ORIGINAL

Experimental study on the convective heat transfer behaviorof microencapsulated phase change material suspensionsin rectangular tube of small aspect ratio

Liang Wang • Guiping Lin

Received: 12 July 2010 / Accepted: 25 June 2011 / Published online: 8 July 2011

� Springer-Verlag 2011

Abstract An experimental study on the heat transfer

performance of microencapsulated phase change material

suspensions flowing in the rectangular tube of small aspect

ratio (b/a = 0.14) is presented in this work. The slurry of

higher MPCM concentration shows better cooling perfor-

mance in the most section of dimensionless axial distance

whereas worse in a small section at the beginning. Up to

20.6% of the dimensionless wall temperature was

decreased by the 20 wt% MPCM suspension as compared

to water.

List of symbols

A Area of the cross-section, m2

a One side length of the cross-section, m

b Another side length of the cross-section, m

c Mass fraction

cp Specific heat, J kg-1 K-1

d Diameter, m

Dh Hydraulic diameter, m

I Total electrical current supplied to heaters, A

g Polynomial parameters, see Eq. 12

k Thermal conductivity, W m-1 K-1

_m Mass flow rate of the fluid, kg s-1

Nu Nusslet number

L Total length of the tube, m

P Perimeter of the cross-section, m

Pr Prandtl number

q Heat flux, W m-2

Re Reynolds number

U Electrical voltage over heaters, V

u Velocity of fluid flow, m s-1

x Length from the entrance to the measure point, m

Greek symbols

b Aspect ratio

u Volume fraction

g Viscosity, kg m-1 s-1

h Dimensionless wall temperature

q Density, kg m-3

m Kinetic viscosity, m2 s-1

Subscripts

a Absorb

b Bulk

cir Circular

eff Effective

f Base fluid

i Inlet

mc MPCM core

ms MPCM suspension

MPCM Microencapsulated phase change material

o Outlet

p MPCM particle

rec Rectangular

s MPCM shell

w Wall of the tube

wt Water

x Distance from the inlet

1 Introduation

The thermal and hydrodynamics behavior of microencap-

sulated phase change material (MPCM) suspensions is of

special interest during the past few decades due to MPCM

particles absorb or release large latent heat during the phase

L. Wang (&) � G. Lin

School of Aeronautic Science and Engineering,

Beihang University, Beijing 100191, China

e-mail: wl@ase.buaa.edu.cn

123

Heat Mass Transfer (2012) 48:83–91

DOI 10.1007/s00231-011-0844-2

change period which improve the apparent heat capacity of

suspensions. Previous experimental and theoretical inves-

tigations were presented on the heat transfer and flow

characteristics of MPCM suspensions [1–11]. Kasza and

Chen performed a theoretical evaluation on the benefits of

using PCM slurries and found that the temperature differ-

ence between source and sink, mass flow, pumping power

can be significantly reduced by using PCM slurries [1].

Charunyakorn et al. developed a numerical simulation of

the laminar flow of a MPCM suspension in circular tubes.

Their work predicted that the Nusselt number for the

MPCM flow was 1.5–3 times higher than that of single

phase flow [2]. Goel et al. presented that up to 50%

reduction in the wall temperature rise can be obtained by

MPCM suspension in comparison with a single phase fluid

[3]. Hu and Zhang et al. analyzed the heat transfer char-

acteristics of MPCM suspensions in circular tubes by the

effective thermal capacity model and heat source model.

They found that the Stefan number and the MPCM con-

centration were the dominant factors [4, 5]. Chen et al.

studied the laminar flow and heat transfer characteristic of

the microencapsulated 1-bromohexadecane (C16H33Br)

suspension in circular tube and found that the increase of

heat transfer rate of 15.8 wt% suspensions over pure water

is 23.6% [6]. Inaba et al. carried out the laminar and tur-

bulent heat transfer characteristics of MPCM suspensions

of different MPCM sizes flowing in a circular tube. They

revealed that the average heat transfer coefficients of the

MPCM suspensions were 2–2.8 times greater than those of

water at the same Reynolds number [7]. Alvarado et al.

found that although the effective specific heat capacity of

MPCM suspensions is 1.4–1.7 times of pure water, but the

average heat transfer coefficient of MPCM suspensions is

lower than water due to the low thermal conductivity of

MPCM [8]. Lu et al. conducted experiments to investigate

the flow and heat transfer characteristics of MPCM slurries

in mini-tube and found that the laminar Nusselt number of

slurry containing small concentration MPCM was about

2.0–2.3 times greater than that of water [9].

There have been numerous investigations concerning

heat transfer performance of MPCM suspensions in cir-

cular tubes while seldom studies concerning that in rect-

angular tubes. Choi and Cho carried out the experimental

study on the flow and convective heat transfer of paraffin

wax slurry in rectangular tubes of different aspect ratios

where the rectangular tubes were heated by discrete heat

sources. They found that the heat transfer coefficient of 5%

slurry was higher than that of water and the aspect ratio of

0.2 showed the best heat transfer performance [10]. Rao

et al. studied the heat transfer characters of MPCM sus-

pensions in mini-rectangular channels (2 mm width and

4.2 mm height) and found that MPCM concentration and

flow rate affected the cooling performance of MPCM

suspensions significantly [11]. Kondle et al. numerically

investigated the laminar heat transfer behavior of MPCM

fluids in circular and rectangular microchannels with dif-

ferent aspect ratios under different boundary conditions

and that the Nusslet number increased due to the phase

change process in all cases [12]. Sabbah et al. carried out a

3D-numerical study on the thermal and hydraulic perfor-

mance of MPCM slurries in the 100 lm width 500 lm

depth micro-channel heat sink. The result indicated that the

heat transfer coefficient increased by 30–50% with the

volume fraction of 25% and the enhancement index was

higher for the low concentration MPCM slurries [13]. As

channels for heat transfer media, flat tubes were widely

used as compact heat exchangers, condenser and evapo-

rators in the power, chemical and electronic industries. In

this work, an experimental system was built to study the

heat transfer performance of MPCM suspension in rect-

angular tube of small aspect ratio (b = 0.14) and the rhe-

ological and laminar heat transfer behavior of MPCM

suspensions of various concentrations (5–20 wt%) were

investigated. The effect of aspect ratio on the heat transfer

performance of MPCM suspensions flowing in rectangular

tube was also analyzed theoretically.

2 Properties of MPCM and suspension

Figure 1 is the photo of MPCM particles by sweep electron

microscope (SEM) used in present study. The particle

diameter was found to be in the range of 0.3–3 lm with an

average diameter about 2 lm. The MPCM particles are

composed by n-Octadecane (C18H38) with a melting tem-

perature of about 28�C as core material and Melamine–

formaldehyde as shell material, respectively. Based on the

mass and energy balance, the bulk density and the bulk

heat capacity of the MPCM suspensions are calculated by:

Fig. 1 SEM photo of MPCM

84 Heat Mass Transfer (2012) 48:83–91

123

qb ¼qpqf

cqf þ ð1� cÞqf

ð1Þ

cp;b ¼ ccp;p þ 1� cð Þcp;f ð2Þ

The bulk thermal conductivity of the MPCM suspensions is

calculated by Maxwell’s relation [14] as follows:

kb ¼ kf �2kf þ kp þ 2u kp � kf

� �

2kf þ kp � u kp � kf

� � ð3Þ

where u is the volume fraction of MPCM particle in

suspension u = c(qb/qp). The conductivity of MPCM

particle was calculated by using the composite sphere

approach described in Ref. [3]:

1

kpdp

¼ 1

kmcdmc

þ dp � dmc

ksdpdmc

: ð4Þ

Figure 2 shows the DSC measurement of 20 wt%

MPCM suspensions at the temperature increase/decrease

rate of 2 K min-1. At the heating period, the onset and

peak temperature of phase change is 26.7 and 28.8�C

respectively and the onset and peak temperature of phase

change is 28.6 and 27.8�C at the cooling period respec-

tively which indicates a low undercooling. The latent heat

of such suspensions is 32.4 kJ kg-1.

The rheological behavior of 5–20 wt% MPCM suspen-

sions was measured using a Bolin CVO rheometer

(Malvern Instruments). Figure 3 shows the shear viscosity

of MPCM suspensions over a range of shear rate

(5–1,000 s-1) and the viscosities are almost independent of

the shear rate which indicates the Newtonian behavior of

the MPCM suspensions up to 20 wt%.

The effect of temperature on the viscosity of the sus-

pensions is shown in Fig. 4 which indicated that the shear

viscosities depend strongly on temperature where as the

relative viscosities gb/gf are almost invariant. All the data

fit well with the VTF equation [15–17]:

ln g ¼ Aþ 1; 000 � BT þ C

ð5Þ

where g is the shear viscosity of the suspensions (mPaS),

T the absolute temperature (K) and A, B and C are constants.

Vand model [18] was commonly used for the phase

change material suspensions and fits well with the experi-

mental data:

gb

gf

¼ 1� u� Au2� ��2:5 ð6Þ

where A is the constant depending on the diameter and

shape of particles and A = 1.16 for the spherical particles

of 130 lm in diameter. Mulligan et al. found that A = 3.4

for the MPCM particles of 10–30 lm in diameter [19],

Yamagishi et al. found that A = 3.7 for the microencap-

sulated n-octadecane suspensions with the average particle

diameter of 6.3 lm [20], Wang et al. found that A = 4.45

for the microencapsulate 1-bromohexadecane suspensions

with the average diameter 10.1 lm [21]. In this work, the

viscosity of MPCM suspensions with the average diameter

2 lm was plotted in Fig. 5 where the prediction values of

Vand model with A = 4.4 fitted well with the experiment

data. Table 1 lists the physical property values of MPCM

particles and suspensions calculated by Eqs. 1–4, 6.

20 22 24 26 28 30 32 34 36-4

-2

0

2

4

6

8

10

onset:28.6°C

peak:28.8°C

peak:27.8°C

onset:26.7°C

cooling progress

Hea

t flo

w (

mW

)

Temperature (°C)

heating progress

Fig. 2 DSC measurement of 20 wt% MPCM suspension

0 200 400 600 800 10000

2

4

6

8

20wt% MPCM suspensions, 30°C20wt% MPCM suspensions, 40°C

Vis

cosi

ty (

mP

aS)

Shear Rate (1/s)

10wt%MPCM suspensions, 30°C10wt%MPCM suspensions, 40°C

Fig. 3 viscosity of MPCM suspensions as a function of shear rate

3.0 3.1 3.2 3.3 3.4 3.50.5

1.0

2.0

4.0

8.0water5wt%10wt%20wt%

Vis

cosi

ty (

mP

as)

1000/T (1/K)

Fig. 4 Effect of temperature on the shear viscosity of MPCM

suspensions

Heat Mass Transfer (2012) 48:83–91 85

123

3 Experimental apparatus for convective heat transfer

As shown in Fig. 6, the experimental apparatus for the

convective heat transfer composes of an experimental

section, a collection tank, a rev controllable peristaltic

pump, a heating apparatus, a fluid tank, a data acquisition

and some valves. The fluid was heated in the experimental

segment and then cooled in the fin tube heat exchanger

which was immersed in the cooling tank with refrigerator.

The experimental segment is a 900.2 mm long aluminum

rectangular tube with the wall thickness of 0.3 mm and the

cross section is 12.8 mm wide and 1.8 mm high (aspect

ratio b = 0.14). Two sheets of electric heater linked to a

DC power supply with the error 0.1 V and 0.1 A were

assembled to the wider sides of the tube which provide

uniform heat flux to the wall. The fluid temperatures at the

inlet and outlet of the tube were measured by T-type

thermocouples inserted into the fluid. Another 8 T-type

thermocouples were welded to the shorter sides of the tube

along the test section at the axial positions of every

100 mm from the inlet of the test section to measure the

wall temperature distribution. The thermocouples were

calibrated in a thermostat water bath and the accuracy was

found to be within ±0.1 K. The heaters and rectangular

tube were surrounded by thick thermal isolating layers to

minimize the heat loss.

0.0 0.1 0.2 0.3

0

5

10

15

20

Rel

ativ

e V

isco

sity

Volume fraction

Experimental results

Vand model [18],A=4.4

Fig. 5 Viscosity as a function of MPCM volume fraction

Table 1 Physical properties of

MPCM suspensions at 298 KDensity

(kg m-3)

Specific heat

(J kg-1 K-1)

Thermal conductivity

(W m-1 K-1)

Latent heat

(kJ kg-1)

Viscosity

(mPa s)

Water 997 4,180 0.610 – 0.87

n-Octadecane (solid) 850 1,800 0.340 223 –

n-Octadecane (liquid) 780 2,200 0.150 – –

Melamine–formaldehyde 1,490 1,670 0.420 – –

MPCM particle

Solid 962 1,765 0.303 162 –

Liquid 905 2,256 0.137

MPCM suspensions (particle mass fraction)

c = 0.05 995 4,059 0.591 8.1 1.58

c = 0.10 993 3,938 0.574 16.2 1.78

c = 0.20 990 3,697 0.539 32.4 5.57

(a) (b)

Fig. 6 a Scheme of convective

heat transfer apparatus b Profile

of experimental section

86 Heat Mass Transfer (2012) 48:83–91

123

4 Error analysis and validity of the experimental

apparatus

The dimensionless wall temperature and dimensionless

axial distance along the rectangular tube were defined as

follows:

hx ¼Tw � Ti

qwDh

kb

¼ 1þ bb� L Tw � Tið Þkb

Qð7Þ

�x ¼ x

DhRePr¼ ð1þ bÞ2

4b� xkb

_mcp;bð8Þ

where x is the distance along the tube, Dh the duct hydraulic

diameter Dh ¼ 4AP ¼ 2ab

aþb, a and b are width and height of the

cross section, qw the wall heat flux, _mthe mass flow rate, Tw

and Ti is the wall and inlet temperature respectively, Q is the

total electrical heating power was obtained by multiplying

the voltage value by the current value from DC power

supply respectively. By comparing Q and the heat trans-

ferred to the flowing fluid through the energy balance

Qa ¼ _mcpðTout � TinÞ, the heat loss through the heat

insulation was assessed and was found to be lower than

5.2% under the conditions of this work. The dimensionless

wall temperature is in inverse proportion to the local Nusselt

number Nux = hxDh/k by theoretical prediction for

convectional single phase fluid on the heat balance:

hwx ¼1

Nuxþ 4�x

1þ bð9Þ

The relative measurement errors of dimensionless wall

temperature and dimensionless axial distance are

calculated by

Dhx

hx

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDL

L

� �2

þ DTw

Tw

� �2

þ DTi

Ti

� �2

þ DQ

Q

� �2s

ð10Þ

D�x

�x¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDx

x

� �2

þ D _m

_m

� �2s

ð11Þ

Hence, the relative measurement errors of dimensionless

wall temperature and dimensionless axial distance are 2.8

and 1.3% by Eqs. 9 and 10 respectively, regardless of heat

loss.

As a validation experiment before systemic experiments

of the MPCM suspensions, the convective heat transfer

behavior of pure water was tested. The Nusselt number of

water at the Reynolds numbers of 822, 1,694 and 2,453 as a

function of dimensionless axial distance �x were plotted in

Fig. 7, the corresponding wall heat flux was 7.10 kW m-2.

Also shown in Fig. 7 is the theoretical approximation of

Nusslet number for full developed flow in rectangular tube

of b = 0.14 under 2L constant heat flux, developed by

Spiga and Morini [22] as below

Nu ¼X5

i¼0

gibi ð12Þ

where gi are the polynomial parameters, g0 = 6.4812,

g1 = -4.4032, g2 = 6.4748, g3 = -10.3513, g4 =

8.6349, g5 = -2.7534. It can be seen that the Nusselt

number decreases with dimensionless axial distance �x and

the experimental results are closed to the theoretical

approximation near the full developed period.

5 Heat transfer experimental results and discussion

In this work, the convective heat transfer experimental

investigations on the 5–20 wt% MPCM suspensions in the

small aspect ratio rectangular tube were carried out. The

mass flow rate range was 4.17–10.0 g s-1 and the heat flux

range was 7.10–15.20 kW m-2. The fluid temperature in

the test section was controlled to involve the phase change

period of MPCM.

5.1 Effective heat capacity of MPCM suspensions

The phase change material would melt and absorb large

latent heat when MPCM suspensions going through the

rectangular tube and the temperature increase of such fluids

was lower than that of pure water. Effective heat capacity

of MPCM suspensions includes the sensible heat capacity

and latent heat of fusion, defined as

cp;eff ¼qw

_m � To � Tið Þ ð13Þ

At the mass flow rate of 7.04–7.3 g s-1 and the heat flux of

7.10 kW m-2, the effective heat capacity of MPCM sus-

pensions as a function of MPCM concentration was plotted

in Fig. 8. It can be seen that compared to pure water, the

effective heat capacity can be improved by about 40 and

125% for 10 and 20 wt% MPCM suspensions respectively.

0.00 0.02 0.04 0.06 0.080

5

10

15

20

25

Nu x

x/(DhRePr)

Experimental Data

Re=822

Re=1694

Re=2453

Approximate Nux for full developed flow

by eq.(12)

Fig. 7 Local Nusselt number at thermal developing period for water

Heat Mass Transfer (2012) 48:83–91 87

123

5.2 Convective heat transfer results

Figure 9a–c shows the differences between the wall tem-

peratures of the rectangular tube (Tw) and the inlet tem-

perature (Ti) along the dimensionless axial distance for

5–20 wt% MPCM suspensions under different heat flux

and flow rates. It can be seen that the temperature differ-

ences strongly depend on the mass flow rate and the

MPCM concentrations.

For the case of minimum mass flow rate of 4.2 g s-1

with wall heat flux of 7.1 kW m-2 as shown in Fig. 9a. At

the entrance region of x/Dh less than 110.2, the wall tem-

peratures of the four suspensions are near. Whereas at the

region of x/Dh higher, the temperature differences decrease

as the MPCM mass concentration increases. The suspen-

sion with the mass concentration of 20 wt% shows the

lowest wall temperature which indicates the best cooling

performance.

For the case of mass flow rate of 7.3 g s-1 with wall

heat flux of 10.5 kW m-2 as shown in Fig. 9b. At the

region of x/Dh less than 82.7, little difference of wall

temperatures between the four suspensions could be found.

At the region of x/Dh higher than 82.7, the temperature

with the mass concentration of 10 wt% shows the lowest

wall temperature and the wall temperature values for 20

and 5 wt% suspension lie between those of water and 10%

suspension.

0.00 0.05 0.10 0.15 0.202

4

6

8

10

12

9.43

5.81

Eff

ecti

ve h

eat

capa

city

(J/

gK)

MPCM mass fraction

mass flow rate: 7.04 ~ 7.3 g/sWall heat flux: 7.10 kW/m2

4.18

5.04

Fig. 8 Effective heat capacity versus MPCM concentration

0 80 160 2404

6

8

10

12

14

16 flow rate=4.2 g/s, q=7.1 kW

pure water 5.0% MPCM suspensions 10.0% MPCM suspensions 20.0% MPCM suspensions

Tw-T

i (K

)

Tw- T

i (K

)

Tw- T

i (K

)

x/Dh

x/Dh

x/Dh

0 80 160 240

6

8

10

12

14

16

18flow rate=7.3g/s, heat flux=10.5 kW/m2

pure water 5.0% MPCM suspensions 10.0% MPCM suspensions 20.0% MPCM suspensions

0 80 160 2406

8

10

12

14

16

18

20

22flow rate=10.0g/s, heat flux=15.20kW/m2

Pure Water 5.0% MPCM suspension 10.0% MPCM suspension 20.0% MPCM suspension

(a)

(b) (c)

Fig. 9 Wall temperatures for MPCM suspensions versus dimensionless axial distance

88 Heat Mass Transfer (2012) 48:83–91

123

For the case of maximum mass flow rate of 10.0 g s-1

with wall heat flux of 15.2 kW m-2 as shown in Fig. 9c. At

the section of x/Dh less than 110.2, a higher concentration

of MPCM suspensions revealed higher wall temperatures.

After that, the wall temperature of MPCM concentrations

were blow water and 5 wt% MPCM suspension shows the

best cooling performance. A similar result was obtained by

Rao et al. that, at the flow rate of 0.05 kg min-1, the wall

temperature decrease with the increase of MPCM con-

centration whereas the revised responds was found at the

flow rate of 0.35 kg min-1 [11].

Figure 10 show the relation of the dimensionless wall

temperature of the 10 and 20 wt% MPCM suspensions and

the dimensionless axial distance at various Re (Re \ 2,000)

respectively, also plotted are the experimental result of

water. It can be seen that, hwx of MPCM suspensions are

close to, even higher than that of water at the region of

small �x. With the increasing of �x, hwx of the MPCM sus-

pensions become lower than water which perform better

cooling ability. It was found that the decrease of hwx of the

5, 10 and 20 wt% MPCM suspensions than water was 7.8,

10.7 and 20.6% respectively at the dimensionless axial

distance of 0.064 measured in this work. A factor that

evaluates the average dimensionless wall temperature of

the MPCM suspensions relative to water is defined as

e ¼ 1

�x

Z�x

0

hms

hwt

� �d�x: ð14Þ

By integration, the factor e is 0.925, 0.89 and 0.84 for the

concentrations of 5, 10 and 20 wt% respectively over the

range of 0 \ �x \ 0.0064.

5.3 Analysis on effect of aspect ratio

Although the effective specific heat capacity of MPCM

suspensions is much higher than that of water, the

convective heat transfer performance was found to be

below water in some conditions especially high flow rate

[8, 11, 20]. The causes were supposed as low thermal

conductivity and insufficient phase change of MPCM while

going through the experimental section [8, 11]. Since the

hydraulic diameter of small aspect ratio rectangular tube is

much thinner than that of circular tube, heat would be

sooner transferred from wall to the core in the rectangular

tube and the phase change of more MPCM would take

place which lead to a better heat transfer performance.

By the comparison between the dimensionless axial

distance of rectangular tube and circular tube by the defi-

nition formula Eq. 2 is

�xrec

�xcir

¼ð1þbÞ2

4bxkb

_mcp;b

p4

xkb

_mcp;b

: ð15Þ

For the circular tube and rectangular tube have the same

cross section area, at the same flow rate and the same axial

distance x, the comparison becomes

�xrec

�xcir

¼ ð1þ bÞ2

bpð16Þ

where b 2 0; 1ð �. By Eq. 16, the value of �xrec=�xcir increase

as the decrease of aspect ratio and the minimum is 4/p at

b = 1.0. For the rectangular tube of aspect ratio b = 0.14,

�xrec is 2.95 times of �xcir. Experimental results of Roy et al.

[23], Chen et al. [6] and Figs. 9 and 10 in this paper

indicate that the dimensionless wall temperature of the

MPCM suspensions become lower than that of pure water

as the increase of the dimensionless axial distances. Thus it

can be concluded that relative large dimensionless axial

distance of small aspect ratio rectangular tube will result in

a lower temperature of wall under the condition of constant

heat flux. Figure 11 shows the dimensionless wall tem-

perature of water and 20 wt% MPCM suspensions flowing

in small aspect ratio rectangular tube (b = 0.14) and

0.00 0.01 0.02 0.03 0.04 0.050.0

0.2

0.4

0.6

0.8

0.003 0.006 0.009 0.012

θ x

x/(DhRePr)

water10 wt%, 884>Re>37120 wt%, 282>Re>119

Fig. 10 Dimensionless wall temperature as a function of dimension-

less axial distance

0.00 0.01 0.02 0.03 0.04 0.05 0.060.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

in circular tube water 20 wt% MPCM suspension

θ x

x/(DhRePr)

in rectangular tube (β =0.14) water 20 wt% MPCM suspension

Fig. 11 Dimensionless wall temperature of MPCM suspension in

circular and rectangular tubes

Heat Mass Transfer (2012) 48:83–91 89

123

circular tube (3.97 mm inner diameter, see Ref. [24])

respectively. It can be seen from the plots that compared

with water, the cooling performance of MPCM suspension

in small aspect ratio rectangular tube is much better than in

that in circular tube. The similar conclusion was also

drawed by Kondle et al. [12] that higher aspect ratio (ratio

of long side to short side) resulted in greater Nusselt

number under the same boundary condition.

Another possible benefit was that due to the small

hydraulic diameter of the rectangular tube, the fluid

velocity gradient and the particle Peclet number in the

rectangular tube is much higher than that in circular tube

where the effective thermal conductivity of the fluid was

improved by the model done by Sohn and Chen [25]. Since

the size of MPCM particles used in this paper is only

several micrometers, the actual effect of the shear induced

micro-convection is very small and could be neglected.

6 Conclusions

In this work, an experimental study on the laminar con-

vective heat transfer behavior of fluids flow with micro-

encapsulated phase change material particles in an

rectangular tube of small aspect ratio (b = 0.14) has been

conducted. It was found that the concentrations of MPCM

and flow rates would affect the cooling performance sig-

nificantly. The other findings are briefly listed below:

1. Evaluated by dimensionless wall temperature, the

MPCM suspensions show better heat transfer perfor-

mance than water at most section whereas worse at the

very small dimensionless axial distance. 20 wt%

MPCM suspensions resulted in a decrease of about

16% of the average dimensionless wall temperature

than water, although its effective heat capacity is 1.25

times higher.

2. 5–20 wt% MPCM suspensions were approximately

Newtonian fluids at over a range of shear rate

(5–1,000 s-1) and the Vand model with parameter

A = 4.4 fits well with the shear viscosity of the

suspensions containing MPCM particles ranged from

0.3 to 3 lm.

3. Lower relative wall temperatures could be obtained

when the fluids flowing in the small aspect ratio

rectangular tube than the circular tube due to the

smaller hydraulic diameter by the comparison of the

dimensionless axial distances.

Acknowledgments This work was supported by the National Nat-

ural Science Foundation of China (50436020) and the Fundamental

Research Funds for the Central Universities of China.

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