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i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 1

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Effect of initial aqueous solution concentration andheating conditions on heat transfer characteristicsof ice slurry

Hiroyuki Kumano a,*, Tatsunori Asaoka b, Seigo Sawada b

aDepartment of Mechanical Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara,

Kanagawa 252-5258, JapanbDepartment of Mechanical Systems Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan

a r t i c l e i n f o

Article history:

Received 7 October 2013

Received in revised form

17 January 2014

Accepted 21 January 2014

Available online 4 February 2014

Keywords:

Ice slurry

Two-phase flow

Heat transfer coefficient

Non-Newtonian fluid

* Corresponding author. Tel.: þ81 42 759 621E-mail address: kumano@me.aoyama.ac.

0140-7007/$ e see front matter ª 2014 Elsevhttp://dx.doi.org/10.1016/j.ijrefrig.2014.01.007

a b s t r a c t

In this study, parameters affecting the heat transfer characteristics of ice slurry were

investigated experimentally. The initial concentration of the ethanol solution from which

the ice slurry was produced was varied as experimental parameter. Moreover, the heat flux

at the test tube surface was varied as the experimental parameters, and the heat transfer

coefficients measured. The effect of initial ethanol solution concentration and heating

conditions on the heat transfer characteristics was not significant, and the Nusselt number

can be expressed as a function of apparent Reynolds number, ice packing factor and ratio

of average ice particle diameter to test tube diameter.

ª 2014 Elsevier Ltd and IIR. All rights reserved.

Effet de la concentration initiale de la solution aqueuse et desconditions de chauffage sur les caracteristiques du transfertde chaleur d’un coulis de glace

Mots cles : Coulis de glace ; Ecoulement diphasique ; Coefficient de transfert de chaleur ; Fluide non-Newtonien

1. Introduction

Thermal energy storage systems using ice as phase-change

material have many advantages in terms of leveling electric

power (Saito, 2002). In particular, cold thermal energy can be

3; fax: þ81 42 759 6212.jp (H. Kumano).ier Ltd and IIR. All rights

transported directly in a dynamic-type ice thermal energy

storage system, since fluid ice slurry is used as phase change

material. The ice slurry is a mixture of fine ice particles and

aqueous solution. It has a high heat transfer rate, because the

latent heat of fusion of the ice particles can be used and the

heat exchange area is wide. Thus, ice slurries could be used

reserved.

Nomenclature

c ice packing factor, %

d average diameter of ice particles in ice slurry, m

D inner tube diameter, m

Fr Froude number

g gravitational acceleration, m s�2

k thermal conductivity, W m�1 K�1

Kʹ coefficient in Eq. (9)

L tube length, m

nʹ exponent in Eq. (13)

Nu Nusselt number

q heat flux, W m�2

Re Reynolds number

ReM apparent Reynolds number for pseudo-plastic

fluid

T temperature, �C

um mean velocity, m s�1

Dp pressure drop, Pa

a heat transfer coefficient, W m�2 K�1

l coefficient of pipe friction

n kinematic viscosity, m2 s�1

r density, kg m�3

sR shearing stress at inner surface, Pa

Subscripts

cal values obtained from Eq. (12)

e phase equilibrium

exp values obtained from experimental results

i ice

lam laminar flow

s aqueous solution

sl ice slurry

w inner tube surface

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 1 73

advantageously in thermal energy storage. Knowledge of the

flow and heat transfer characteristics of the ice slurry is

therefore important. Many researchers have investigated ice

slurry flow and heat transfer characteristics over the past

decade. Niezgoda-Zelasko and Zalewski (2006) investigated

these flow characteristics experimentally in horizontal tubes.

The critical velocity and mass fraction corresponding to a

change in ice slurry character from laminar to turbulent flow

were determined. Knodel et al. (2000) reported on the flow and

heat transfer characteristics of ice slurry in a 24 mm diameter

tube. The ice slurry velocity was varied from 2.8 to 5.0 m s�1,

and a reduction in pressure was observed from flow relami-

narization for a large ice packing factor (IPF). The flow and

melting characteristics of ice slurry have also been investi-

gated by a number of researchers (Guilpart et al., 1999; Lee

et al., 2006; Doetsch, 2001; Bellas et al., 2002). Ayel et al.

(2003) reviewed the flow and heat transfer behavior of ice

slurries, and Egolf and Kauffeld (2005) reviewed their physical

properties. In particular, in previous studies, parameters

affecting the heat transfer characteristics of the ice slurry

were considered by some researchers. Guilpart et al. (1999)

showed that the Nusselt number of the ice slurry under

laminar flow condition was determined by the Graetz number

and the IPF. Horibe et al. (2001) reported that the Nusselt

number can be expressed as a function of Reynolds number,

Stefan number and IPF. Niezgoda-Zelasko (2006) reported that

the Nusselt number can be determined from the Peclet

number, Stefan number, IPF and ratio of average ice particle

diameter to test tube diameter. However, parameters used to

determine the Nusselt number of the ice slurry have not been

identified, and there is no unified understanding of the heat

transfer characteristics of the ice slurry.

We have established the fundamental characteristics of

flowandheat transfer of ice slurryandhave found that it canbe

treated as a pseudo-plastic fluid under laminar flow condition

(Kumano et al., 2010a, 2010b, 2013). Then, the heat transfer

coefficient can be treated as a function of apparent Reynolds

number, IPF and ratio of average ice particle diameter to test

tube diameter. In these studies, the ice slurry was generated

froma5wt%ethanol solution.Theapparent enthalpy of the ice

slurry varies with initial aqueous solution concentration.

Moreover, the effects of heating condition have not been

revealed, and it has not been clarified which parameter domi-

nates the heat transfer characteristics. Especially, Stefan

numberused in theseveralapproximationequations ispointed

out in this study, and can be varied by varying the initial

aqueous concentration and the heating condition. That is,

amount of latent heat of fusion to temperature variation canbe

varied due to varying the initial concentration. Moreover,

temperature difference between the ice slurry and inner sur-

face of the tube can be varied by changing theheat flux given at

the tube surface. Therefore, the heat transfer characteristics of

ice slurry are investigated experimentally to clarify the pa-

rameters affecting heat transfer. The initial ethanol solution

concentration and heating condition were varied as experi-

mental parameters, and the heat transfer coefficients were

measured. An approximation equation for determination of

theNusseltnumberwasderived fromtheexperimental results.

2. Experimental apparatus and procedure

2.1. Experimental apparatus

Fig. 1(a) shows a schematic diagram of the experimental

apparatus. Details of the apparatus have been described

previously (Kumano et al., 2010b), and it is only described

briefly here. The experimental apparatus consisted of a cir-

culation, storage and measurement unit. The circulation

unit consisted of an ice slurry storage tank, gear pump,

entrance section, test section and Coriolis-type mass flow-

meter. The entrance and test sections were 1 m in length

with a 7.5 mm tube diameter. Fig. 1(b) shows the detail of the

test section. The test section consisted of a stainless steel

tube wrapped with nichrome foil heater. The tube was

heated at a constant heat flux, and the heat flux was varied

as an experimental parameter. The heating section was

inserted 0.8 m into the test section. T-type thermocouples,

0.1 mm in diameter, were inserted inside the stainless steel

tube to measure the temperature of the inner surface. The

Constant temperature box

Ice slurry storage tankAgitator

Gear pump

Thermocouple

Test section Entrance section

DC power supply

Coriolis-type mass flowmeter

Thermocouple

Differential manometer

(a) whole system

300mm100mm 100mm300mm

Thermocouple

Heat insulating material

Electrical insulator

Stainless tube

Nichrome foilThermocouple

x flow

100mm100mm

(b) test section

Fig. 1 e Schematic diagram of experimental apparatus (a) whole system (b) test section.

Table 1 e Uncertainty analysis of measurement values.

Measured values

Density of ice slurry, rsl �0.6 kg m�3

Heat flux, q �0.5 W m�2

Inner tube diameter, D �0.015 mm

Mean velocity, um �0.004 m s�1

Pressure drop, Dp �0.06 kPa

Temperature of inner tube surface, Tw �0.2 �CTemperature of ice slurry, Tsl �0.2 �C

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 174

thermocouples were inserted 0.1, 0.4 and 0.7 m from the

beginning of the heating section at upper, middle and lower

positions. During the experiments, the pressure drop and

heat transfer coefficients were measured in the test section,

and the flow rate and density of the ice slurry were

measured simultaneously by the Coriolis-type mass flow-

meter. The flow rate was used to calculate Re for the ice

slurry, and the ice slurry density was used to calculate the

IPF. The temperature of the ice slurry was measured using

T-type thermocouples at the front of the entrance section

and the rear of the test section to determine the coefficient

of kinematic viscosity and the ethanol solution density in

the ice slurry. Moreover, uncertainties of the measured and

derived values are summarized in Table 1.

Derived values

Ice packing factor, c �0.1%

Reynolds number, Re �0.6%

Nusselt number, Nu �5.7%

Pipe friction coefficient, l �1.4%

2.2. Properties of ice slurry and ethanol solution

Ice slurry was produced using the apparatus shown in Fig. 2.

The production unit consisted of an ice production, storage,

heating and cooling tank for the ethanol solution. The ice

production, storage and heating tanks were located in a

constant temperature box. The box temperature was set at

the freezing point of the ethanol solution. After the ethanol

Constant temperature box

Gear pump

Thermocouple

Agitator

Ice slurry storage tank

Refrigerator

Ice production tank

Heating tank

Cooling tank

Fig. 2 e Schematic diagram of apparatus for producing ice slurry.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 1 75

solution had been transferred from the storage to the

heating tank, it was heated above the ethanol solution

melting point by a heater to melt the ice particles. The

ethanol solution was then transported to the cooling tank by

a gear pump. The ethanol solution flowed in a rubber sili-

cone tube approximately 30 m in length and was cooled by

brine in the cooling tank. The ethanol solution then reached

a supercooled state in the cooling tank. Thereafter, it flowed

to the ice-production tank, the supercooled state was

released, and ice slurry was produced. In the ice slurry

production, it was desirable for the degree of supercooling to

be constant through the process to obtain ice particles of

uniform size in the ice slurry. However, the concentration of

the ethanol solution increases with the IPF of the ice slurry.

Therefore, the brine temperature in the cooling tank was

controlled, and the difference between the temperature in

the storage tank and the brine temperature was set at 4 K

and was constant throughout production. These processes

continued until a particular IPF was obtained, after which

the ice slurry was used in the experiments.

The initial concentration of ethanol solution was varied at

2, 5 and 10wt%as experimental parameter. The size and shape

of the ice particles in the ice slurrymay vary depending on the

ethanol solution concentration. Ice particles were observed by

microscopy as shown in Fig. 3, and their diameter measured

using the photographs produced. The diameter was defined as

the average of the longest and shortest dimensions, and the

number of samples was approximately 100. Table 2 shows the

average particle diameter at 20% IPF. It was found that the ice

particle size depends on the initial ethanol solution concen-

tration and is smaller for high initial concentrations.

Previous studies showed that the enthalpy of the ice

slurry also depends on initial concentration. The freezing-

point depression and dilution heat in the aqueous solution

affects the apparent latent heat of fusion of ice in an

aqueous solution (Kumano et al., 2007). Fig. 4 shows the

relationship between specific enthalpy of the ice slurry and

the temperature for each concentration. The enthalpy was

calculated by considering the freezing-point depression and

dilution heat of the ethanol solution. The enthalpy at the

freezing point for each concentration is defined as 0 kJ kg�1.

That is, the enthalpy is 0 kJ kg�1, when IPF is 0 and the

temperature is phase equilibrium temperature. IPF increases

with the decrease in the temperature, and the enthalpy of

the ice slurry decreases with the temperature. The enthalpy

decreases sharply with decrease in ice slurry temperature

near the freezing point for low initial concentrations. The

gradient of enthalpy variation decreases for high initial

concentrations.

In this study, the Reynolds number, Re and IPF were

varied as experimental parameters. The Re for the ice slurry

was calculated using the flow rate and kinematic viscosity of

the ethanol solution. In particular, since the ice slurry is a

mixture of ice particles and ethanol solution, its tempera-

ture remained at the phase equilibrium temperature corre-

sponding to the solution concentration. From the

measurements, the approximate equations for the kine-

matic viscosity of the ethanol solution at the phase equi-

librium temperatures can be obtained as follows (Kumano

et al., 2010a):

ns ¼ 1:792� 10�6 � 2:590� 10�7Te þ 6:908� 10�8T2e þ 1:995

� 10�9T3e (1)

Values obtained from Eq. (1) were used to calculate Re as

the experimental condition. The density of the ethanol solu-

tion at the freezing point is required to calculate the IPF of the

ice slurry, and the following equation is used to obtain the

ethanol solution density (Kumano et al., 2010a):

rs ¼ 999:7þ 4:118Te þ 1:256� 10�1T2e � 1:89� 10�2T3

e (2)

The IPF of the ice slurry was calculated from the densities

of ice, ethanol solution and ice slurry using the following

equation:

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 176

c ¼ rs � rsl

rs � ri� 100 (3)

2.3. Experimental conditions and procedure

Table 3 shows the experimental conditions used. The initial

ethanol solution concentration was varied at 2, 5 and 10 wt%.

The concentration of ethanol solution in the ice slurry is larger

than the initial concentration since the solution concentration

in the ice slurry increases with IPF. The tube diameter was set

at 7.5 mm. Experiments were carried out under laminar flow

conditions, and the Re was varied from 1000 to 2000. The heat

flux at the tube surface was varied from 5000 to 15,000 W m�2

to determine the effect of heating condition.

The pressure drop and heat transfer coefficients of the ice

slurry were measured as follows. An ice slurry of 20% IPF was

produced. The ice slurry was circulated through the test sec-

tion and the differential pressure, flow rate and temperatures

of the inner surface in the test section were measured

simultaneously at 5 s intervals. The IPF decreased during

measurements because heat flowed from the heater and

pump. Therefore, the viscosity of the ethanol solution in the

ice slurry varied. The flow rate was controlled to maintain a

constant Re throughout the measurements. Moreover, IPF

variation in back and forth of the heating section was about

1.8%, when the heat flux is 5000 W m�2 and Re is 1000.

Therefore, the IPF variation was small and the measurements

were carried out in quasi-steady state. The size of the ice

particles decreases due to the decrease in IPF. Therefore, after

the IPF decreased about 10% from its initial value, the mea-

surements were ended to exclude the effect of the variation in

the size of the ice particles. The heat transfer coefficientswere

determined from the temperatures of the ice slurry and the

inner surface of the tube and the heat flux from the heater as

follows.

a ¼ qTw � Tsl

(4)

In preliminary experiment, heat transfer coefficients of

water in turbulent flow condition were measured, and the

accuracy of the heat transfer measurement was confirmed.

The experimental results were compared with value obtained

from Colburn’s equation. As the results, it was found that the

difference between the experimental results and theoretical

value was less than 7%.

Fig. 3 e Photograph of ice particles in ice slurry (a) 2 wt% (b)

5 wt% (c) 10 wt%.

3. Results and discussion

3.1. Effect of initial ethanol solution concentration

In this study, the heat transfer coefficientswere obtained from

the experiments. The Nusselt number, Nu, was introduced to

clarify the effect of the parameters. Nuexp is defined as:

Nuexp ¼ aDk

(5)

The thermal conductivity of water at 273.15 K was used to

determineNuexp in order to compare with the results obtained

in our previous studies. The theoretical values of the Nusselt

number can be calculated using the following equation for

laminar flow conditions:

Nulam ¼ 4:364 (6)

In a previous study (Kumano et al., 2010b), we found that

the heat transfer coefficient of the ice slurry is almost

-10 -5 0

-200

-100

0

Temperature, oC

Spec

ific

ent

halp

y, k

J kg

-1

10wt.%5wt.% 2wt.%

IPF 10%

IPF 20%

IPF 30%

Fig. 4 e Specific enthalpy variation for each initial

concentration of ethanol solution.

0 10 200

1000

2000

3000

4000

5000

Hea

t tra

nsfe

r co

effi

cien

t, W

m-2

K-1

IPF, %

upper middle lower

(a) 2 wt%

0 10 200

1000

2000

3000

4000

5000

Hea

t tra

nsfe

r co

effi

cien

t, W

m-2

K-1

IPF, %

upper middle lower

(b) 5 wt%

1000

2000

3000

4000

5000

rans

fer

coef

fici

ent,

W m

-2 K

-1

upper middle lower

Table 2 e Average diameter of ice particles in ice slurry.

Initial solution concentration Average diameter, mm

2 wt% 0.146

5 wt% 0.157

10 wt% 0.109

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 1 77

unchanged and a thermal boundary layer develops rapidly.

Therefore, the Nusselt number under a developed tempera-

ture distribution was used. Moreover, the ratios of experi-

mental to theoretical Nuwere used to clarify the heat transfer

characteristics of the ice slurry. Here, theoreticalNu is defined

as Eq. (6).

Fig. 5 shows the relationship between the heat transfer

coefficients and the IPF at the upper, middle and lower posi-

tions 0.7 m from the beginning of the heating section. Re was

set at 1500, and the initial ethanol solution concentration was

varied at 2, 5 and 10 wt%. The heat flux at the tube surface was

set at 5000 W m�2. Differences resulting from the position are

not significant for the 5 and 10 wt% solution concentration.

Therefore, homogeneous ice particles exist in the ice slurry

flow. The heat transfer coefficient at the upper position in-

creases at 2 wt%. Many ice particles exist in the ice slurry in

the upper side of the tube because of buoyancy force effects.

This tendency was observed for all conditions at 2 wt%

concentration.

The Reynolds number was maintained at a constant value

through the experiment. Therefore, for an initial 2 wt% con-

centration, the average velocity of the ice slurry is small to

maintain a constant Reynolds number, since the kinematic

viscosity of the solution is small. The effect of the buoyancy

force on the average slurry velocity was considered. Table 4

Table 3 e Experimental conditions.

Initial solution concentration 2, 5, 10 wt.%

Heat flux, W m�2 5000, 10,000, 15,000

Tube diameter, mm 7.5

Reynolds number 1000, 1500, 2000

Ice packing factor, % 0e20

shows Froude numbers for each concentration and the Rey-

nolds number for a 15% IPF. The Froude number is defined as:

Fr ¼ u2m

gD���rirs� 1

��� (7)

0 10 200

Hea

t t

IPF, %

(c) 10 wt%

Fig. 5 e Relationship between heat transfer coefficient and

IPF (a) 2 wt% (b) 5 wt% (c) 10 wt%.

Table 4 e Froude number for each experimentalcondition.

Re 1000 1500 2000 3000

2 wt.% 12.6 24.6 46.7 110

5 wt.% 21.1 49.4 84.5

10 wt.% 67.2 151 263

0 10 200

5

10

15

Rat

io o

f N

usse

lt n

umbe

rs

IPF, %

Re 1000 1500 2000

(a) 5 wt%

0 10 200

5

10

15

Rat

io o

f N

usse

lt n

umbe

rs

IPF, %

Re 1000 1500 2000

(b) 10 wt%

Fig. 7 e Relationship between ratio of Nusselt numbers and

IPF (a) 5 wt% (b) 10 wt%.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 178

The Froude numbers at the condition for which the dif-

ference in heat transfer coefficient appears because of the

effect of the buoyancy force are shown in bold. Results for a

Reynolds number of 3000 and a 2 wt% ethanol solution con-

centration are shown in Table 4, and the difference in heat

transfer coefficient was not observed as shown in Fig. 6. The

Froude number for a Reynolds number of 1000 at a 5 wt%

ethanol solution concentration is smaller than that for the

Reynolds number of 2000 at a 2 wt% concentration. However,

no difference in heat transfer coefficient was observed for the

5 wt% concentration. Therefore, conditions for homogeneous

flow cannot be determined from the Froude number and may

depend on solution concentration, size and shape of the ice

particles.

We aimed to investigate experimentally the heat transfer

characteristics of ice slurry to clarify the parameters affecting

the heat transfer. It is difficult to establish the effect of the

parameters, when a distribution of ice particles in the ice

slurry exists because of the buoyancy force. Therefore, only

homogeneous flow was considered, and the results from the

initial 5 and 10 wt% concentrations are given. The Nusselt

number obtained from the experiments was calculated from

the average heat transfer coefficient of the upper, middle and

lower positions 0.7 m from the beginning of the heating

section.

Fig. 7 shows the relationship between the ratio of the

Nusselt number and IPF for each concentration. From the re-

sults, the ratio of the Nusselt numbers increased with IPF, and

the effect of the Reynolds number was not significant for each

concentration. The particle size for the 10 wt% concentration

was smaller than that for the 5 wt% concentration, as shown

0 10 200

1000

2000

3000

4000

5000

Hea

t tra

nsfe

r co

effi

cien

t, W

m-2

K-1

IPF, %

upper middle lower

Fig. 6 e Relationship between heat transfer coefficient and

IPF (2 wt%, Re [ 3000).

in Fig. 3. However, the effect of particle size was also

insignificant.

3.2. Effect of heating condition

In this study, the heat flux was varied as experimental

parameter. Experiments were carried out using ice slurry ob-

tained from the ethanol solution of 5 wt% initial concentra-

tion. Fig. 8 shows the relationship between the ratio of Nusselt

numbers and IPF. The heat flux was varied at 5000, 10,000 and

15,000Wm�2. The effect of heat flux is not significant for each

Reynolds number. Table 5 shows the temperature at the inner

tube surface for a Reynolds number of 1500 and IPF of 15%. The

ethanol solution concentration in the slurry at an IPF of 15% is

approximately 5.9 wt%, and the phase equilibrium tempera-

ture of the slurry is approximately �2.4 �C. Here, the con-

centration can be calculated from the initial ethanol solution

and IPF, because the ice particles do not include the solute.

Therefore, the temperature difference between the tempera-

ture of ice slurry and the inner tube surface temperature

varied from 2.3 to 5.9 K due to the variation of the heat flux.

0 10 200

5

10

15R

atio

of

Nus

selt

num

bers

IPF, %

5000W m-2

10000W m-2

15000W m-2

(a) Re = 1000

0 10 200

5

10

15

Rat

io o

f N

usse

lt n

umbe

rs

IPF, %

5000W m-2

10000W m-2

15000W m-2

(b) Re = 2000

Fig. 8 e Effect of heat flux on ratio of Nusselt numbers (a)

Re [ 1000 (b) Re [ 2000.0 10 20

0

2

4

6

8

IPF, %

Rai

o of

coe

ffic

ient

s of

pip

e fr

icti

on

Re 1000 1500 2000

(a) 5 wt%

n

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 1 79

The Nusselt number is therefore independent of the temper-

ature difference in this temperature range.

2

4

6

8

of

coef

fici

ents

of

pipe

fri

ctio

Re 1000 1500 2000

3.3. Approximation equation of Nusselt number

The derivation of an approximate equation for the Nusselt

number of the ice slurry was attempted using the results

above. From previous studies, the ice slurry can be treated as a

pseudo-plastic fluid (Kumano et al., 2010a), and the Nusselt

number of the ice slurry can be determined from the apparent

Reynolds number, IPF and ratio of average diameter of the ice

particles to test tube diameter (Kumano et al., 2010b). The

apparent Reynolds number is derived from the experimental

Table 5 e Temperature at inner tube surface (Re [ 1500,IPF [ 15%).

Heat flux, W m�2 Surface temperature, �C

5000 �0.1

10,000 1.8

15,000 3.5

results of the pressure drop. In this experiment, the pressure

drop was measured simultaneously and the flow character-

istics for the ice slurry generated from each initial concen-

tration was considered.

The coefficient of pipe friction was obtained from the

pressure drop of the experimental results, and the theoretical

value of the pipe friction coefficient under laminar flow can be

calculated as follows:

llam ¼ 64=Re (8)

The ratio of the experimental to theoretical coefficient of

pipe friction was used to clarify the flow characteristics of the

ice slurry. Fig. 9 shows the relationship between the ratio of

the coefficients of pipe friction and IPF for each initial con-

centration. The ratio of the pipe friction coefficients increases

with IPF, and the rate of increase of the ratio for the 5 wt%

initial concentration is higher than that for the 10 wt% initial

concentration. The flow characteristics of the ice slurry

change because of the size and shape of the ice particles in the

0 10 200

Rai

o

IPF, %

(b) 10 wt%

Fig. 9 e Relationship between ratio of coefficients of pipe

friction and IPF (a) 5 wt% (b) 10 wt%.

0 20 40 600

20

40

60

Nuexp

Nu c

al

10%Re 5wt.% 10wt.%1000 1500 2000

Fig. 11 e Relationship between Nucal and Nuexp.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 7 2e8 180

ice slurry. The flow characteristics of the ice slurry as pseudo-

plastic fluid were derived using the experimental results.

The relationship between the shearing stress at the inner

surface of the tube and the flow rate can be derived as follows

(Metzner and Reed, 1955):

sR ¼ DDp4L

¼ K0�8um

D

�n0

(9)

nʹ and Kʹ can be determined from the experimental results

and are usually determined by the fluid characteristics. Here,

nʹ is defined as:

n0 ¼ d�ln DDp

4L

�d�ln 8um

D

� (10)

Kʹ can be determined using Eq. (9). Fig. 10 shows the vari-

ation of nʹ and Kʹ for the ice slurry obtained from each initial

concentration. The flow characteristics of the ice slurry show

a pseudo-plastic fluid tendency, since the value of nʹ is smaller

than 1. Moreover, nʹ decreases with increase in IPF, and Kʹ

increaseswith IPF. However, the variation tendencies of nʹ and

Kʹ depend on the initial concentration. The apparent Reynolds

number can be obtained using these parameters as follows:

ReM ¼ Dn0u2�n0m r

8n0�1K0 (11)

Under laminar flow conditions, the coefficient of pipe

friction for the Newtonian fluid can be expressed as Eq. (8).

Thus, ReM is defined to derive the coefficient of pipe friction for

the ice slurry using Eq. (8).

In our previous study (Kumano et al., 2010b), the approxi-

mation equation of the Nusselt number was obtained using

ReM, IPF and the ratio of average ice particle diameter to test

tube diameter as parameters. In this study, the approximation

equation for the Nusselt number is derived in the same way

and the following equation is obtained from the experimental

results:

Nucal ¼ 34:3Re0:0741M

�c

100

�0:822�Dd

�0:292�166 � ReM � 1841;5 � c � 20; 47:8 � D

d � 68:8� (12)

Fig. 11 shows the relationship between the Nusselt

number obtained from the experimental results and that

calculated using Eq. (12). Here, the values of ReM and IPF are

based on the experimental measurements and the Nusselt

0 10 200

0.5

1

1.5

0

0.2

0.4

0.6

0.8

n'

IPF, %

n' K'5wt.% 10wt.%

K'

Fig. 10 e Relationship between nʹ, Kʹ and IPF.

number obtained from the experimental results, Nuexp,

was calculated from the heat transfer coefficients. In

Fig. 11, dashed lines represent ranges of �10% of the dif-

ference in Nusselt numbers. The Nusselt number can

therefore be expressed as a function of ReM, IPF and ratio of

average ice particle diameter to test tube diameter and is

independent of initial ethanol solution concentration in

this range.

4. Conclusion

In this study, the heat transfer characteristics of the ice

slurry were investigated experimentally to clarify the pa-

rameters affecting the heat transfer of the ice slurry. The ice

slurry was produced from ethanol solution, and the initial

ethanol solution concentration was varied as experimental

parameter. The heat flux at the test tube surface was also

varied and the heat transfer coefficients measured. It was

found that the effect of initial ethanol solution concentra-

tion and heating condition on the heat transfer character-

istics of the ice slurry is not significant in the range of this

study. The Nusselt number can be expressed as a function of

apparent Reynolds number, IPF and ratio of average ice

particle diameter to test tube diameter, when the initial

ethanol solution concentration and heat flux at the test tube

wall were varied.

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