass thermometers and an electrical heater. The specimen to be studied

is sandwiched between the plates A and B and the heater is sandwiched between plates B

and C. After tightening the clamp screw to hold all the disks together as shown in f�igure 2.7.

The power to the heater is switched and

Figure 2.7: Lees' disk apparatus

the temperature gradient is measured when the apparatus reaches thermal equilibrium. This

allows the thermal conductivity to be calculated using equation 2.11

κ =ed

ε(TB − TA)(as

TA + TB2

+ 2aATA) (2.11)


where e is energy emitted from the exposed area of surface, aA, aS are the exposed surface

areas of the copper plates and specimen respectively, TA and TB are the temperatures of

the disks A and B, d is the thickness of the specimen and ε is the cross sectional area of the

specimen.

2.5.2 Transient state methods for measurement of thermal conduc-

tivity

The main disadvantage of steady state methods is the long measurement time involved. Con-

sequently, a steady state method will fail to measure representative thermal properties like

thermal dif�fusivity and specif�ic heat capacity. Therefore, transient methods are preferred for

measuring the thermal conductivity of materials. They are rapid as data are obtained in

minutes or even less compared to hours for a steady state measurement.

Steady state methods are only capable of measuring thermal conductivity. When the mea-

sured properties are to be used in the study of transient heat transfer, density and specif�ic

heat have to be found independently. They are combined with thermal conductivity to f�ind

the thermal dif�fusivity, For lack of accurate methods of direct measurement of thermal con-

ductivity, this approach is recommended [63]. Methods based on transient heat transfer have

the potential of directly determining thermal dif�fusivity, but they are not as accurate as

steady state methods applied to dry materials [62]

F�itch method

The Fitch method was developed by F�itch in 1935 [62] and uses a plane source of heat. It is

applicable to poor conductors of heat that can be formed into a slab. The F�itch apparatus

consists of a heat source and a heat sink. The heat source is a constant temperature vessel,

insulated on the sides and with a highly conductive bottom. The heat sink is a copper block,

insulated on all sides but the one facing the vessel. The heat transfer areas are made smooth


to minimize contact resistance. The roles of heat sink and heat source are reversed when the

vessel is maintained at a temperature lower than that of the copper block. Initially the sam-

ple is in thermal equilibrium with the copper block. Thermocouples record the temperature

history of the copper block, which is assumed to have a uniform temperature distribution,

and the temperature of the bottom of the vessel.

The model assumes a linear temperature prof�ile, negligible heat storage in the sample, and

negligible surface contact resistance. Heat transfer between the copper block and its insu-

lation is assumed negligible. Using these assumptions, an expression was derived for the

temperature of the copper block:

ln

(T0 − T∞T − T∞

)=

κA

LmcCct (2.12)

where A is the heat transfer area, κ is the thermal conductivity of sample, L is the thickness

of sample, mc is the mass of copper block, Cc is the specif�ic heat of copper, t is the time, T

is the temperature of copper block,T0 is the initial temperature and T∞ is constant temper-

ature of vessel bottom.

The plot of the dimensionless temperature(T0−T∞T−T∞

)against time on semilog paper is linear

with an initial curved part. The thermal conductivity of the sample is calculated from the

slope of linear part of this plot, the heat capacity of the copper block, the thickness and heat

transfer area of the sample.

This method is more accurate for thin samples.

Thermistor Based Method

A thermistor is a thermally sensitive resistor which exhibits a change in electrical resistance

with a change in temperature [64]. Those used for thermal property measurement have a


negative temperature coef�f�icient of resistance, indicating that their resistance will decrease

when their temperature is increased. Being resistive devices, a thermistor will heat up when

a current is passed through it. The thermistor is used both as a temperature sensor and as

a point heating source. The relationship between temperature and resistance is non-linear

and is usually described by the empirical Steinhart-Hart equation [64].

1

T= a0 + a1 + lnR + a2[lnR]

3 (2.13)

where T is the temperature, R is the resistance,a0, a1and a2 are derived constants.

At steady state (when the resistance has reached a constant value) the equation for measuring

thermal conductivity κ of a sample is given by [65]:

1

κ= 4πa

4TPss− 0.2

κb(2.14)

where 4T is the temperature change, P ss is the steady state power dissipation in the ther-

mistor required for maintaining 4T, a is the ef�fective probe radius and κb is the ef�fective

probe thermal conductivity.

Transient Hot Wire method

Transient hot wire is one of the most commonly used transient methods especially for gran-

ular materials [62]. It is also known as the line heat source method. The theory is based

on a linear heat source of inf�inite length and inf�initesimal diameter. The line heat source is

embedded in the material whose thermal conductivity is to be measured. From a condition

of thermal equilibrium, the heat source is energized and heats the medium with constant

power. The temperature response of the medium is a function of its thermal properties. The

thermal conductivity is found from the temperature rise measured at a known distance from

the heat source.


The value of the thermal conductivity κ is given by the following formula [66]:

κ =qln( t2

t1)

4π(T2 − T1)(2.15)

where q is heat generated per unit length of heating wire, t1 and t2 are the measured time

and T1and T2 are temperature at times t1 and t2 respectively.

2.6 Measurement of specif�ic heat capacity

Method of mixtures or the direct water immersion method

The method of mixtures consists of dropping a specimen of known mass and temperature

into a calorimeter of known specif�ic heat capacity containing a known mass of water at known

temperature. The unknown specif�ic heat capacity Cs is then calculated from a heat balance

equation after the thermal equilibrium has been attained [62].

Cs =CwWw(Te − Tw)− CcWc(Ti − Te)

Ws(Ti − Te)(2.16)

where, Cs, Cw and Cc are specif�ic heat capacity of sample, water and calorimeter respec-

tively; Ww, Wc, and Ws are weights of water, calorimeter and sample, respectively; Teis the

equilibrium temperature of the mixture, Tw is the initial temperature of water and Ti is the

initial temperature of the sample and calorimeter.

The heat losses to the surroundings is the greatest concern in such experimental units [67].

To avoid heat losses the calorimeter should be maintained at the same temperature as that

of the surroundings and also a cooling correction should be made.


Dif�ferential scanning calorimeter (DSC)

The DSC is the most suitable equipment for measuring speci�c heat capacity but it is ex-

pensive [68]. As discussed by Mohesnin [62], the DSC produces a thermogram in accordance

with the heat energy gained or lost by the sample. This is done by a scanner which scans the

sample at the desired rate over a specif�ied temperature level of interest. The test material

and the reference material are held in a cell. They are heated by individual heaters but

maintained at the same temperature and the amount of heat energy required to maintain

this temperature is recorded.

The dual-needle heat-pulse (DNHP) sensor

Campbell et al. [69] developed a dual-needle heat pulse (DNHP) probe that can determine

simultaneously C, κ and α. In addition to its economical advantage, measurements are

rapid. The DNHP has successfully been used to rapidly and accurately measure the thermal

properties of soils [69, 70].

The Dual-Needle Heat-Pulse (DNHP) sensor consists of two 304 stainless steel parallel needles

spaced 6mm apart (F�igure 2.8). One needle contains a line heat source and the other contains

a thermocouple.

A short duration pulse is applied to the heater and the temperature of the thermocouple is

monitored. The thermocouple's temperature response to the heat pulse is used to simultane-

ously determine the thermal conductivity κ and thermal dif�fusivity α, and to calculate the

volumetric heat capacity, Cρ,which is the product of the heat capacity and the density, of

the sample.

This method was developed from the transient heat pulse technique. This technique is com-


Figure 2.8: Schematic representation of the dual-needle heat-pulse (DNHP) sensor

monly used because of its convenience, applicability to a variety of sample types and ability

to determine specif�ic heat capacity, thermal conductivity and thermal dif�fusivities in a single

measurement . The technique is based on the application of a heat pulse to a line source

and analysis of the temperature response at the line source or at some distance from the line

source [71].

Two equivalent solutions to the heat dif�fusion equation for an inf�inite slab of thickness a,

which is excited by an instantaneous input heat pulse are given below [71].

δT =

(Q

2πwCραt

)exp (−x2/4αt) +

(1 + 2

∑n=1

exp (−n2a2/αt)

)(2.17)

δT =

(Q

2awCρ (παt)1/2

)exp (−x2/4αt) +

(1 + 2

∑n=1

exp (−n2π2αt/a2)

)(2.18)

where Q is the total heat input, x is the distance between the heater and the thermocouple

and w, α, Cρ are the width, thermal dif�fusivity and volumetric specif�ic heat capacity of the

sample respectively.

The second terms in the brackets of equations 2.17 and 2.18 are negligible for short and long

measurement times. Initially the heat pulse dif�fuses outward in two dimensions as though

the sample was semi inf�inite but for long measurement times one observes one-dimensional


Figure 2.9: Temperature response measured for a sample.

heat f�low.

There are two ways of determining the specif�ic heat capacity and thermal dif�fusivity of the

sample.

One can plot a graph of temperature response measured for the sample (F�igure 2.9) . From

the graph the maximum temperature Tmax , attained and the time, tmax taken to reach that

temperature are recorded .

From equation (2.17)

α = x2/4tmax (2.19)

and

Cρ = 2Q/δTmaxπwex2 (2.20)

where δTmax is the maximum temperature change.

The second way to obtain α and Cρ is by plotting a graph of ln (δT )against 1/t . The graph


Figure 2.10: A plot of the linearisation ln (δT ) against 1t.

gives a straight line with a negative slope f�igure 2.10. α is determined from the slope while

Cρ is determined from the intercept.

The operation of the transient heat pulse technique is based on the following assumptions:

1. The heating wire is long enough so that the end ef�fects are negligible.

2. The size of the sample is su�ciently large to allow the heat pulse to propagate without

reaching any boundary during the time the measurement takes place.

3. No movement of any kind is induced during the measurement.

The analysis of error [72] showed that assuming an inf�inite length for a heat source of f�inite

length caused errors < 2% and assuming the cylindrically shaped heater to be a line heat

source caused errors of < 0.6% in the measurement of thermal properties. In order to minimise

errors in measurement in this study, the wire used as a heater was wound in cylindrical form.

Chapter 3

METHODS AND MATERIALS

3.1 Sample collection and preparation

Sample collection

In this study, the materials used include: clay, kaolin, ash, charcoal dust, saw dust, banana

f�ibres and sugar cane f�ibres.

The clay samples used in the study were collected from Ntawo in Mukono District and kaolin

was obtained from Buwambo in Wakiso district.

Ash was collected from the deposits at the bottom of local stoves used for cooking. It is a

waste material from combustion of mainly agricultural products in Uganda. The biomass

which was burned to produce this ash used in this study was not put in consideration.

The charcoal dust was collected from local charcoal selling sites. The type of wood from

which the charcoal was processed was not considered.

The sawdust was collected from carpentry workshops as a waste material from processing of

wood timber. The timber from which the sawdust waste was obtained was not considered in

this study.

The banana f�ibers were extracted from pseudo banana stems by hand. The f�ibres were then

39

METHODS AND MATERIALS 40

washed and dried in sunlight for about 12 hours.

The sugar cane f�ibres were obtained from sugar cane vendors after the juice has been extracted

by the customers from the sugar canes. The f�ibres were then dried.

The banana f�ibres and sugar cane f�ibres were f�irst ground to obtain f�ibres of smaller sizes

which were used in the measurement.

Sample preparation for thermal conductivity measurement

The clay and kaolin collected from the deposit were soaked in water and massive particles

were separated by gravity sedimentation. Thereafter, the samples were sun dried for three

days then placed inside the oven and further dried for a period of eight hours at a temperature

of 50oC. The dried samples were f�inally crushed down to smaller sizes.

The clay, kaolin, saw dust, ash and charcoal dust were sieved through a 500µm sieve to

remove coarse particles and foreign materials which are larger than 500µm that might have

been present in the samples.

Sieving by hand is dif�f�icult to perform because it is both time consuming and labor intensive

and the results are somewhat subjective. A mechanical test sieve shaker or vibrator was used

in the study.

A stack of sieves of f�ive dif�ferent sizes was mounted on the vibrator and covered at the top

so that the stack can be easily secured in the shaker as shown in f�igure 3.1. Care was taken

to ensure that there were no loose sieves on the shaker.The top sieve had the largest screen

openings of 355µm. Each lower sieve in the column had smaller openings than the one above.

At the base is a round pan, called the receiver.

A small quantity of about 200g of a sample was introduced in the top sieve at a time. The

process timer knob was rotated clockwise and set to run for 60 seconds. The sieve shaker

was set into vibrations by switching it on and the excitation produced was strong enough to

produce the desired particle sizes.


Figure 3.1: Nested sieves on a mechanical vibrator

After the set time of 60 seconds, the vibrator stops and the contents from each sieve were

removed and graded.

The particle sizes obtained were in the range <90µm, 90 -125µm, 125 - 150µm , 150 -180µm

and 180 - 355µm.

Banana and sugar cane f�ibres samples were sieved in the same way to obtain dif�ferent f�ibre

sizes

Fabrication of the rectangular plates

According to the principle of hot wire method, inf�initely long and rectangular plates are

desired for measurement. These samples should be large enough so that the heat from the

hot wire is not lost through the surrounding hence leading to errors in measurement. These

rectangular plates of the samples were achieved through the following steps.


Figure 3.2: Arrangement of a metal plate and a hollow rigid metal frame.

(i) A rectangular mould was obtained by assembling the rectangular metal block, hollow

rigid metal frame and a metal plate fabricated from mild steel as shown in the �gure .

(ii) A sample of mass 200g was poured in the mould and then covered with a metal plate.

The sample was then compacted slowly and gently using a hydraulic manual press type

PW40 (�gure 3.2) available in the department to avoid cracking of the samples. These

samples were compacted until a set pressure was attained. When the set pressure was

attained, it was maintained for about 5 minutes to allow the pressure to stabilize. The

press was then released and the rectangular blocks were then removed. As required

by the hot wire measurement, rectangular samples of 10x5x2 cm, were obtained after

compacting the powdered samples at di�erent pressures.

(iii) The samples were dried for 8h in the oven at 100oC to remove the moisture present .

(iv) The samples were then ready for thermal conductivity measurements.

To study the ef�fect of compaction pressure on the thermal conductivity, the samples were

compacted at pressures of 18.2, 36.4, 54.6 and 72.9 MPa.

When the charcoal dust sample was compacted, a weakly cohesive structure was formed so

the sample was not removed from the mould otherwise it would break. Thermal conductivity

measurements were done when the sample was still in the mould. To study the ef�fect of


Figure 3.3: Hydraulic manual press type PW40 with die between its upper and lower plates.

particle sizes on the thermal conductivity, the dif�ferent particle sizes of the graded charcoal

dust samples were compacted at a pressure of 54.6MPa.

3.2 Measurement of thermal conductivity

Thermal conductivity measurement is relatively complicated for some materials under real

conditions. The main problem in most cases lies in the preparation of test samples whose

characteristics will be identical to those of the actual material. With regard to the preparation

of test samples and their properties, problems may arise due to the cohesion of a material

which depends on the forces acting between the particles.

The Quick thermal conductivity meter (QTM-500) which uses the hot wire method was used

in the study. It does quick and easy measurement on all kinds and types of sample materials.

Measurements of thermal conductivity using QTM-500 are carried out on test samples shaped

as rectangular plates of dimensions of about 5cm x10 cm and thickness between 2 to 4 cm.


The QTM-500 has a sensor probe which consists of a constantan wire heater and a chromel-

alumel thermocouple. The heating wire is used to supply heat to the test sample and the

thermocouple monitors the heat f�low rate.

The measurement of thermal conductivity involved placing the rectangular block sample in

the probe box and then placing the sensor probe (PD-11) on sample surface (f�igure 3.4).

Figure 3.4: Experimental set up for thermal conductivity measurement

The Quick thermal conductivity meter was then switched on. The meter displays �Meas.

wait� on the LCD display (f�igure 3.6a) if the temperature of the probe is not in equilibrium

with the sample. This stabilization process takes about 30 minutes. When the temperature of

the meter has stabilized it displays on the screen �Meas. Ok�on the LCD display (f�igure 3.6b)

and the measurement is started by pressing the �START� button. When START button is

pressed, the heater is supplied with constant power by the heater current.

During the measurement, temperature of the wire against time curve is plotted on the display.

This curve is exponential and the angle of the curve is large with low conducting samples

because the temperature of the wire rises rapidly The angle becomes smaller with a sample

of high conductivity as shown in f�igure 3.5. The temperature rise, 4T , of the sample probe


Figure 3.5: Typical curves displayed on QTM-500 for small and large thermal conductivities

from the start to the end of the measurement aganist time is also displayed by the meter

(f�igure 3.6c).

The measurement result is shown on display immediately after the measurement is f�inished

in 60s (f�igure 3.6d).


(a) Stand by mode (b) Ready to start measurement

(c) Graph during measurement (d) Measurement result

Figure 3.6: Display of the QTM-500

3.3 Measurement of thermal dif�fusivity

Sample preparation

Samples were sieved to obtain particle/�bre sizes of <180 µm. In order to obtain large

rectangular block samples to allow the heat pulse to propagate without reaching any boundary

during the time of the measurement, the samples were mixed with water. The ratio of mass

of sample to volume of water was 5:2 /gcm−3 for clay, ash , kaolin and charcoal dust while

for sawdust, bagasse and banana �bres was 1:4 /gcm−3 . Rectangular boxes of dimensions

of 12×7× 6cm were used as moulds in which the mixture was poured.

A nichrome wire (heater) was embedded in the middle of the sample. The wire was selected

as a heating element in the study because of its high resistivity and high melting point of

about 1400o C.


Figure 3.7: Experimental set up for measurement of temperature response of a sample to aheat pulse

At the opposite sides of the embedded nichrome wire, holes were drilled at equal distances,

x, from the heater recorded in Table 4.7 . During measurements the thermocouples were

inserted to measure the temperature response of the samples to a transient heat pulse.

Samples were then dried in the oven at 100oC for about 48h to remove all the moisture content.

After the drying,the samples were then removed from the oven, weighed and their masses

were recorded. Also the dimensions of the samples were measured and used in calculating

the volume. Using the values obtained from mass and volume of the samples the density was

obtained.

Measurement of thermal dif�fusivity

The block sample was clamped at both ends to prevent movement of any kind. The thermo-

couples were then inserted in the holes drilled at the opposite sides of the heater. Figure 3.7

shows the experimental set up for the measurement of temperature response of a sample to

a supplied heat pulse.

An instantaneous heat pulse was introduced into the sample by energising the heater with a


voltage pulse.

After every 30 seconds the temperature on the thermocouples was noted. This was done

until a steadytemperature was attained.

Graphs of lnδT vs 1/t were drawn for the samples and their slopes determined. The thermal

di�usivities were calculated from equation (3.1).

α = − x2

4slope(3.1)

3.4 Determination of specif�ic heat capacity

. Volumetric heat capacity was obtained from the thermal di�usivity and thermal conduc-

tivity of the samples using equation (3.2) [21].

Cρ =κ

α(3.2)

Speci�c heat capacity (C) for the samples was calculated from equation (3.3).

C =Cρρ

(3.3)

This approach was taken because heat losses would not permit determination of volumetric

heat capacity from the intercepts of the graphs of lnδT vs 1/t .

Chapter 4

RESULTS AND DISCUSSION

Introduction

This chapter discusses the various results obtained for thermal conductivity (κ), thermal dif� -

fusivity (α) and speci�c heat capacity (C) of seven dif�ferent types of materials that included:

clay, kaolin, ash, charcoal dust, sugar cane f�ibre, banana f�ibre and saw dust.

4.1 Thermal conductivity tests

The measured thermal conductivity values are presented in Table 4.1. All measurements

were carried out at room temperature (approximately 25oc).

4.1.1 Ef�fect of particle/f�ibre size on thermal conductivity

The measured thermal conductivity values (Table 4.1) conf�irm that thermal conductivity is

related to particle/f�ibre size. F�igures 4.1 and 4.2 show the variation of thermal conductivity

with f�ibre/particle size for the samples respectively.

49

RESULTS AND DISCUSSION 50

Table 4.1: Thermal conductivity of the samples at di�f�ferent compaction pressures and parti-cle/f�ibre sizes

Thermal Conductivity,κ ±0.005 /Wm−1K−1

Sample Average particle/ 18.2 MPa 36.4 MPa 54.6 MPa 72.9 MPaf�ibre size (µm)

Sugar cane f�ibres/ 125 0.104 0.107 0.111 0.113bagasse 150 0.103 0.105 0.105 0.111

180 0.103 0.104 0.108 0.107355 0.084 0.078 0.076 0.086

Ash 90 0.301 0.318 0.343 0.361125 0.286 0.299 0.324 0.338150 0.272 0.288 0.314 0.326180 0.250 0.263 0.281 0.297

Banana f�ibres 125 0.317 0.318 0.327 0.338150 0.290 0.296 0.313 0.320180 0.287 0.300 0.294 0.304355 0.275 0.275 0.276 0.276

Saw dust 90 0.200 0.216 0.222 0.240125 0.198 0.212 0.219 0.232150 0.195 0.211 0.215 0.226180 0.190 0.202 0.211 0.218355 0.185 0.199 0.209 0.213

Kaolin 90 0.518 0.527 0.542 0.554125 0.505 0.513 0.529 0.537150 0.486 0.491 0.512 0.523180 0.466 0.472 0.493 0.500

Clay 90 0.240 0.275 0.295 0.308125 0.232 0.268 0.292 0.298150 0.217 0.257 0.288 0.291180 0.210 0.236 0.272 0.285

Charcoal dust 90 0.219125 0.213150 0.192180 0.184355 0.158


(4.1a) Sugar cane f�ibres/bagasse

(4.1b) Banana f�ibre

Figure 4.1: Thermal conductivity against f�ibre size at various compaction pressures


(4.2a) Ash

(4.2b)Sawdust


(4.2c) Kaolin

(4.2d) Clay


(4.2e) Charcoal dust

Figure 4.2: Thermal conductivity against particle size at various compaction pressures

F�itting the results using MatLab software indicates that the best f�it could be obtained when

the relationship between the thermal conductivity and f�iber /particle size is of the form

κ = εs−β (4.1)

where s is the f�ibre/particle size, ε is a constant which is independent of the processing

conditions of a material and β is a constant which shows the bonding power of a material.

This �t was chosen because the data provided the lowest average Root Mean Square Error

(RMSE) values compared to linear polynomial, Gaussian and Weibul �ts. The average RMSE

values obtained for the di�erent �ts are presented in Table 4.4.

This same trend has been observed in many studies in the literature [33, 34] for the variation

of thermal conductivity with particle size. Thermal conductivity generally increases with

decreasing particle size. This could be explained by the fact that small particles interlock


Table 4.2: RMSE values for the di�erent �ts for thermal conductivity variation with parti-cle/�bre size.

Fit Average RMSE valuePower 0.00418

linear polynomial 0.00482Gaussian 0.00551Weibul 0.37885

Table 4.3: Values of ε and β for dif�ferent particle/f�ibre sizes

SampleCompa- Bagasse Ash Banana Saw- Clay Kaolin Charcoalction f�ibres dust Dust

pressure(MPa) ε β ε β ε β ε β ε β ε β ε β

18.2 0.12 0.02 0.95 0.25 0.54 0.12 0.26 0.06 0.58 0.20 1.03 0.1536.4 0.12 0.03 1.01 0.26 0.43 0.07 0.29 0.06 0.69 0.20 1.08 0.1654.6 0.13 0.04 1.10 0.26 0.51 0.10 0.27 0.05 0.47 0.10 0.98 0.13 0.68 0.2572.9 0.14 0.04 1.18 0.26 0.58 0.12 0.31 0.07 0.51 0.11 1.04 0.14

closely leading to low porosity.

However no clear variation between thermal conductivity and f�ibre sizes (Figure 4.1) could

be ascertained. This could be due to the orientation or alignment of the f�ibres in the sample

with respect to direction of heat �ow. The f�ibres can be aligned horizontally, vertically or

inclined at an angle to the direction of heat �ow. Highest thermal conductivity is expected

when the f�ibres are aligned horizontally and lowest when aligned vertically [73].

Statistical analysis was done to study the ef�fect of particle/f�ibre size on the constants ε and

β . The results are presented in Table 4.3. The range of ε is between 0.12 to 1.08 and β

ranges from 0.02 to 0.26 for the samples.

4.1.2 Ef�fect of compaction pressure on thermal conductivity

Values of thermal conductivity obtained for the di�f�ferent samples were used to analyse the

ef�fect of compaction pressure on thermal conductivity. F�igures 4.3 and 4.4 show the ef�fect of


compaction pressure on the the di�f�ferent f�ibres and particle sizes respectively.


(4.3a) Sugar cane f�ibres

(4.3b) Banana f�ibres

Figure 4.3: Variation of thermal conductivity with compaction pressure for di�f�ferent f�ibresizes


Generally, results obtained show that thermal conductivity increases with increase in com-

paction pressure. This thermal conductivity increase is attributed to reduction in porosity

with increase in compaction pressure. The reduction in porosity is due to the fact that

increase in compaction pressure increases the particle - particle contact area. Materials gen-

erally have a higher thermal conductivity than that of air and hence increasing the particle-

particle contact area reduces the air spaces between and thus increasing the heat transfer in

the material.

This analysis was not performed on the charcoal dust sample because this sample could not

be compacted to form rectangular blocks.

The graphs in Figure 4.3 for the di�f�ferent f�ibre sizes do not show any marked variation of

thermal conductivity with compaction pressure. Thermal conductivity of large �bre sizes

was almost constant. This is because the �bres could not stay in the compacted state for

long. The block samples of the �bres could relax after the pressure has been released leading

to increase in air within the sample.

Analysis of the graphs in f�igure 4.3 and 4.4 show that thermal conductivity varies with

compaction pressure according to equation 4.2 .

κ = ξP γ (4.2)

where P is the compaction pressure, ξ is a constant which is independent of the processing

parameters of the sample and γ reperesents the bonding power of a material.

The power �t was preferred on the basis of lowest average RMSE compared to other �ts

obtained with the measured data. The average RMSE values obtained for the di�erent �ts

are presented in the Table 4.4.

The values of ξand γ for the di�f�ferent samples are given in Table 4.5. The value of ξ ranges

from 0.08 to 0.45 and γ ranges from 0.04 to 0.23.


(4.4a) Ash

(4.4b) Sawdust


(4.4c) Clay

(4.4d) Kaolin

Figure 4.4: Variation of thermal conductivity with compaction pressure for di�f�ferent particlesizes


Table 4.4: RMSE values for the di�erent �ts of thermal conductivity variation with com-paction pressure

Fit Average RMSE valuePower 0.00510

linear polynomial 0.00589Gaussian 0.00778Weibul 0.38678

Table 4.5: Values of ξ and γ for the di�f�ferent samples and particle/ f�ibre sizes

SampleDiameters/ Bagasse Ash Banana Saw- Clay Kaolinsizes/µm f�ibres dust

ξ γ ξ γ ξ γ ξ γ ξ γ ξ γ

90 0.20 0.13 0.15 0.11 0.14 0.18 0.45 0.05125 0.08 0.06 0.19 0.13 0.28 0.04 0.16 0.08 0.14 0.18 0.44 0.05150 0.09 0.05 0.18 0.14 0.23 0.07 0.16 0.08 0.12 0.21 0.41 0.05180 0.09 0.04 0.17 0.13 0.26 0.04 0.15 0.09 0.10 0.23 0.39 0.05355 0.09 -0.01 0.24 0.05 0.14 0.10

4.2 Thermal di�f�fusivity tests

The measured values for temperature response for the di�f�ferent samples are presented in

AppendixI. The maximum error in temperature recorded was 0.05 oC and the maximum

error in time was 1s. F�igure 4.5 and 4.6 show the temperature response of the f�ibrous and

particulate samples respectively.

The analysis showed that the curves of best f�it could be obtained using the Gaussian relation

in equation (4.3).

T =∑i

ai exp

(−((t− bi)ci

))2

(4.3)

where T is the temperature, t is the time and ai, bi, ci are constants and i = 1, 2, 3 · · · , labels

the samples.

The constants ai, bi, ci obtained for each sample are presented in Table 4.6


(4.5a)Sugarcane �bres

(4.5b) Banana �bres

Figure 4.5: Temperature response of the �brous samples to a heat pulse


Thermal di�f�fusivities of the samples were obtained using slopes of F�igure 4.7 for the f�ibres

and F�igure 4.8 for the particulate samples. Results of thermal di�f�fusivities obtained are of

the order of 10−7m2s which shows that all the samples have a low response to temperature

change.


(4.6a) Ash

(4.6b) Sawdust


(4.6c) Clay

(4.6d) Kaolin



Figure 4.6: Temperature response of the particulate sample to a heat pulse


Table 4.6: Constants ai, bi, ci for the di�erent samples

Sample i ai bi ciSugar cane �bres 1 34.33 3723 8103

2 -10.87 867.2 11693 10.21 918.1 10054 -2.166 140.9 328.95 2.226 1758 1174

Ash 1 33.86 3700 56852 2.398 1282 1031

Banana �bres 1 38.28 7937 115102 4.534 1998 11073 3.503 1067 739.44 3.017 563 14115 1.756 562 311.5

Sawdust 1 37.98 3036 43022 2.922 926 497.93 4.004 574.3 326.24 3.51 1414 8505 2.723 321 198

Clay 1 55.38 12310 84032 2.998 4125 10883 17.38 1923 15104 28.41 4364 40615 10.06 619.8 867.2

Kaolin 1 50.81 24010 55572 72.21 14680 82953 40.98 6036 48534 21.67 2828 26795 9.993 1224 1505

Charcoal dust 1 38.53 11230 162702 4.076 1630 12283 1.47 32.2 5694 2.948 3455 1399


(4.7a) Sugarcane �bres

(4.7b) Banana �bres

Figure 4.7: Graphs of ln(δT ) versus 1/t for �brous samples


Table 4.7: Thermal dif�fussivities of the samples

Sample x± 0.05× 10−3/m slope ±3.2/s−1 α± 0.23× 10−7/m2s

Sugarcane �bres 3.50 606.2 5.05Ash 3.50 834.8 3.67

Banana �bres 3.50 376.8 8.13Sawdust 3.50 255.5 1.12Clay 1.50 355.7 1.58Kaolin 3.50 716.7 4.27

Charcoal dust 3.50 503.2 6.09

Table 4.7 shows the values of the thermal dif�fusivities of the samples obtained using the slopes

from the graphs in f�igures 4.7 and 4.8 and x (distance between heater and thermocouple).

The values for thermal dif�fusivities obtained show that the samples have a very low response

to heat.

4.3 Specif�ic heat capacity determination

The specif�ic heat capacities of the samples could not be obtained using the intercepts from

the �gures 4.7 and 4.7 and the quantity of heat supplied (q = ivt) because of the heat losses

which could not be accurately measured. Using the density, thermal dif�fusivities, and thermal

conductivities of the samples, the specif�ic heat capacities of the samples were obtained using

equation (3.2). Table 4.8 shows the determined specif�ic heat capacities of the sample.

Table 4.8: Specif�ic heat capacity of the samples

Sample κ± 0.005/ α± 0.23× 10−7 ρ± 0.3 C ± 17Wm−1K−1 /m2s /kgm−3 /Jkg−1K−1

Sugarcane �bres 0.110 5.05 194.0 1125Ash 0.280 3.67 863.0 900

Banana �bres 0.270 8.13 380.0 874Sawdust 0.230 11.2 218.0 942Clay 0.240 1.58 1650.0 919Kaolin 0.480 4.27 1665.0 677

Charcoal dust 0.220 6.09 450.0 800

Results obtained show that sugarcane �bres have the highest specif�ic heat capacity therefore


(4.8a) Ash

(4.8b) Sawdust


(4.8c) Clay

(4.8d) Kaolin



Figure 4.8: Graphs of ln(δT ) versus 1/t for particulate samples


has a high capacity to retain heat and kaolin has the lowest specif�ic heat capacity.

Chapter 5

CONCLUSIONS AND

RECOMMENDATIONS

5.1 Conclusions

Thermal conductivity at room temperature, thermal dif�fusivitiy and specif�ic heat capacity

have been determined for the selected samples.

The results show that all the samples studied are good insulating materials because they

have:

(i) Low thermal conductivities hence the rate of heat transfer in these samples is low.Their

thermal conductivities ranged from 0.08 to 0.55Wm−1K−1.

(ii) Low thermal di�usivities of the order of therefore these samples have a low response to

a heat pulse.

(iii) Moderate speci�c heat capacity which means that these materials have the ability to

retain heat. The speci�c heat capacity of the samples obtained were in the range of 900

to 1125 Jkg−1K−1 for clay, ash, sawdust and sugarcane �bres and 677 to 872Jkg−1K−1

for kaolin, charcoal dust and banana �bres .

74

CONCLUSIONS AND RECOMMENDATIONS 75

It has also been noted that among the materials studied, sugarcane f�ibres can provide the

best thermal insulation for thermal energy storage systems (TES) since it has the lowest

thermal conductivity and highest specif�ic heat capacity.

The variation of thermal conductivity with particle/f�ibre size and with compaction pressure

has been clearly established. Thermal conductivity increases with decreasing particle size

and increases with increasing compaction pressure due to a decrease in porosity.

5.2 Recommendation for future work

This study has covered only seven materials. There are other materials available in Uganda

which can be used as thermal insulating materials such as sisal, paper, cotton lint and others.

The thermal properties of these materials would be studied so as to obtain the best thermal

insulating material.

To fully characterise the studied materials as insulating materials, properties like compressive

strength and water absorption should be investigated.

Also a study to consider application of the recommended material (sugarcane f�ibres) as a

thermal insulation material using life cycle analysis to evaluate environmental and health

impacts need be carried out.

There is need to investigate the appropriate form in which sugarcane f�ibres can be used for

insulation in TES systems. This study should analyse whether sugarcane f�ibres are best used

for insulation as dried crushed samples or just dried.

Bibliography

[1] Hazami M, Kooli S, Lazaar M, Farhat A, and Belingthith A. Performance of a solar

collector. J Desalination, 183:167�172, 2005.

[2] Abhat A, DeWinter F, and Cox M. Performance studies of heat pipes latent heat thermal

energy storage system. Man kind's future source energy, 2:541�546, 1978.

[3] Abhat A. Low temperature latent heat thermal energy storage: heat storage materials.

Solar Energy, 30:313�332, 1983.

[4] Dincer Ibrahim and Marc Rosen. Thermal Energy Storage: Systems and Applications.

John Wiley and Sons Inc, �rst edition, 2002.

[5] Turner W.C and Malloy J.F. Thermal Insulation Handbook. Published by McGraw-Hill

Book Company New York, 1988.

[6] Novo A. V, Bayon J.R, Castro-Fresno D, and Rodriguez-Hernandez J. Review of seasonal

heat storage in large basins: Water tanks and gravel water pits. Applied Energy, 87:390�

397, 2010.

[7] Bauer D, Marx R, Nuÿbicker-Lux J, Ochs F, Heidemann W, and Müller-Steinhagen H.

German central solar heating plants with seasonal heat storage. Solar Energy, 84:612�

623, 2010.

[8] Occupational Safety and Health Administration. Synthetic mineral �bers: Health haz-

ards. United State Department of Labor, 2003.

76

BIBLIOGRAPHY 77

[9] Mc Donalds J.C. Lung dust analysis in the assesment of past exposure of man made

mineral �bres workers. Annals occupation of hygiene, 34:427�441, 1990.

[10] Kamal Al-Malah and Basim Abu-Jdayil. Clay-based heat insulator composites: Thermal

and water retention properties. Applied Clay Science, 37:90�96, 2007.

[11] Voumbo M.L, Wereme A, and Sissoko G. Characterization of local insulators: Sawdust

and wool of kapok. J Applied Sciences, Engineering and Technology, 2:138�142, 2010.

[12] Clausen A. U. Environmental payback of stone wool in a societal energy perspective. In

International Conference Central Europe towards sustainable Building, 2007.

[13] Al-Homoud M. S. Performance characteristics and practical applications of common

building thermal insulation materials. Building and Environment, 40:351�364, 2005.

[14] Personal protective equipment: Retrieved from. Occupation safety and health adminis-

tration, october, 4, 2011, from www.osha.gov/publication/osha3151.pdf.

[15] Manish Khandelwal .Thermal insulation. Retrieved. December 3, 2011, from

www.energymanagertraining.com/documents/manish-(a)-ee07.pdf.

[16] Chi T.D, Bentz D.P, and Stutzman P.E. Microstructure and thermal conductivity of

hydrated calcium silicate board materials. Journal of Building Physics, 31:55�67, 2007.

[17] Zheng Q and Chung D.D.L. Microporous calicium silicate thermal insulator. Material

science and technology, 6:666�670, 1990.

[18] Industrial insulation group .Calcium Silicate Insulation. Retrieved. November, 10, 2010,

from http://www.amerisafe.net/uploads/msds/172387b9d2ce4f7186d62e111dac696e.pdf,

October 6 2003.

[19] Saleh A. Measurements of thermal properties of insulation materials by using transient

plane source technique. Applied thermal engineering, 26:2184�2191, 2006.

BIBLIOGRAPHY 78

[20] Industrial insulation group Fiberglass Insulation.Retrieved. November, 10, 2010, from

http://composite.about.com/od/aboutglass/l/aa980630.htm, June 1998.

[21] P. Frank and David P. De Witt. Fundamentals of Heat and Mass Transfer. John Wiley

& Sons., third edition edition, 1990.

[22] Vishnevskii I.I, Akselrod E. I, Talyanskaya N. D, Melentev N. D, and Glushkova D. B.

The thermal conductivity of refractory �ber products. J.Refractories and Industrial

Ceramics, 16:408�413, 1975.

[23] Thermal Energy Equipment: Furnaces and Bureau of Energy E�ciency Refractories. Re-

trieved. November, 15, 2010, from www.energye�ciencyasia.org, 2005.

[24] Wilkes K.E, Gabbard W.A, and Weaver F.J. Aging of polyurethane foam insulation in

simulated refrigilator panel- two year results with third generation blowing agents. In

Polyurethane conference Boston, 2000.

[25] BING TECH REP .Thermal insulation materials made of rigid polyurethane foam.

Retrieved. May, 5, 2011, from www.excellence-in-insulation.eu/.../thermal insulation

materials made of rigid polyurethane foam.pdf, October 2006.

[26] Federation of European Rigid polyurethane foam associations .Durability of

polyurethane insulation products. Retrieved. March, 2, 2011, from http://www.pu-

europe.eu/site/�leadmin/factsheets public/factsheet 16 durability of polyurethane insu-

lation products.pdf.

[27] American Society for Testing Materials (C 417-84).

[28] Meredith W. Minimum number of genes controlling cotton �ber strength in a backcross

population. Crop science, pages 1114 � 1119, 2005.

BIBLIOGRAPHY 79

[29] Sumrerng Rukzon and Prinya Chindaprasirt. Strength and carbonation model of rice

husk ash cement mortar with di�erent �neness. Materials in civil engineering, pages

253�259, 2010.

[30] Norton. Understanding Pottery Techniques. New York studio Vista Publisher, 1972.

[31] Bamigbala P.A. Determination of thermal conductivity of clay samples. The College

Review- A multi disciplinary Journal. OSSCE, 8:56�64, 2001.

[32] Nottingham Energy Partnership .Thermal Energy Storage. Retrieved. April, 2, 2011,

from www.nottenergy.com/�les/thermal stores.pdf, 2007.

[33] Mukwasibwe S. Thermal conductivity of selected uganda clays. Master's thesis, Makerere

University, 2005.

[34] Owalu J. A. E�ects of relative porosity on thermal conductivity of sintered kaolin from

buwambo quarry in uganda. Master's thesis, Makerere University, 2008.

[35] Allen L.R, Steven G.B, Nancy Y, and Larry L.B. Experimental measurements of the

thermal conductivity of ash deposits: Part 2. e�ects of sintering and deposit microstruc-

ture. Energy and Fuels, 15:75�84, 2001.

[36] Mulcahy M. F. R, Boow J, and Goard P.R.C. Fineside deposits and their e�ect on heat

transfer in pulverised fuel boiler. J. Inst. Fuel, 39:385�394, 1966.

[37] Baxter L. L. In�uence of ash deposit chemistry and structure on physical and transport

properties. Fuel Process. Technol, 56:81�88, 1998.

[38] Torquato S. Random heterogeneous media: Micrstructure and improved bonds on the

e�ective properties. Appl. Mech, 44:37�76, 1991.

[39] Information about bagasse .Burning Bagasse. Retrieved. April 3, 2011, from

http://energyconcepts.tripod.com/energyconcepts/bagasse.htm, 2004.

BIBLIOGRAPHY 80

[40] Cerqueira D.F. Optimization of sugarcane bagasse cellulose acetylation. Carbohydrate

Polymers, 69:579�582, 2007.

[41] Elsunni M. M and Collier J. R. Processing of sugarcane rind into non-woven �bers.

Journal of American Society of Sugar Cane Technologists, 16:94�110, 1996.

[42] Ovidiu I. C. Bagasse �bre for production of nonwoven materials. PhD thesis, Louisiana

State University, 2004.

[43] Krishpersad M. Biodegradable �brous thermal insulation. Journal of the Brazilian

Society of Mechanical Sciences and Engineering, 28:45�47, 2006.

[44] Uganda Bureau of Statistics. Statistical Abstract 2003. Uganda Bureau of Statis-

tics,Entebbe, Uganda., 2003.

[45] Kulkarni A.G, Satyanarayana K.G, and Rohatgi P.K. Mechanical properties of banana

�bres. J Material Science, 18:2290�2296, 1983.

[46] Paul S. A, Boudene A, Joseph K, and Thomas S. E�ect of �ber loading and chemical

treatments on thermo physical properties of banana �ber/polypropylene commingled

composite materials. Composites, 39:1582�1588, 2008.

[47] Ogunleye I.O and Awogbemi O. Thermo-physical properties of eight varieties of sawdust.

Journal of Research in Engineering, 4:9�11, 2007.

[48] U.S.D.A. Forest Service. Uses for sawdust, shavings, and waste chips. 1969.

[49] Paulo R. W, Carlos R. A, and Ronaldo M. B. Assessment of a small sawdust gasi�cation

unit. J Biomass and Bioenergy, 27:467�476, 2004.

[50] Murlidhar Gupta, Jin Yang, and Christian Roy. Speci�c heat and thermal conductivity

of softwood bark and softwood char particles. Fuel, 82:919�927, 2003.

BIBLIOGRAPHY 81

[51] Mohammad Al-Homoud S. Performance characteristics andpractical application of com-

mon building thermal insulation materials. Building and Environment, 40:353�366, 2005.

[52] Rajput. Engineering Thermodynamics. New Delhi: Laxmi Publications, 2005.

[53] Blumm Jurgen .Measuring Thermal Conductivity. Retrieved. March,

2, 2011, from http://www.ceramicindustry.com/articles/feature arti-

cle/ddb42604d0ac7010vgnvcm100000f932a8c0, 2002.

[54] Bagel L. Structural parameters of clay bricks. Bratislava., 2001.

[55] Budaiwi I, Abdou A, and Al-Homoud M. Variations of thermal conductivity of insulation

materials under di�erent operating temperatures: Impact on envelope-induced cooling

load. Architectural engineering, 8:125�132, 2002.

[56] Xu Yibin, Tanaka Yoshihisa, Guo Hongbo, and Yamazaki Masayoshi. Prediction of

thermal conductivity of composite materials. Power and Energy Systems, 2:1048�1059,

2008.

[57] Maxwell J. C. A treatise on electricity and magnetism, volume 1. Oxford University

Press, London, 3rd edn edition, 1892.

[58] Rayleigh L. The in�uence of obstacles arranged in rectangular order upon the properties

of a medium. Phil. Mag, 34:481�500, 1892.

[59] Nicole Dooley and Sophia Leung. E�ective thermal conductiv-

ity of composite solids, retrieved on november, 15, 2010, from

http://www.owlnet.rice.edu/ ceng402/proj02/sleung/�nalproject.htm, April 2002.

[60] Casalini A, Felisari R, Ghidoni D, and A. Simonelli A, Ponticiello and. Composite

material based on vinyl aromatic polymers having enhanced thermal insulation properties.

2010.

BIBLIOGRAPHY 82

[61] Closmann P.J and Bradley W.B. The e�ect of temperature on tensile and compressive

strengths and young's modulus of oil shale. SPE Journal, 19:301�312, 1979.

[62] Mohesnin N.M. Thermal properties of food and agricultural materials. Gordon and

Breach Science Publishers, New York, 1980.

[63] Sweat V.E, Rhao M, and Rizvi S.S.H. Thermal properties of foods. in "Engineering

properties of foods". Marcel Dekker, New York, 1986.

[64] Thermometrics. Thermistor sensor hand book. Thermometrics Inc., 1987.

[65] Van Gelder M.F and Diehl K.C. A thermistor based method for measuring thermal

conductivity and thermal di�usivity of moist food materials at high temperatures.Thermal

conductivity. Academic Press, London., 1996.

[66] Kyoto Electronics Manufacturing Company Limited. Thermal conductivity Meter

(QTM-500) operation manual. Tokyo- Japan.

[67] M.J. Lewis. Physical properties of foods and food processing systems. Ellis Horwood

Ltd., Chichester, England, 1987.

[68] Polley S.L, Snyder O.P, and Kotnour P. A compilation of thermal properties of foods.

Food Tech, 11:76�94, 1980.

[69] Campbell G.S, Calissendor� C, and Williams J.H. Probe for measuring soil speci�c heat

using a heat-pulse method. Soil Sci. Soc. Am. J, 55:291�293, 1991.

[70] Bristov K.L, Kluitenberg G.J, and Horton R. Measurement of soil thermal properties

with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J., 58:1288�1294, 1994.

[71] Carslaw H.S and Jaeger J.C. Conduction of heat in solids. Oxford Univ. Press,Oxford,

England, second edition edition, 1986.

BIBLIOGRAPHY 83

[72] Kluitrenberg G.J, Bristow K.L, and Das B.S. Error analysis of heat pulse method for

measuring soil heat capacity, di�usivity and conductivity. Soil Sci. Soc. Am. J, 59:719�

726, 1995.

[73] Yves Jannot, Alain Degiovanni, Vincent F�elix, and Harouna Bal. Measurement of the

thermal conductivity of thin insulating anisotropic material with a stationary hot strip

method. Meas. Sci. Technol., 22, 2011.

APPENDIX I 84

Appendix I: Temperature response of the samples to a heat pulse.

pulse.AVERAGE TEMPERATURE±0.05oCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust

0 24.4 24.8 23.5 24.2 25.1 25.1 25.130 24.4 24.8 23.5 24.2 25.1 25.1 25.160 24.4 24.9 23.5 24.4 25.3 25.1 25.190 24.4 25.0 23.5 25.2 25.8 25.2 25.2120 24.5 25.1 23.5 26.0 26.6 25.3 25.3150 24.6 25.4 23.6 26.9 27.7 25.7 25.4180 24.8 25.7 23.6 27.8 28.7 26.0 25.6210 25.1 26.0 23.7 28.8 29.8 26.6 25.8240 25.4 26.4 23.8 29.8 30.6 27.3 26.0270 25.6 26.8 24.1 30.4 31.6 28.0 26.2300 25.9 27.1 24.2 31.2 32.5 28.8 26.3330 26.2 27.6 24.5 31.9 33.1 29.5 26.5360 26.5 28.0 24.7 32.5 33.8 30.4 26.7390 26.9 28.3 25.0 33.0 34.6 31.2 27.1420 27.2 28.7 25.2 33.4 35.3 31.7 27.3450 27.5 29.1 25.4 33.9 35.8 32.4 27.5480 27.8 29.5 25.6 34.2 36.3 33.3 27.7510 28.2 29.8 25.9 34.5 36.8 33.9 27.9540 28.5 30.0 26.2 34.8 37.3 34.6 28.1570 28.8 30.3 26.4 35.1 37.7 35.2 28.2600 29.0 30.5 26.6 35.2 38.2 35.8 28.4630 29.3 30.7 26.8 35.5 38.6 36.3 28.6660 29.6 30.8 27 35.6 39.0 36.8 28.8690 29.8 31.0 27.2 35.8 39.4 37.4 29.0720 30.0 31.2 27.4 35.9 39.8 37.8 29.2750 30.1 31.3 27.8 36.1 40.2 38.3 29.5780 30.3 31.5 28.1 36.3 40.6 38.9 29.7810 30.5 31.6 28.2 36.4 40.9 39.3 29.8840 30.7 31.8 28.4 36.4 41.3 39.7 30.0870 30.9 31.9 28.6 36.5 41.7 40.2 30.1900 31.0 32.1 28.9 36.5 42.1 40.7 30.2930 31.2 32.2 29.0 36.6 42.5 41.2 30.3960 31.4 32.4 29.3 36.7 42.8 41.6 30.5990 31.5 32.45 29.7 36.7 43.1 42.1 30.61020 31.6 32.6 29.8 36.8 43.5 42.4 30.61050 31.8 32.8 29.9 36.8 43.8 42.9 30.61080 31.9 32.9 30 36.8 44.2 43.4 30.71110 32.0 33.0 30.1 36.9 45.1 43.9 30.71140 32.1 33.1 30.1 37.1 45.2 44.3 30.81170 32.2 33.3 30.3 37.2 45.4 44.7 30.91200 32.4 33.4 30.4 37.2 45.6 45.2 31.01230 32.4 33.5 30.7 37.3 45.9 45.6 31.11260 32.5 33.7 30.8 37.3 46.1 46.0 31.11290 32.6 33.8 30.9 37.4 46.2 46.4 31.21320 32.7 34.0 30.9 37.4 46.5 46.8 31.41350 32.8 34.1 30.9 37.5 46.7 47.2 31.61380 32.9 34.2 30.9 37.6 46.9 47.5 31.61410 33.0 34.2 31.0 37.6 47.1 47.9 31.81440 33.0 34.3 31.0 37.6 47.2 48.3 31.81470 33.1 34.4 31.0 37.6 47.5 48.8 31.81500 33.1 34.5 31.1 37.7 47.7 49.1 31.9

Apendix I: Temperature response of the samples to a heat pulse 85

AVERAGE TEMPERATURE ±0.05/OCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust

1530 33.2 34.6 31.1 37.7 47.8 50.0 31.9

1560 33.2 34.7 31.3 37.7 47.9 50.3 32.0

1590 33.3 34.8 31.5 37.8 48.1 50.7 32.0

1620 33.4 34.8 31.6 37.8 48.3 51.0 32.0

1650 33.4 34.9 31.8 37.9 48.5 51.3 32.1

1680 33.5 35.0 31.6 37.9 48.7 51.7 32.1

1710 33.5 35.1 32.0 37.9 48.8 52.0 32.2

1740 33.6 35.1 31.9 38.0 49.0 52.3 32.1

1770 33.6 35.1 31.7 37.9 49.1 52.6 32.2

1800 33.7 35.2 31.8 37.9 49.3 52.8 32.2

1830 33.7 35.2 31.8 38.0 50.0 53.1 32.4

1860 33.8 35.3 31.9 38.0 50.1 53.4 32.5

1890 33.8 35.4 32.1 38.0 50.4 53.7 32.5

1920 33.9 35.4 32.2 38.0 50.5 54.0 32.6

1950 33.9 35.4 32.2 38.0 50.6 54.3 32.7

1980 34.0 35.4 32.2 38.1 50.8 54.6 32.7

2010 34.0 35.5 32.4 38.0 51.0 54.8 32.7

2040 34.0 35.5 32.5 38.0 51.1 55.1 32.7

2070 34.0 35.5 32.7 38.0 51.1 55.4 32.7

2100 34.0 35.6 32.8 38.1 51.2 55.6 32.7

2130 34.0 35.6 32.9 38.1 51.3 55.8 32.7

2160 34.0 35.6 33.1 38.1 51.7 56.0 32.7

2190 34.0 35.7 33.0 38.1 51.7 56.3 32.7

2220 34.0 35.8 32.9 38.1 51.9 56.6 32.8

2250 34.2 35.8 33.0 38.1 51.9 56.8 32.9

2280 34.2 35.8 33.0 38.0 52.0 57.0 32.8

2310 34.2 35.8 32.8 38.0 52.0 57.2 32.9

2340 34.2 35.9 32.9 38.0 52.1 57.4 33.0

2370 34.2 36.0 33.0 38.0 52.2 57.7 33.1

2400 34.3 36.0 33.0 38.0 52.0 58.0 33.1

2430 34.3 36.1 33.0 38.0 52.0 58.2 33.3

2460 34.3 36.1 33.1 38.1 51.9 58.4 33.3

2490 34.2 36.1 33.2 38.1 52.0 58.6 33.4

2520 34.3 36.2 33.1 38.1 52.4 58.8 33.4

2550 34.5 36.2 33.1 38.1 52.5 59.0 33.4

2580 34.5 36.2 33.1 38.2 52.4 59.2 33.6

2610 34.5 36.2 33.2 38.2 52.3 59.4 33.5

2640 34.5 36.2 33.1 38.2 52.3 59.6 33.5

2670 34.5 36.2 33.1 38.2 52.7 59.8 33.5

2700 34.5 36.3 33.2 38.2 52.9 60.1 33.4

2730 34.5 36.3 33.2 38.2 52.8 60.4 33.4

2760 34.5 36.3 33.1 38.1 52.7 60.6 33.3

2790 34.5 36.3 33.1 38.1 52.7 60.8 33.2

2820 34.5 36.4 33.3 38.1 53.3 60.9 33.4

2850 34.5 36.4 33.4 38.1 53.3 61.0 33.4

2880 34.5 36.4 33.4 38.1 53.1 61.2 33.7

2910 34.5 36.4 33.3 38.0 53.1 61.4 33.7

2940 34.5 36.4 33.3 38.0 53.0 61.5 33.7


AVERAGE TEMPERATURE ±0.05OCTime/s Sugarcane �bres Banana �bres Ash Sawdust Clay Kaolin Charcoal dust

2970 34.5 36.4 33.4 38.0 53.0 61.8 33.7

3000 34.5 36.4 33.4 38.0 53.1 61.8 33.7

3030 34.5 36.4 33.5 38.0 53.7 62.1 33.7

3060 34.6 36.4 33.6 38.0 53.5 62.4 33.6

3090 34.6 36.4 33.6 38.0 53.3 62.4 33.6

3120 34.6 36.4 33.7 38.0 53.2 62.5 33.6

3150 34.6 36.5 33.7 38.0 53.2 62.7 33.7

3180 34.5 36.5 33.7 38.0 53.2 62.8 33.7

3210 34.5 36.6 33.8 38.0 53.2 62.9 33.8

3240 34.5 36.6 33.8 38.0 53.9 63.0 33.8

3270 34.5 36.6 33.9 38.0 53.8 63.3 33.9

3300 34.5 36.6 33.9 53.6 63.8 33.8

3330 34.5 36.7 33.9 53.9 63.9 33.9

3360 34.5 36.7 34.0 53.4 63.9 33.9

3390 34.5 36.7 33.8 53.4 63.9 33.9

3420 34.5 36.7 33.6 53.4 64.0 34.0

3450 34.5 36.7 33.8 53.4 64.1 34.1

3480 34.5 36.7 33.9 53.4 64.3 34.3

3510 34.5 36.7 34.1 53.4 64.5 34.2

3540 34.5 36.7 34.0 53.4 64.6 34.3

3570 34.5 36.7 33.8 53.5 64.6 34.1

3600 34.5 36.8 33.7 53.7 64.7 34.1

3630 34.5 36.7 33.8 54.3 64.8 34.3

3660 34.5 36.7 33.5 53.3 64.9 34.2

3690 34.4 36.8 33.4 53.8 65.0 34.2

3720 34.4 36.9 33.4 53.7 65.1 34.2

3750 34.4 36.9 33.4 53.6 65.2 34.2

3780 34.4 36.9 33.5 54.4 65.3 34.2

3810 34.4 36.9 33.7 54.7 65.4 34.2

3840 34.4 36.9 33.6 54.7 65.5 34.2

3870 34.4 36.9 33.6 54.6 65.6 34.2

3900 34.4 36.9 33.5 54.6 65.8 34.2

3930 36.9 33.4 54.5 65.9 34.2

3960 37.0 33.6 54.5 66.0 34.3

3990 37.0 33.8 54.6 66.1 34.3

4020 37.0 33.9 54.6 66.2 34.3

4050 37.0 34.0 54.7 66.4 34.3

4080 37.0 33.9 54.7 66.6 34.3

4110 37.0 33.9 54.8 66.9 34.3

4140 37.0 34.0 54.8 66.9 34.3

4170 37.0 34.1 54.9 66.9 34.3

4200 37.0 33.8 54.9 67.0 34.2

4230 37.0 33.8 54.9 67.0 34.2

4260 37.1 33.6 55.0 66.9 34.1

4290 37.1 33.5 55.1 66.9 34.2

4320 37.1 33.5 55.2 67.1 34.2

4350 37.0 55.3 67.2 34.2

4380 37.0 55.5 67.4 34.2

4410 37.0 55.5 67.4 34.2

4440 37.0 55.4 67.5 34.1

4470 36.9 55.4 67.6 34.2

4500 37.0 55.3 67.6 34.1


AVERAGE TEMPERATURE±0.05OCTime±1/s Banana �bres Clay Kaolin Charcoal dust

4530 36.9 55.2 67.6 34.2

4560 36.8 55.0 67.7 34.2

4590 36.8 55.0 67.8 34.2

4620 36.8 55.0 67.9 34.2

4650 36.9 55.0 68.1 34.1

4680 37.0 55.0 68.2 34.0

4710 37.0 55.1 68.2 34.0

4740 37.0 55.3 68.2 34.1

4770 37.0 55.3 68.3 34.1

4800 37.0 55.4 68.3 34.1

4830 37.0 55.4 68.3 34.2

4860 37.0 55.4 68.4 34.2

4890 37.1 55.4 68.5 34.2

4920 37.0 55.5 68.8 34.2

4950 36.9 55.5 68.7 34.2

4980 36.9 55.5 68.7 34.1

5010 36.9 55.5 68.8 34.1

5040 36.9 55.6 69.1

5070 55.5 69.1

5100 55.5 69.2

5130 55.4 69.3

5160 55.4 69.3

5190 55.4 69.3

5220 55.6 69.4

5250 55.6 69.4

5280 55.6 69.5

5310 55.6 69.5

5340 55.6 69.6

5370 55.7 69.6

5400 55.7 69.7

5430 55.7 69.7

5460 55.7 69.7

5490 55.7 69.7

5520 55.7 70.0

5550 55.7 70.0

5580 55.7 70.0

5610 55.7 70.1

5640 55.8 70.1

5670 55.8 70.1

5700 55.9 70.1

5730 55.9 70.1

5760 55.9 70.1

5790 55.9 70.3

5820 55.9 70.6

5850 55.8 70.7

5880 55.9 70.7

5910 55.9 70.7

5940 55.9 70.9

5970 56.0 71.1

6000 56.1 71.1


Time±1/s Clay Kaolin Time±1/s Clay Kaolin Time±1/s Clay Kaolin

6030 56.0 71.0 7530 54.9 72.6 9030 55.5 73.7

6060 56.0 71.0 7560 54.9 72.6 9060 55.5 73.7

6090 55.9 70.9 7590 54.9 72.7 9090 55.5 73.6

6120 55.9 70.9 7620 54.7 72.6 9120 55.5 73.6

6150 56.1 70.9 7650 54.7 72.5 9150 55.5 73.5

6180 56.1 70.8 7680 54.7 72.5 9180 55.5 73.5

6210 56.0 70.9 7710 54.8 72.5 9210 55.4 73.5

6240 56.0 70.9 7740 54.8 72.6 9240 55.4 73.4

6270 55.9 71.0 7770 54.8 72.8 9270 55.5 73.3

6300 56.0 71.0 7800 54.9 72.8 9300 55.5 73.3

6330 56.1 71.0 7830 55.0 72.8 9330 55.5 73.2

6360 56.0 71.2 7860 55.1 72.9 9360 55.5 73.1

6390 56.0 71.2 7890 55.2 72.9 9390 55.4 73.1

6420 56.0 71.2 7920 55.2 72.9 9420 55.4 73.2

6450 55.9 71.2 7950 55.2 72.8 9450 55.4 73.2

6480 55.8 71.2 7980 55.3 72.8 9480 55.4 73.2

6510 55.4 71.3 8010 55.6 72.8 9510 55.4 73.2

6540 55.7 71.2 8040 55.6 72.9 9540 55.4 73.2

6570 55.6 71.2 8070 55.6 72.9 9570 55.5 73.5

6600 55.7 71.3 8100 55.6 72.9 9600 55.5 74.0

6630 55.6 71.4 8130 55.6 72.9 9630 55.5 74.1

6660 55.6 71.4 8160 55.7 72.9 9660 55.5 74.1

6690 55.8 71.4 8190 55.7 72.9 9690 55.4 74.0

6720 55.9 71.5 8220 55.6 72.9 9720 55.5 73.9

6750 55.8 71.5 8250 55.6 73.0 9750 55.5 73.7

6780 55.9 71.5 8280 55.6 73.0 9780 55.5 73.7

6810 56.0 71.6 8310 55.5 73.0 9810 55.4 73.6

6840 55.1 71.6 8340 55.4 73.0 9840 55.4 73.6

6870 56.0 71.7 8370 55.3 73.1 9870 55.4 73.6

6900 55.9 71.7 8400 55.3 73.1 9900 55.4 73.6

6930 55.7 71.8 8430 55.3 73.1 9930 55.3 73.6

6960 55.9 71.9 8460 55.2 73.1 9960 55.3 73.5

6990 55.9 71.8 8490 55.2 73.2 9990 55.5 73.5

7020 55.7 71.8 8520 55.2 73.2 10020 55.4 73.5

7050 55.7 71.9 8550 55.2 73.2 10050 55.4 73.4

7080 55.8 72.1 8580 55.2 73.1 10080 55.5 73.4

7110 55.7 72.3 8610 55.2 73.1 10110 55.5 73.5

7140 55.7 72.6 8640 55.1 73.1 10140 55.4 73.5

7170 55.6 72.6 8670 55.2 73.2 10170 55.5 73.5

7200 55.5 72.6 8700 55.3 73.4 10200 55.4 73.7

7230 55.4 72.4 8730 55.3 73.3 10230 55.5 73.7

7260 55.6 72.4 8760 55.3 73.4 10260 55.6 73.6

7290 55.7 72.4 8790 55.3 73.4 10290 55.6 73.9

7320 55.7 72.5 8820 55.3 73.5 10320 55.5 73.9

7350 55.6 72.5 8850 55.4 73.5 10350 55.5 73.9

7380 55.4 72.5 8880 55.4 73.5 10380 55.5 73.8

7410 55.4 72.5 8910 55.5 73.5 10410 55.5 73.7

7440 55.3 72.6 8940 55.5 73.7 10440 55.6 73.6

7470 55.2 72.5 8970 55.4 73.9 10470 55.6 73.5

7500 55.0 75.6 9000 55.4 73.8 10500 55.6 73.7


Time±1/s Clay Kaolin Time±1/s Kaolin Time±1/s Kaolin Time±1/s Kaolin

10530 55.5 74.3 12000 74.7 13470 76.2 14940 77.1

10560 55.6 74.5 12030 74.6 13500 76.2 14970 77.0

10590 55.6 74.4 12060 74.6 13530 76.2 15000 76.9

10620 55.6 74.2 12090 74.8 13560 76.1 15030 76.9

10650 55.6 74.2 12120 74.9 13590 76.1 15060 77.0

10680 55.5 74.0 12150 74.8 13620 76.2 15090 77.0

10710 55.5 73.9 12180 74.9 13650 76.2 15120 77.1

10740 55.5 73.7 12210 74.9 13680 76.1 15150 77.1

10770 55.5 73.7 12240 74.9 13710 76.2 15180 76.9

10800 55.4 73.6 12270 75.0 13740 76.2 15210 76.9

10830 55.4 73.7 12300 74.9 13770 76.2 15240 77.1

10860 55.4 73.7 12330 74.9 13800 76.1 15270 77.1

10890 55.5 73.7 12360 75.0 13830 76.2 15300 77.2

10920 55.6 73.7 12390 75.0 13860 76.2 15330 77.1

10950 55.7 73.8 12420 75.1 13890 76.2 15360 77..0

10980 55.7 73.8 12450 75.1 13920 76.1 15390 77.1

11010 55.8 73.8 12480 75.2 13950 76.0 15420 77.0

11040 55.8 73.8 12510 75.2 13980 76.1 15450 76.9

11070 55.9 73.9 12540 75.2 14010 76.2 15480 77.0

11100 55.9 74.1 12570 75.3 14040 76.2 15510 77.1

11130 55.9 74.4 12600 75.3 14070 76.2 15540 77.2

11160 55.9 74.4 12630 75.3 14100 76.3 15570 77.1

11190 55.8 74.3 12660 75.4 14130 76.3 15600 77.2

11220 55.7 74.3 12690 75.4 14160 76.4 15630 77.1

11250 55.8 74.2 12720 75.4 14190 76.4 15660 77.2

11280 55.9 74.2 12750 75.4 14220 76.3 15690 77.1

11310 56.0 74.0 12780 75.4 14250 76.4 15720 77.1

11340 56.0 74.0 12810 75.5 14280 76.4 15750 77.2

11370 56.1 74.1 12840 75.4 14310 76.5 15780 77.1

11400 56.1 74.1 12870 75.4 14340 76.4 15810 77.2

11430 56.1 74.3 12900 75.4 14370 76.6 15840 77.2

11460 56.2 74.4 124930 75.5 14400 76.9 15870 77.1

11490 56.2 74.5 12960 75.5 14430 76.8 15900 77.4

11520 56.4 74.6 12990 75.5 14460 76.8 15930 77.4

11550 56.5 74.7 13020 75.7 14490 76.7 15960 77.4

11580 56.6 74.8 13050 75.7 14520 76.5 15990 77.4

11610 56.7 74.7 13080 75.7 14550 76.5 16020 77.5

11640 56.7 74.6 13110 75.7 14580 76.5 16050 77.5

11670 56.7 74.6 13140 75.7 14610 76.5 16080 77.5

11700 56.6 74.5 13170 75.7 14640 76.5 16110 77.4

11730 56.6 74.5 13200 75.7 14670 76.6 16140 77.5

11760 56.6 74.5 13230 75.8 14700 76.6 16170 77.5

11790 74.6 13260 75.8 14730 76.5 16200 77.5

11820 74.6 13290 75.7 14760 76.7 16230 77.5

11850 74.7 13320 75.7 14790 76.7 16260 77.4

11880 74.6 13350 75.7 14820 76.7 16290 77.4

11910 74.6 13380 75.7 14850 76.8 16320 77.4

11940 74.7 13410 75.8 14880 77.0 16350 77.4

11970 74.8 13440 76.1 14910 77.0 16380 77.5


Time±1/s Kaolin Time±1/s Kaolin Time/s Time±1/s Time±1/s Kaolin Time±1/s Kaolin

16410 77.5 17880 77.5 19350 77.5 20820 78.5 22290 76.9

16440 77.4 17910 77.6 19380 77.6 20850 78.6 22320 76.8

16470 77.4 17940 77.6 19410 77.6 20880 78.6 22350 76.8

16500 77.5 17970 77.7 19440 77.5 20910 78.5 22380 76.8

16530 77.7 18000 77.7 19470 77.6 20940 78.6 22410 76.8

16560 77.7 18030 77.7 19500 78.4 20970 78.4 22440 76.7

16590 77.6 18060 77.6 19530 78.4 21000 78.4 22470 76.7

16620 77.5 18090 77.6 19560 78.3 21030 78.4 22500 756.7

16650 77.7 18120 77.5 19590 78.1 21060 78.3 22530 76.7

16680 77.6 18150 77.4 19620 78.1 21090 78.3 22560 76.7

16710 77.5 18180 77.4 19650 78.0 21120 78.4 22590 76.7

16740 77.6 18210 77.5 19680 78.1 21150 78.8 22620 76.6

16770 77.6 18240 77.7 19710 78.1 21180 78.7 22650 76.5

16800 77.6 18270 77.7 19740 78.0 21210 78.9 22680 76.5

16830 77.5 18300 77.6 19770 78.0 21240 79.0 22710 76.5

16860 77.6 18330 77.6 19800 78.0 21270 78.9 22740 76.5

16890 77.5 18360 77.6 19830 78.0 21300 79.2 22770 76.5

16920 77.6 18390 77.6 19860 78.0 21330 78.8 22800 76.4

16950 77.6 18420 77.6 19890 78.0 21360 79.0

16980 77.6 18450 77.5 19920 78.0 21390 78.8

17010 77.6 18480 77.6 19950 78.0 21420 78.8

17040 77.6 18510 77.5 19980 78.0 21450 78.6

17070 77.5 18540 77.5 20010 78.0 21480 78.3

17100 77.5 18570 77.4 20040 78.0 21510 78.3

17130 77.6 18600 77.4 20070 78.0 21540 78.1

17160 77.7 18630 77.4 20100 78.1 21570 78.3

17190 77.8 18660 77.4 20130 78.0 21600 78.3

17220 77.7 18690 77.2 20160 77.8 21630 78.2

17250 77.7 18720 77.2 20190 77.9 21660 78.2

17280 77.7 18750 77.1 20220 78.1 21690 78.0

17310 77.8 18780 77.2 20250 78.1 21720 78.0

17340 77.7 18810 77.2 20280 78.1 21750 77.9

17370 77.7 18840 77.2 20310 78.2 21780 77.8

17400 77.7 18870 77.2 20340 78.2 21810 77.8

17430 77.7 18900 77.2 20370 78.1 21840 77.8

17460 77.8 18930 77.2 20400 78.2 21870 77.7

17490 77.8 18960 77.3 20430 78.2 21900 77.7

17520 77.7 18990 77.3 20460 78.2 21930 77.7

17550 77.6 19020 77.4 20490 78.4 21960 77.6

17580 77.7 19050 77.4 20520 78.4 21990 77.5

17610 77.8 19080 77.4 20550 78.3 22020 77.5

17640 77.8 19110 77.4 20580 78.4 22050 77.4

17670 77.7 19140 77.5 20610 78.4 22080 77.3

17700 77.7 19170 77.5 20640 78.4 22110 77.3

17730 77.7 19200 77.5 20670 78.4 22140 77.2

17760 77.7 19230 77.4 20700 78.4 22170 77.2

17790 77.6 19260 77.5 20730 78.5 22200 77.1

17820 77.4 19290 77.6 20760 78.4 22230 77.1

17850 77.5 19320 77.5 20790 78.5 22260 77.0

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thermal properties of selected materials for thermal insulation

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