international journal of heat and mass...

International Journal of Heat and Mass Transfer 56 (2013) 561–573

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Three dimensional numerical study of heat-transfer enhancementby nano-encapsulated phase change material slurry in microtube heat sinkswith tangential impingement

Hamid Reza Seyf, Zhou Zhou, H.B. Ma ⇑, Yuwen ZhangDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 July 2012Received in revised form 24 August 2012Accepted 25 August 2012Available online 27 October 2012

Keywords:Nanoencapsulated phase change materialMicrotube heat sinkTemperature uniformity

0017-9310/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.08

⇑ Corresponding author. Tel.: +1 573 884 5944.E-mail address: [email protected] (H.B. Ma).

This paper presents a three-dimensional model describing thermal and hydrodynamic characteristics of aMicrotube heat sink with tangential impingement with nanoencapsulated phase change materials (NEP-CM) slurry as coolant. In this study, octadecane for NEPCM and polyalphaolefin (PAO) is used as a basefluid. The continuity, momentum, and energy equations are solved using a finite volume method. Themodel is validated by comparing results with available data in the literature. The effects of dominantparameters including mass concentration and melting range of NEPCM as well as Reynolds number ontemperature uniformity, thermal resistance, Nusselt number, pressure drop and generated entropies inthe system are investigated. Results indicated that adding NEPCM to base fluid leads to considerable heattransfer enhancement. However, using NEPCM slurry as coolant has also induced drastic effects on thepressure drop that increases with mass concentration and Reynolds number. It was found that that anincrease in nanoparticles mass concentration, inlet Reynolds number and melting range of NEPCM,results in a higher Nusselt number, better temperature uniformity and lower thermal resistance. Further-more, the effects of different parameters on slurry entropy production are demonstrated. It is found thatgenerated total entropy decreases with increasing mass concentration and Reynolds number.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the miniaturization of electronic components or sys-tems, problems associated with overheating of electronic compo-nents have increased drastically. Most electronic components orsystems, from microprocessors to high power converters generateheat which is necessary to reject it for optimum operation so ther-mal management of electronic devices becomes more and moreimportant. Traditional microchannel heat sinks using conventionalcoolants for computer chip cooling are reaching their maximumpotential. The limit of the heat transport capability of a microchan-nel heat sink with conventional fluids such as water or ethyleneglycol coolants will be exceeded, leading to the use of new typesof heat sinks with a new class of coolants such as a mixture ofnano-encapsulated phase change material to dissipate the heatfrom the heat source. The microtube heat sink with tangentialimpingement represents a new class of heat sinks which have highthermal performance and is destined to become a thermal man-agement tool in the future. The innovative design allows the cool-ant to flow in tangentially through the gaps on the top surface of

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heat sink which results in distributing thermal and hydrodynamicsboundary layers in microchannels. Many studies have been per-formed in recent years, which show how tangential impingementinjection of fluid inside the channels enhances heat transfer signif-icantly [1–4]. Lelea [5] optimized geometry of tangential micro-heat sink with straight circular microchannels. The cross-sectionof the injection channel was in the form of rectangular shape andpositioned tangentially to the tube axis. In Lelea’s second paper[6], he studied the thermal and hydrodynamic of a tangential char-acteristics of heat sink with multiple inlet jets. The results showedthat at a fixed pumping power, the minimum temperatures arelower for a single inlet compared with multiple inlet jets. He alsoshowed where a microchannel heat sink with multiple inlet jetshas a lower temperature difference on the microtube’s bottom sur-face between the inlet and outlet. Recently, Shalchi and Seyf [7]investigated the effect of nanofluid on thermal performance of atangential microchannel heat sink. Results showed that withdecreasing nanoparticles’ diameter and increasing volume fraction,the system’s thermal performance increases significantly.

With the high heat power generated in modern electronic com-ponents or systems, more advanced coolants need to be used.Recently, a new coolant that utilizes nanoencapsulated phasechange material (NEPCM) in a heat transfer fluid such as water

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Nomenclature

Cp heat capacity of fluid at constant pressure (J/kg K)dp particle diameter (m)k thermal conductivity (w/m K)Di diameter of single microtube (m)H height of heat sink (m)L length of heat sink (m)B total width of microchannel heat sinkbch inlet channel widthWm module widthHch inlet channel heightLch half of inlet channel lengthP pressure (Pa)DP pressure drop (Pa)qw heat flux of the hot wall (W/m2)Q dissipated heat rate (W)Re Reynolds number based on tube diameterNu Nusselt numberPe Peclet numberRth thermal resistance of heat sink (K/W)DTs temperature uniformity (K)_S000gen total entropy generation rate (kW/m3 K)_S000ðFÞgen frictional entropy generation rate (kW/m3 K)_S000ðHÞgen heat transfer entropy generation rate (kW/m3 K)T temperature (K)T1 lower melting temperature (K)T2 higher melting temperature (K)

TMr melting range (T2 � T1)Tm average melting temperature (K)hsf latent heat of fusion of PCM (J/kg)u, v, w velocity components in x, y and z directions (m/s)

Greek symbolsCm mass concentration of nanoparticlesl dynamic viscosity (kg/m s2)t kinematic viscosity (m2/s)q density (kg/m3)_U viscous dissipation_c shear rate (1/s)n volume concentration of NEPCM

Subscriptsf fluidinlet inlet of computational domainoutlet outlet of computational domainmin minimum valuemax maximum valuep particles solidS–F solid–liquid interfacew walleff effectivepcm phase change materialpao polyalphaolefin

562 H.R. Seyf et al. / International Journal of Heat and Mass Transfer 56 (2013) 561–573

has been proposed. In general, NEPCM particles are composed of acore of paraffin wax phase change material (PCM) with a wallaround it which is made of cross-linked polymer. The wall materialis usually 14–20% of the total capsule mass and is sufficiently flex-ible to accommodate volume changes that accompany solid/liquidphase change [8]. The latent heat of the NEPCM particles providesan approach to store energy and enhance heat transfer when theparticles experience phase change. In this approach to thermalmanagement, high effective thermal conductivity of mixture dueto micro-convection induced by nanoparticles is coupled withlarge latent heat of NEPCM, achieving high heat fluxes with littletemperature variation. Therefore, using these types of coolants iswell suited for use in high performance compact heat exchangersand heat sinks used in electronic equipment. Many experimentaland numerical studies have shown the heat transfer capability ofphase change materials slurry with different base fluids [9–25].Most of these analyses assume a fully developed hydrodynamicflow and homogeneous mixture. Recent studies [26,27] investi-gated the effect of PCM slurry coolant on thermal performance ofmicrochannel heat sinks. Kuravi et al. [26] numerically analyzedthe effect of NEPCM slurry on the thermal and hydrodynamic char-acteristics of manifold microchannel heat sinks. They used octade-cane for PCM and polyalphaolefin (PAO) as a base fluiddemonstrating how suspension of NEPCM slurry leads to increas-ing the system’s Nusselt number and decreasing the bulk meantemperature of the fluid. Sabbah et al. [27] studied the influenceof micro-encapsulated phase change material (MEPCM) on thermaland hydrodynamic behavior of conventional microchannel heatsinks. Their results indicate that using MEPCM slurry as base fluidcauses lower and more uniform temperatures across the electronicdevice.

In order to discover the advantages of utilizing NEPCM slurry ascoolant in microchannel heat sinks, this paper will look at boththermal and hydrodynamic performance of a microtube heat sinkwith tangential impingement. A three dimensional conjugate heat

transfer model will be used to determine the effect of NEPCM massconcentration and melting range as well as inlet Reynolds numberon the temperature uniformity, thermal resistance, pressure drop,and Nusselt number as well as generated entropies in the system.This paper also summarizes the effects of certain parameters onthe temperature and melting fraction distributions. To the best ofthe authors’ knowledge, there is no experimental, analytical andnumerical work to study thermal performance of microtube heatsink with tangential impingement using NEPCM slurry as coolant,and the present study is the first attempt that surveys these typesof coolant in microtube heat sink with tangential impingement.Therefore, this study offers a new direction for ultra-high coolingperformance of microtube heat sinks.

2. Mathematical modeling and governing equations

The schematic diagram of the heat sink is shown in Fig. 1.Tangential microchannel heat sinks (TMHS), coolant or NEPCM slur-ry flows in tangentially through the gaps on the top surface of theheat sink at a specified temperature and velocity, and its tempera-ture increases as it moves through the channels and reaches themelting temperature of phase change material (PCM). There is nomass transfer between the carrier fluid and capsules because whenPCM melts inside the capsules; the melted PCM will not mix withthe carrier fluid because it remains contained in the capsules. Thecarrier fluid exhibits lower temperature change when the PCMmelts. Different geometries for inlet cross cross-section of systemcan be used, but in the present study, the rectangular inlet cross-section is adopted based on previous studies in literature [5,6].The NEPCM slurry consists of octadecane as nanoparticle and poly-alphaolefin (PAO) as base fluid [26]. The total height, length, widthand number of heat sink channels are 1.5 mm, 1 cm, 1 cm and 9,respectively. The area of inlet cross-section and tube diameter are0.45 mm2 and 900 lm, respectively. The center of tube is 900 lmaway from the bottom surface of the heat sink. Because of the heat

Fig. 1. Schematic of microtube microchannel heat sink with tangentialimpingement.

H.R. Seyf et al. / International Journal of Heat and Mass Transfer 56 (2013) 561–573 563

sink’s geometry, only one symmetrical microtube region is selectedwithin the heat sink for computational domain.

The present model is based on the following assumptions:

1. The coolant flow is incompressible, laminar.2. Radiation and compressibility effects are very small in the

current investigation so are not considered in this study.3. The particle concentration is less than 0.3; therefore, the

fluid is Newtonian [18].4. The melting range of NEPCM particles is between T1 and T2.5. The micro-convection caused by the particle–wall interac-

tions, particle–fluid and particle–particle is lumpedtogether, and its effect is accounted by an effective thermalconductivity.

6. The difference in the particle and fluid velocities is negligi-ble, i.e., the particles follow the fluid without any lag [26].

7. The particle distribution is homogeneous so that the bulkproperties are assumed constant except for thermal conduc-tivity and heat capacity, which are functions of space andtemperature, respectively [26].

8. The particle melts instantaneously; there is no temperaturegradient inside the particle [26].

_U ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 leff

@u@x

� �2

þ leff@v@y

� �2

þ leff@w@z

� �2" #

þ leff@u@yþ leff

@v@x

� �(vuut

9. NEPCM–PAO slurry properties are functions of NEPCM con-centration and slurry temperature.

10. The effect of the particle depletion layer is negligible. Theparticle depletion layer is of the order of the particle radiusif the channel size to particle size is large [28,29].

11. The shape of the encapsulated particles is spherical.12. The effect of the shell material is neglected.13. The NEPCM–PAO slurry enthalpy consists of two parts: sen-

sible heat and PCM latent heat.

The governing equations of flow and heat transfer inside aMicrotube heat sink with tangential impingement and tempera-ture dependent material properties can be expressed as follows:

Continuity equation:

@u@xþ @v@yþ @w@z¼ 0 ð1Þ

X-Momentum equation:

qeff u@u@xþ v @u

@yþw

@u@z

� �¼ � @p

@xþ @

@xleff

@u@x

� �

þ @

@yleff

@u@y

� �þ @

@zleff

@u@z

� �ð2Þ

Y-Momentum equation:

qeff u@v@xþ v @v

@yþw

@v@z

� �¼ � @p

@yþ @

@xleff

@v@x

� �

þ @

@yleff

@v@y

� �þ @

@zleff

@v@z

� �ð3Þ

Z-Momentum equation:

qeff u@w@xþ v @w

@yþw

@w@z

� �¼ � @p

@zþ @

@xleff

@w@x

� �

þ @

@yleff

@w@y

� �þ @

@zleff

@w@z

� �ð4Þ

Energy:

qeff Cp;eff u@Tf

@xþ v @Tf

@yþw

@Tf

@z

� �

¼ @

@xkeff

@Tf

@x

� �þ @

@ykeff

@Tf

@y

� �þ @

@zkeff

@Tf

@z

� �þ _U2 ð5Þ

where u, v, and w are velocity components in x, y, z directions,respectively. p and T are pressure and temperature, respectively. qeff

and Cp,eff are the density and heat capacitance of the NEPCM slurry,respectively. Heat transfer in TMHS is a conjugate problem whichcombines heat conduction in the solid and convective heat transferto the flowing fluid. The energy equation in solid region is expressedas:

@

@xks@Ts

@x

� �þ @

@yks@Ts

@y

� �þ @

@zks@Ts

@z

� �¼ 0 ð6Þ

Index s and f shown in Eqs. (5) and (6) respectively refer to solidmaterial of heat sink and fluid region of computational domain. ks

is thermal conductivity of solid material. _U2 shown in Eq. (5) is vis-cous dissipation term and it represents the time rate at which en-ergy is being dissipated per unit volume through the action ofviscosity. For an incompressible flow, it is written as follows:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

þ leff@v@zþ leff

@w@y

� �2

þ leff@w@xþ leff

@u@z

� �2)

ð7Þ


The thermal conductivity of silicon can be calculated using the fol-lowing equation [34,35]

ksilicon ¼ 290� 0:4T ð8Þ

It is assumed the heat goes to computational domain only from thebottom wall of the heat sink so a constant heat flux is applied at theheated wall (qw = 10,000 W/m2). A constant and uniform velocityand temperature is applied at the inlet of computational domain.The boundary conditions for all surfaces are described as follows:

Inlet condition (y = H):

u ¼ w ¼ 0; v ¼ �v in; Tf ¼ Tin ð9Þ

Outlet condition (Z = L):

@u@z¼ @v@z¼ @w@z¼ @Tf

@z¼ 0 ð10Þ

Symmetry condition (Z = 0):

@u@z¼ @v@z¼ @Tf

@z¼ @Ts

@z¼ 0 and u ¼ v ¼ 0 ð11Þ

Symmetry condition (x = ±wm/2):

@Tf

@x¼ @Ts

@x¼ 0 ð12Þ

All external walls are insulated except for the bottom wall, onein contact with chip (Y = 0):

qw ¼ ks@T@y

ð13Þ

Solid–liquid interfaces:

knf@Tf

@n¼ ks

@Ts

@nð14Þ

where n is normal vector drawn outward the boundary.In order to satisfy the energy conservation across solid inter-

faces, the grids coincide on the fluid–solid boundaries heat sinksand the conservative interface flux condition for heat transfer isadopted at the interface between solid and fluid:

k@T@y

� �f¼ k

@T@y

� �s) ks

Ts�TS—F

dys¼ kf

TS—F �Tf

dyf) TS—F ¼

cksTsþkf Tf

cksþkf

ð15Þ

TS–F is the temperature at the common boundary and is applied forcalculation of temperature gradients k @T

@y

� �within each elementary

grid volume (s, f). c is the ratio of the normal distance between thefirst cell node and the solid-fluid boundary of the solid (dys) andfluid (dyf) side (Fig. 2):

c ¼dyf

dysð16Þ

Fig. 2. Detail of local grid at solid–fluid interface.

3. Bulk properties of slurry

In order to calculate the heat transfer rate of NEPCM slurry,thermal properties of NEPCM slurry such as heat capacity, thermalconductivity and viscosity should be calculated. In this study, it isassumed that the slurry consists of PAO and NEPCM with octade-cane as the phase change material with melting point of 301.9 K.The properties used are summarized in Table 1. The dynamic vis-cosity of slurry calculated using following equation [30,31]:

leff

lPAO¼ ð1� n� 1:16n2Þ�2:5 ð17Þ

where n is volume concentration of NEPCM and lPAO is the PAO vis-cosity, which is function of temperature.

The static thermal conductivity of the suspension or thermalconductivity of slurry at rest (no shear rate) can be expressed as[21]:

kb ¼ kPAO �2þ kp

kPAOþ 2n kp

kPAO� 1

� �2þ kp

kPAO� n kp

kPAO� 1

� � ð18Þ

Due to particle–particle, particle–liquid and particle–wall interac-tion, the effective thermal conductivity of slurry under motion in-creases. These interactions have the major role in enhancement ofthermal conductivity of mixture. The effective thermal conductivityof slurry flow is specified by the following correlation [26]:

keff

kb¼ f ¼ 1þ BnPem

p

B ¼ 3; m ¼ 1:5; Pep < 0:67B ¼ 1:8; m ¼ 0:18; 0:67 < Pep < 250

B ¼ 3; m ¼ 111

; Pep > 250

ð19Þ

The particle Peclet number is defined as

Pep ¼ed2

p

aPAOð20Þ

where aPAO is thermal diffusivity of PAO. The shear rate is a functionof all the spatial coordinates and corresponding velocities. The mag-nitude of the shear rate can be calculated using the followingequation:

e ¼ 12

Xi

Xj

cijcji

" #ð21Þ

where c is the shear rate. The effective thermal conductivity corre-lation given above shows that the thermal conductivity is stronglydependent on (i) the shear rate, which can be increased by decreas-ing the conduction dimension or increasing slurry flow rate, and (ii)particle size due to the interactions (drag force, lift force, and virtualmass) between the liquid and the particles. Slurry specific heatcapacity and density are given by

Cp;eff ¼ ð1� CmÞCp;PAO þ CmCp;p ð22aÞqeff ¼ ð1� CmÞqPAO þ Cmqp ð22bÞ

where Cp,PAO, qPAO, Cm and qp are the specific heat and density ofPAO, mass concentration or loading fraction of slurry and densityof NEPCM, respectively. According to Alisetti and Roy [23], thedifference between using various profiles for calculating the spe-cific heat of PCM is less than 4%. Therefore, in this study we usedthe sine profile to represent the NEPCM particle specific heat(Fig. 3) of

Cp;p ¼ Cp;pcm þp2� hsf

TMr� Cp;pcm

� �� sin p ðT � T1Þ

TMr

� � ð23Þ

Table 1Physical properties for the MEPCM.

Density (kg/m3) Viscosity (Pa s) Specific heat (J/kg K) Thermal conductivity (W/m K) Latent heat (J/kg)

PAO 784 4.45 � 10�3 2242 143 � 10�3 –Octadecane 774 – 2180 0.15 244 � 10�3

Fig. 3. Specific heat of NEPCM as a function of temperature.


where TMr is the melting range (TMr = T2 � T1). For temperatureshigher or lower than melting range the value of specific heat of par-ticle is equal to Cp,pcm and for temperatures in melting range, thespecific heat of particle is calculated using above equation.

4. Numerical solution and validation

In the present study, a validated finite volume code has beenemployed as the numerical solver [7]. The three-dimensional gov-erning equations are discretized by applying a finite volume meth-od in which conservation laws are applied over finite-sized controlvolumes around grid points, and the governing equations are thenintegrated over the volume. The collocated grid arrangement isadopted where all variables are stored at the control volume

Fig. 4. Computational domain and det

geometrical center. Quick scheme is used to discretize convec-tion/diffusion terms in momentum and energy equations. Thenumerical simulation is accomplished by using SIMPLE algorithm.In this technique, using a guessed pressure field, the velocity com-ponents in three directions is first calculated from the Navier–Stokes equations, and then to satisfy the continuity equation, thepressure and velocities are corrected. The numerical solution is re-garded as convergent at an iteration in which the summation ofabsolute values of relative errors of temperature, velocity compo-nents and pressure reach 10�8, 10�7 and 10�5, respectively.

The computation was carried out using hexahedral volume ele-ments in both solid and fluid regions of computational domain. Therelatively fine grids are used in the regions of the boundary layerswhere the gradients of velocity and temperatures are steeper. Fig. 4illustrates the detailed generated meshes in each section of com-putational domain. For grid independency test, three different gridsystems are investigated which include about 619,059, 896,548,and 1,104,584 cells, respectively. The predicted temperature uni-formity and pressure drop for the three grid systems are shownin Table 2. From the table, it is obvious that the change of the tem-perature uniformity and pressure drop respectively is less than0.32% and 0.64% among the third and second grid systems. There-fore, for the present study, the final grid number is selected asabout 1,104,584. It is important to note that the grid independencywas performed for worst Reynolds scenario, i.e., highest Reynoldsnumber.

To the knowledge of authors, there are no available data in thepublished literature related to study of Microtube heat sink withtangential impingement in laminar flow regime and with NEPCMslurry as coolant. Furthermore, since the concept of Microtube heatsink with tangential impingement is novel, there is no experimen-tal study in the literature on this type of heat sink. Therefore, inorder to validate the reliability of the numerical method beingused, the numerical simulation is conducted for a tangential

ailed meshes in different regions.

Fig. 5. The validation of numerical model with results presented by Lelea [32].

Table 2Grid independent results for temperature uniformity and thermal resistance.

Number of grid DTs (K) diff% DP (Pa) diff%

Pure PAO 619,059 0.26834 – 5.45 –896,548 0.29266 8.31 5.94 8.12

1,104,584 0.29544 0.32 5.98 0.64

NEPCM slurry TMr = 20�, Cm = 0.3 619,059 0.17585 – 79.31 –896,548 0.19304 8.9 85.56 7.31

1,104,584 0.19403 0.51 85.99 0.49


microchannel heat sink with the same geometrical configurationsas presented in Lelea [32]. Lelea numerically analyzed the perfor-mance of microtube heat sink with tangential impingement withwater as coolant. The length of microchannel, tube diameter andinlet cross-section are 1 cm, 300 lm, 1 mm, and 50 lm, respec-tively. In the simulation, a constant heat flux of 100 W/cm2 was ap-plied at the bottom of heat sink, while all other walls wereinsulated. The inlet mass flow rate and temperature were 110 kg/s and 293 K, respectively. Further numerical details can be foundin the original paper by Lelea [32]. The predicted results are com-pared with the numerical results from Lelea. The temperature dis-tribution at bottom wall of heat sink is shown in Fig. 5 whichshows the maximum discrepancy between the predicted resultswith the one for Lelea [32] as 0.5%.

5. Prediction procedure

The definitions of Re number is as follows:

Re ¼ 4pðM=2ÞD � l ð24Þ

where M and D are the inlet mass flow rate of single microtube andtube diameter, respectively. The pressure drop can be calculated asfollows:

DP ¼Z

Aout

P dA�Z

Ain

P dA ð25Þ

where Aout and Ain are the areas of outlet and inlet of computationaldomain. One of the main parameters for evaluating the thermal per-formance of heat sink is thermal resistance which can be defined as

Rth ¼Tw;max � Tw;min

Qð26Þ

where Tw,max and Tw,min are the maximum and minimum tempera-ture of heat sink at bottom wall, respectively. Q is dissipated heatrate and Tc,in is the coolant inlet temperature. In MCHS, the gener-ated heat by semiconductor chips results in high temperature risesalong the microchannels because the heat is carried out by a rela-tively small amount of coolant. High temperature rise causes thenon-uniform temperature distribution on the chip. Non-uniformwall temperature can produce destructive thermal stresses in pack-ages and elements due to the differences in thermal expansion coef-ficient, which poses reliability concerns to the devices. Furthermore,the spatial temperature gradient may adversely affect the stabilityand performance of chips. The temperature uniformity is oftenquantified by

DTs ¼ Tw;max � Tw;min ð27Þ

The overall Nusslet number can be calculated from the followingequation [26]

Nu ¼ q � DðTw � TinÞkf

ð28Þ

where Tw and Tin are average temperature of wall and inlet temper-atures, respectively,

Tw ¼1

Aw

ZAw

T dAw ð29Þ

In this paper, the entropy generation which characterizes theirreversible behavior of system is used to optimize a deviceperformance by evaluating best operational parameters as well asfluid-properties. In the flow of viscous fluid inside the microtubeheat sink with tangential impingements, the entropy generationmust consider irreversibilities caused by heat flow and fluid friction.The entropy generation rate per unit volume can be written as [33]

S000gen ¼ S000ðHÞgen þ S000ðFÞgen ð30Þ

In the above equation, the first term expresses for irreversibilitiesdue to heat transfer and the second term is related to viscous dissi-pation in the fluid which can be defined as follows:

S000ðHÞgen ¼keff

T2

@T@x

� �2

þ @T@y

� �2

þ @T@z

� �2" #

ð31Þ

S000ðFÞgen ¼ 2 leff@u@x

� �2

þ leff@v@y

� �2

þ leff@w@z

� �2" #(

þ leff@u@yþ leff

@v@x

� �2

þ leff@v@zþ leff

@w@y

� �2

þ leff@w@xþ leff

@u@z

� �2)

ð32Þ

It is worth mentioning that for all the simulations presented in thispaper, the entropy source due to frictional effect is much smallerthan the one due to heat transfer, i.e., S000ðHÞgen � S000ðFÞgen .


6. Results and discussion

In order to study the influence of Reynolds number and massconcentration of NEPCM slurry on the heat transfer characteristicsof microtube heat sink with tangential impingement, a compara-tive investigation for different inlet Reynolds numbers and massconcentrations of NEPCM slurry was performed. Fig. 6 shows thecontour of temperature distribution for both pure PAO and NEPCMslurry as coolant in a plane which possesses through center of tubeand parallel to Y axis. As expected the temperature is higher at bot-tom wall where the heat from chip comes in the heat sink. It can beseen that the temperature distributions in solid and liquid phasesare non-uniform, and using NEPCM slurry as coolant will causethe bulk temperature of coolant as well as temperature of solidphase to decrease which means more energy transfers throughthe fluid with little increase in coolant temperature. It is clear thatincreasing the mass concentration of slurry intensifies the reduc-tion of wall temperature. Such behavior is obviously due to the factthat with increasing mass concentration, the specific heat of cool-ant increases considerably which results in more effective cooling.Another important result shown in Fig. 6 is that the thermalboundary layer growth for NEPCM slurry coolant is slower thanthat of pure PAO; thus, the entry length is longer for slurry flow.

Fig. 6. Effect of mass concentration of s

This is mainly due to the NEPCM particles latent heat, which actsas a heat sink and slows the growth of thermal boundary layeralong the heat sink.

In microtube heat sink with tangential impingement, the flow-ing fluid heated gradually along the length of microtube. Therefore,when it arrives at the end of heat sink, it has already been heated toa relatively high temperature. It is interesting to note that the fluidregion of computational domain can be divided into three distinctregions according to temperature of coolant. In the first regionwhich is near the inlet of device, the PCM is at solid state andhas a constant and approximately low NEPCM solid phase heatcapacity; hence, the main mechanism for heat transfer in this re-gion is the high temperature difference between walls of micro-channel and coolant—not the heat capacity of coolant. In thesecond region, which is somewhere in the middle of heat sink,the PCM melts inside the NEPCM particles and coolant has a heatcapacity equal to the summation of the latent and sensible heatof the NEPCM particles so the main mechanism of heat transferenhancement in this region is a high effective heat capacity of cool-ant. In the third region, which is near the end of device, the tem-perature of coolant is very high, and the PCM is completelymelted; in addition, the specific heat has a constant value equalto the liquid specific heat of the NEPCM slurry so the minimum

lurry on temperature distribution.


heat transfer enhancement is occurring in this region. Therefore,the cooling capability of coolant in the computational domain firstincreases and then decreases causing a non-uniform temperaturedistribution at the bottom wall of heat sink. It is worth mentioningthat the formation of hotspots at the base plate of device is mainlydue to various cooling capability of coolant along the length of heatsink. Therefore, in order to evaluate the performance of a heat sink,both thermal resistance and temperature uniformity should beevaluated. The effect of Reynolds number and mass concentrationon thermal resistance and temperature uniformity of heat sink arepresented in Fig. 7. It is clear that for the pure PAO case, thermal

Fig. 7. Effect of mass concentration on therma

Fig. 8. Effect of mass concentration on

resistance and temperature uniformity is high while for the casesusing NEPCM slurry as coolant, the cooling performance increaseswith increasing mass concentration. The improved performancemainly occurs due to the enhanced thermal properties of slurrycoolant especially specific heat. Furthermore, it is obvious thatwith increasing Reynolds number, the thermal resistance and tem-perature uniformity decreases because increasing the Reynoldsnumber leads to decreasing thermal boundary layers’ thicknessin microtube and consequently yields a higher heat transfer coeffi-cient. It is interesting to note that higher Reynolds numbers in-creases convection heat transfer not only because of higher

l resistance and temperature uniformity.

Nusselt number and pressure drop.

Fig. 9. Thermal and frictional entropy generation rate as a function of Reynolds number for different mass concentration.

Fig. 10. Total entropy generation rate as a function of Reynolds number for different mass concentration.


inertia but also due to the NEPCM slurry absorbing the sameamount of heat with less temperature rise.

The pressure drop between inlet and outlet of the heat sink andNusselt number is depicted in Fig. 8. As seen, both pressure dropand Nusselt number increase dramatically with the increment ofthe Reynolds number and mass concentration. The enhancementof pressure drop with increasing mass concentration of slurry isconsiderably high at higher Reynolds numbers. Therefore, the highpressure drop for the NEPCM slurry coolant at higher Reynoldsnumbers should be given careful consideration in designing heatsinks. It is worth mentioning that the sensitivity of the pressuredrop to mass concentration of NEPCM is related to the increasedviscosity at higher mass concentrations because high values of

Cm leads the fluid to become more viscous which causes an in-creased pressure drop. The reason for higher values of Nussletnumber at higher mass concentration is due to the fact that withincreasing mass concentration of NEPCM, the thermal conductivityand capability of heat absorption by the coolant increase whichcauses yields a better heat transfer coefficient.

The influence of NEPCM mass concentration on entropy gener-ation rate in the TMHS is shown by Figs. 9 and 10. It is clear thatcompared to pure PAO, NEPCM slurry coolant has a smaller totalentropy generation rate, and with increasing mass concentration,the total heat transfer entropy generation rate decreases. There-fore, using NEPCM slurry may lead to improved heat transfer per-formance for greater system efficiency when compared to pure

Fig. 11. Effect of melting range of PCM on temperature distribution.

Fig. 12. Thermal resistance and temperature uniformity as a function of Reynolds number for different melting ranges.


PAO. Furthermore, it is obvious that the frictional contribution ofentropy generation rate increases with increasing mass concentra-tion, which means that the hydrodynamic efficiency of the system

decreases with increasing mass concentration, but the amount ofenhancement in entropy is very small, especially at lower Reynoldsnumbers.

Fig. 13. Nusselt number and pressure drop as a function of Reynolds number for different melting ranges.

Fig. 14. Thermal and frictional entropy generation rate as a function of Reynolds number for different melting range.


Fig. 11 shows the effect of melting range on temperature con-tour. It can be seen that the wall temperature is not same whenusing NEPCM slurry with different melting ranges and higher melt-ing ranges lead to lower temperature in solid region of heat sinkand smaller values of temperatures at hot spots. Therefore, as willbe shown, an additional benefit of using NEPCM slurry with highermelting range is the decrease of temperature difference betweenthe hotspots and the low temperature areas, thereby improvingthe temperature uniformity of heat sink. It is important to mentionthat the melting range depends on the purity of PCM; hence, it canbe concluded that the purity of PCM helps increase the heatabsorbing capacity of the bulk fluid and also the heat transfer.

Fig. 12 illustrates the effect of melting range on thermal resis-tance and temperature uniformity of heat sink. Although all the re-

sults have shown a similar trend regarding the decreasing thermalresistance and temperature uniformity with respect to the Rey-nolds number, it is obvious that melting range of PCM has signifi-cant effect on thermal resistance while its effect on temperatureuniformity is not significant. It is clear that increasing the meltingrange decreases both thermal resistance and temperature unifor-mity. Furthermore, according to Fig. 12, the changes in thermalresistance and temperature uniformity are not pronounced forhigher Reynolds number, i.e., Re = 600. This also holds true forother mass concentrations, e.g., for Cm = 0.1 and 0.2. Fig. 13 pre-sents the relation of the pressure drop and Nusselt number withthe Reynolds number. Compared with NEPCM slurry with lowermelting range, the Nusselt number enhancement for the slurrywith higher melting range is increased by 46% for Re = 600. It is

Fig. 15. Total entropy generation rate as a function of Reynolds number for different melting range.


interesting to note that the NEPCM with higher melting range canenhance the heat transfer in the system and still maintain the pres-sure drop as constant.

Figs. 14 and 15 depict the effect of melting range on the entropygeneration rates caused by individual and combined sources forNEPCM slurry flow in microtube heat sink with tangentialimpingement. It is clear that the effect of melting range on heattransfer contribution of entropy generation rate is significant,while its effect on frictional entropy is not significant. An increasein melting range, increases heat transfer and total entropy genera-tion rates consequently yielding a higher heat transfer enhance-ment. Therefore, a higher melting range yields more favorableresults in the system’s cooling efficiency than larger ones.

Reynolds number has significant effect on entropy generationrates. From the above figures, it can be seen that the frictional en-tropy generation rate is not very sensitive to mass concentration ofNEPCM particles at lower values of Reynolds numbers. Moreover,with increasing inlet Reynolds number the frictional irreversibili-ties of entropy generation rate increases, while the heat transfercontribution and total entropy generation rate decreases. In otherwords, higher inlet Reynolds number causes higher cooling effi-ciency for the heat sink.

7. Conclusions

The heat transfer enhancement in the microtube heat sink withtangential impingement by using NEPCM slurry coolant was stud-ied numerically. Three-dimensional governing equations of lami-nar, incompressible fluid flow have been solved using the finitevolume method. The heat conduction in the solid part of heat sinkis taken into account. The influence of mass concentration andmelting range of NEPCM, as well as Reynolds number on the ther-mal-hydraulic performance of a microchannel heat sink is exam-ined. The results indicated that combination of NEPCM with PAObase fluid do measurably enhance the thermal performance ofthe device. Although with increasing mass concentration, the ther-mal performance increases but the extra pressure drop will some-what decrease the beneficial effect. Furthermore, it was observedthat decreasing temperature uniformity (DTs) is another advantageof using NEPCM slurry as coolant in TMHS. Moreover, the effect ofReynolds number, mass concentration and nanoparticle size on

frictional, heat transfer and overall entropy generation found thatusing NEPCM slurry as coolant can help achieve lower entropy gen-eration due to their high thermal properties. With increasing massconcentration, Reynolds number and melting range, the overall en-tropy generation rate decreases.

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