International Journal of Heat and Mass Transfer 91 (2015) 52–62

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International Journal of Heat and Mass Transfer

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

Optimum design of triangular shaped micro mixer in micro channel heatsink

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.07.0880017-9310/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors. Tel.: +966 13 860 7531; fax: +966 13 860 7312(R. Saidur).

E-mail addresses: nik_nazri@um.edu.my (N.N.N. Ghazali), saidur@kfupm.edu.sa,saidur912@yahoo.com (R. Saidur).

Navin Raja Kuppusamy a, N.N.N. Ghazali a,⇑, R. Saidur b,⇑, M.E. Niza a

a Department of Mechanical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiab Center of Research Excellence in Renewable Energy (CoRERE), Research Institute, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia

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

Article history:Received 5 February 2015Received in revised form 19 July 2015Accepted 22 July 2015Available online 6 August 2015

Keywords:Micro channel heat sinkMicro mixerOptimum designOverall enhancement factor

The focus of the present study is on the effect of triangular shaped micro mixers placed between the mainstream channels in micro channel heat sink (MCHS). These micro mixers are constructed based on threeparameters (inner and outer angle and depth of the joining point) and positioned periodically at anassigned distance. A single unit wall with separated channels is selected from the simple MCHS and microchannel with a triangular shaped micro mixer (MTM) as the computational domain for the numericalsimulation. The performance of both micro channels are compared at identical boundary conditions.The effect of volume flow rate of the fluid, flow direction, position of the micro mixer (parallel oralternating), and geometrical parameters of micro mixer on the flow and heat transfer performance ofMTM is studied. It is found that the performance of MTM is greatly dependent on the variation of allgeometrical parameters. It has to be also highlighted that overall enhancement factor of MTM improvedup to 1.53 times compared to simple MCHS with slight reduction in friction factor. This binary benefit ofMTM makes it highly possible to be implemented in the practical application.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Micro channel heat sink (MCHS) appears to be one of the mostpromising and highly effective thermal management technologiesthat are prominently used in a variety of devices especially in elec-tronic cooling. The electronic chips are widely used and mainlyreferred to central processing unit and graphic cards in computers.Many engineers have shown great interest in using micro levelcooling for data centers to improve the overall cooling capabilityand energy efficiency. Researchers have given great deal of interestto investigate the fluid flow and heat transfer in micro channel heatsink after the pioneering work done by Tuckerman and Pease [1].Steinke and Kandlikar [2] proposed that for single-phase liquidflow in micro channel, the classical theory Stokes and Poiseuilleflow is still applicable from their review on existing literature ofexperimental data on the friction in microchannels. In anotherreview of heat transfer in microchannels, Rosa et al. [3] suggestedthat standard theory and correlations to describe heat transfer inmicrochannels but scaling effects has to be considered critically.

However, the simple MCHS does not seem sufficient for coolingas a result of tremendous accession of power density and minus-cule of electronic packages. According to Moore’s Law, the micro-processor transistor count doubles up every two year andincrease the cooling demand of the device to run in operating tem-perature. Thus, intensive researches have been actively conductedto improve the heat transfer and fluid flow characteristics in MCHSin an attempt to resolve the issue.

Xu et al. [4,5] provided three-dimensional numerical simula-tions of conjugate heat transfer in a newly proposed interruptedmicro channel heat sink. The new silicon micro channel heat sinkconsists of parallel longitudinal micro channels and several trans-verse micro channels. Cheng [6] numerically studied the flow andheat transfer in a stacked two-layer micro channels witheasy-processing passive microstructures and found that stackedmicro channel has better thermal performance compared to simpleone. Korichi and Oufer [7] studied the flow and thermal perfor-mance of a horizontal channel with obstacles mounted alternat-ingly on both upper and lower walls numerically. It was foundthat a travelling wave generated by the vortex shedding from theconstriction and expansion contributes mainly to heat transferenhancement.

Promvonge et al. [8] numerically studied the laminar flow andheat transfer characteristics in a three-dimensional isothermalwall square channel with 45� angled baffles. Sui et al. [9] examined

Nomenclature

A area (m2)A1 arrangement 1A2 arrangement 2cp heat capacity (J/kg K)d depth of micro mixer (lm)D1 direction 1D2 direction 2Dh hydraulic diameter (m)ks thermal conductivity (W/K m)G mass flow rate (kg/s)�h heat transfer coefficient (W/K m2)k thermal conductivity (W/K m)L length of micro channel (mm)n number of micro mixerN improvement factorNu Nusselt numberDp pressure drop (kPa)q00 heat flux (W/m2)T temperature (K)

uin inlet velocity (m/s)u, v, w velocity vectorx, y, z Cartesian coordinate

Greek symbolsq density (kg/m3)h inner angle (�)s outer angle (�)l viscosity (Pa s)

Subscriptsavg averagef fluidFD fully developedin inletm meanMTM micro channel with triangular shaped micro mixerr ratios solid

N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62 53

the performance rectangular wavy micro channels at laminar con-dition. An enormous thermal enhancement was obtained due tothe secondary flow (Dean Vortices). Foong et al. [10] performednumerical simulation on the fluid flow and heat transfer character-istics of a square micro channel with four longitudinal internal finsand analyzed the effect of the pin height and flow condition on theperformance of micro channels. It was found there is an optimumpin height to achieve the best performance. Dogan and Sivrioglu[11] performed experimental study on the mixed convection heattransfer from longitudinal fins in a horizontal channel with a uni-form heat flux at the bottom surface and found optimum fin thatdependent on the fin height and modified Rayleigh number forheat transfer enhancement. Danish et al. [12] investigated numer-ically the thermal-resistance and pumping-power characteristicsof MCHS with a grooved structure optimized the shape using amulti-objective evolutionary algorithm. Decline in thermal resis-tance and increment in Nusselt number observed in a groovedmicrochannels compared to a smooth MCHS with a small incre-ment of pumping power.

Liu et al. [13] used CFD (computational fluid dynamics) and LB(lattice Boltzmann) approaches to the numerical study of forcedconvection heat transfer occurring in microchannels. The resultsimplied that the shield shaped groove microchannel possessedhigh heat exchange performance with the increment of Nusseltnumber at about 1.3 times of the plain surface structure. Chaiet al. [14] studied the pressure drop and heat transfer characteris-tics of the interrupted microchannel heat sink with rectangularribs in the transverse micro chambers and analyzed the effects ofdimension and position parameters of rectangular rib on thesecharacteristics.

Xia et al. and Chai et al. [15–17] analyzed the effect of geometricparameters of fan-shaped and triangular reentrant cavities onwater flow and heat transfer characteristics in MCHS. Optimal geo-metric parameter was obtained based on thermal enhancementfactor performance.

In numerical investigation of microchannel heat sink withgrooved wall, Abouali and Baghernezhad [18] found that groovedmicrochannel with thicker wall and lower mass flow rate of cool-ing water has a higher heat dissipation and coefficient of perfor-mance compared to simple microchannel with small wallthickness. Kuppusamy et al. [19,20] performed numerical analysis

on the thermal and flow performance of the MCHS with differentshapes of grooves on the sidewall of the MCHS using nanofluid.It was found that thermal enhancement enhanced significantlycompared to simple MCHS using water with negligible pressureloss.

Lee et al. [21] attempted to enhance the performance of copperMCHS by introducing periodic oblique cuts on the fins of MCHS inorder to transform the fluid flow. This could induce redevelopmentof the thermal boundary layer that would result in significant heattransfer enhancement with negligible pressure drop penalty. Theaverage Nusselt number increased up to 103%, from 11.3 to 22.9and the maximum temperature rise reduced by 12.6 �C.Kuppusamy et al. [22] introduced secondary passage in the sepa-rating wall of the MCHS and found that the slanted secondary pas-sage significantly enhanced the Nusselt number of the MCHS aswell the with reduction in pressure drop compared to the simpleone. Therefore, significant overall enhancement is obtained com-pared to the simple MCHS. Beside various optimization techniqueshave been implemented to optimize thermal performance ofMHCS.

Recently, there are numbers of articles published related tooptimization of micro channel heat sink. Leng et al. performed anoptimization study on double-layered micro channel heat sink[23,24]. Khan et al. [25] performed multi-objective optimizationon inverse trapezoidal microchannel heat sink. Shi et al. studiedthe effect of staggered arrays of pin fin structure with tip clearanceand optimized the entropy generation in microchannel.

From the literatures, it is clear that the substantial techniques toenhance micro scale heat transfer are vortices generation, thermalboundary layer interruption, and induce the mainstream separa-tion and mixing. Considering this mechanism, the present workfocuses on the introduction of micro sized mixers in MCHS thatcould result in all the effects mentioned above. The effect of thegeometrical parameters of the micro mixers in MCHS on thethermal and flow performance is analyzed. The thermal and flowperformance are presented in terms of friction factor andaverage Nusselt number respectively. Both of these results arecompared in terms of overall enhancement coefficient. The heattransfer enhancement of micro channel heat sinks with periodictriangular shaped transverse micro mixer (MTM) is numericallyinvestigated.

Fig. 2. Schematic diagram of simple MCHS with (a) single channel and (b) singlewall.

54 N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62

2. Description of the numerical model

A single unit wall with separated channels is chosen to performthe numerical analysis in order to conserve the computationaltime. Fig. 1 portrays the schematic diagram of MTM.

Fig. 2 shows the computational domain of MTM together withits geometrical parameters. A single micro channel has the widthof 0.1 mm and the depth of 0.2 mm and therefore the hydraulicdiameter is 0.1333 mm [2,16]. The total length, width and heightof the channel are 10 mm, 0.3 mm and 0.35 mm respectively. Theparameters of MTM; h, s and d represent the inner and outer angleand the depth of meeting point of the two edges of the micro mixer(depth of micro mixer). The geometrical parameters of the micromixers are not dependent on each other. The distance of the twoadjacent micro mixers depends on its quantity where the total dis-tance of the channel is divided equally with the numbers of themicro mixers and the integer value considered as the pitchbetween the micro mixers and the floats are divided equally atthe entrance and exit of the channel.

3. Mathematical foundation

The numerical model was developed based on several assump-tion as follows:

(1) steady laminar flow and heat transfer,(2) properties of the fluid are not dependent on temperature

except for viscosity,(3) no radiation heat transfer,(4) no viscous dissipation in fluid.

Based on the aforementioned assumptions, the governing equa-tions are developed as follows:

Continuity equation:

@

@xðuÞ ¼ 0 ð1Þ

Momentum equation:

Fig. 1. (a) Schematic diagram of MCHS with secondary channel (b) computationaldomain and (c) the geometrical parameters of the secondary channel.

@

@xðqf uvÞ ¼ @q

@yþ @

@xlf

@v@xþ @u@y

� �� �ð2Þ

Energy equation:

@

@xðqf ucpTÞ ¼ @

@xkf@T@x

� �ð3Þ

Governing equation for solid:

@

@xks@T@x

� �¼ 0 ðSolidÞ ð4Þ

The governing equations were solved using the finite volumebased computational fluid dynamics (CFD) solver FLUENT 6.3.26.The momentum and energy convective term are discretized bythe second order upwind differencing scheme and the pressure–velocity decoupling is done with the SIMPLE algorithm. The solu-tions were considered to be converged when the normalized resid-ual values were less than 10�7 for all variables except for theenergy equation less than 10�8.

3.1. Boundary conditions

The thermal and flow boundary conditions are given as follows:

(1) at the inlet, x = 0 (for D1) and x = 10 (for D2): uf = uin andTf = Tin = 293 K for water; �ksð@Ts=@xÞ ¼ 0 for siliconsubstrate

(2) at the outlet, x = 10 mm (for D1), x = 0 (for D2): pf = pout =1 atm and �kf ð@Tf =@xÞ ¼ 0 for water, �ksð@Ts=@xÞ ¼ 0 forsilicon substrate

(3) at the inner wall/fluid surface u = v = w = 0; �ksð@Ts=@zÞ ¼ 0;(4) y = 0, @=@y ¼ 0 (symmetry); y = 0.30 mm, @=@y ¼ 0

(symmetry);(5) z = 0, �ksð@Ts=@zÞ ¼ q00 ¼ 1:2� 106 W=m2; z = 0.35 mm,�kf ð@Tf =@nÞ ¼ �ksð@Ts=@nÞ, n is the local coordinate normalto the wall.

The computational domain is generated using hex–wedgecooper scheme. A grid independence study is conducted for simpleMCHS with single wall and two channels. For uin = 4 m/s andq = 106 W/m2, the deviations of average Nusselt number using0.347, 0.465 and 0.667 million grids from that of 1.04 million gridsare 9.53%, 5.32%, 2.01% and 0.34% respectively. Considering thedeviation is less than 0.5%, MCHS with 0.667 million grids isselected for analysis to achieve desirable accuracy and computa-tional time.

Fig. 3. Validation of simple MCHS with (a) single channel and (b) single wall.

N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62 55

3.2. Calculation of thermal and flow performance

The thermal performance of micro channel heat sink is deter-mined by its Nusselt number that can be calculated using Eq. (5).

Nu ¼�hDh

kfð5Þ

where �h, Dh ¼ 2WcHcðWcþHcÞ and kf are the average heat convection coeffi-

cient, hydraulic diameter of the channel, and thermal conductivityof the fluid.

The average convective heat coefficient �h can be calculated as:

�h ¼ 1L

ZL

hðxÞ � dx ð6Þ

where L is the length of the channel.The local convective heat transfer coefficient, h(x), can be

evaluated using the following equation:

hðxÞ ¼ 1Xx;y

dAðx; y; zÞ

Px;yq00ðx; y; zÞdAðx; y; zÞP

xy½Twðx; y; zÞ � TmðzÞ�dAðx; y; zÞ

" #ð7Þ

Tw(x,y,z) is the local wall temperature and Tm(x) is the local fluidbulk-mean temperature given by:

TmðxÞ ¼ Tin þ1

Gcp

Xx;y;z

q00ðx; y; zÞdAðx; y; zÞ ð8Þ

The friction factor can be calculated as follows:

f ¼ DpDh

2u2mL

ð9Þ

where Dp and um are the pressure drop and mean velocity. In orderto evaluate the increment ratio compared to the simple MCHS,Nusselt number and improvement factor are calculated as:

f r ¼ f MTMf FD

, Nur ¼ NuMTMNuFD

and N r ¼ Nur

f 1=3r

respectively.

4. Results and discussion

4.1. Verification of numerical model

Numerical model that consists of a single wall and two channelswith half of the actual channel width is selected for the presentstudy. This numerical model is compared with a single micro chan-nel and two walls with identical geometries and both of thesemodels are validated with existing analytical equations as shownin Fig. 3. The Nusselt number and frictional factor at variousReynolds number matched well with the analytical equation [26]for similar boundary conditions (uin = 4 m/s, q00 = 106 W/m2).

4.2. Effect of micro mixer orientation, cooling fluid volume flow rateand its flow direction

Micro mixers are designed in 2 orientations in order to predictthe effect of flow pattern in MTM; parallel and alternating. Thevolume flow rate of the cooling fluid is studied from G = 4 to10 � 10�7 m3/s with different inlet direction; D1 and D2. Theboundary conditions associated with different flow direction areexplained in Section 3.1. The arrangement of the micro mixer isdefined as A1 and A2 for alternating and parallel arrangementrespectively. Fig. 4 shows the schematic diagram of the flowarrangement and the flow direction. It can be seen that the micromixer is converging with the flow direction in D1 and divergingin D1. A1 provides alternating flow between one to another chan-nel whereas flow diverts consistently into only channel in A2. Heat

flux of 1.2 � 106 W/m2 is supplied at the bottom surface of thesilicon substrate. Both the inner (h) and outer angle (s) areconstrained at 30�. The numbers of the micro mixers betweenchannels are fixed at 6.

4.2.1. Heat transfer characteristicThe evaluation of the thermal characteristic is performed based

on the Nusselt number since heat transfer through advection isdominant. The propensity of Nuavg and Nur with increment of Gat different flow direction and micro mixer arrangement is shownin Fig. 5. Nuavg increases with G for both MTM and simple MCHS.Aside of that, for all value of G, Nuavg of MTM is much higher com-pared to simple MCHS. It is also observed that Nuavg for all MTMincrease with greater rising extent compared to simple MCHS.For instance, at G = 4 � 10�7 m3/s, MTM (A1, D2) bettered the sim-ple MCHS by 17.6% whereas at G = 4 � 10�7 m3/s, improvement hasincreased to 25.2%. A very trivial difference is found between D1and D2 at G = 4 � 10�7 m3/s for both arrangement. The flow direc-tion does not seem to affect the thermal of MTM for both arrange-ments at the lower flow rate. This trend prolonged for A1 untilG = 5 � 10�7 m3/s where Nuavg in both direction lie at the samepoint and gradually disperses after that. In Direction 2, Nuavg

begins to rise with larger accretion compared to Direction 1 in botharrangements as G passes 5 � 10�7 m3/s. Arrangement A1 exhibitshigher Nuavg for both flow direction until G < 6 � 10�7 m3/s.However, ascend of A2 becomes more precipitous and outperformsothers at G = 10 � 10�7 m3/s.

The trend of Nur is presented in 3D surface in Fig. 5(b) in orderto provide clearer perception of variation in Nur at different flowrate, flow direction and micro mixer arrangement. Generally, agradual increment is observed in Nur for all configuration and D2,A1 reaches to the peak value at G = 10 � 10�7 m3/s. Higher heattransfer can be achieved in a diverging micro mixer because ofthe reverse pressure gradient micro mixer encourage the fluid toenter the micro mixer and spool up into vortices before exiting thatimprove the convection heat transfer. Aside of that, alternatingflow orientation enhance the flow oscillations that too signifiesthe heat transfer.

4.2.2. Friction factor characteristicIt is known according to the Moody chart, f through a straight

channel reduces with increase in flow rate in laminar flow beforeit reaches to transition zone. On the other side, f of MCHS with pas-sive enhance typically will increase compared to simple MCHS

Fig. 4. Arrangement of micro mixer in the channel wall.

Fig. 5. Variation of Nuavg and Nur with variation of G, flow orientation and micromixer arrangement.

Fig. 6. Variation of f avg and f r with variation of G, flow orientation and micro mixerarrangement.

56 N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62

N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62 57

with increase of flow rate [15–17,19,20,27,28]. As expected, inFig. 6, f reduces gradually for both MTM and simple MCHS as Gincreases from 4 to 10 � 10�7 m3/s. Ironically, f of simple MCHSis higher compared all MTM at 4 � 10�7 < G < 5 � 10�7 m3/s.However, since descend degree of f in simple micro channel islarge compared to MTM, it overlie all MTM except ‘D2, A2’ atG = 7 � 10�7 m3/s. Since f of ‘D2, A2’ is much lower compared toother, simple MCHS only overlaps it at G = 9 � 10�7 m3/s. It isfound that flow direction has negligible effect on f for A2 for allgiven flow direction and eventually had the least value of f atG = 9 � 10�7.

In Fig. 6, the 3D surface plot shows that f r increases graduallywith G. f r of ‘A2, D2’ is found expressively smaller compared toothers and it meet lowest point at G = 4 � 10�7. Apical point of f r

is observed at ‘A2, D1’ at G = 10 � 10�7. The fluid flow in micromixer in alternating direction has better performance comparedto parallel direction. This is because in parallel direction, the cool-ing fluid is repeatedly forced into one channel while the otherchannel discharge the cooling fluid from the mainstream continu-ously that results in pressure built up. On the other side, the con-vergent micro mixers with flow direction have smaller outlet thaninlet that impedes the flow and deteriorates the pressure drop.Diverging micro mixers with flow direction at alternating positiondemonstrates the least pressure loss and overlap simple MCHS atG = 9 � 10�7.

Water from the main stream channel slips over the micro mixerensues less friction factor compared simple channel at lower flowrate especially in Direction 2. Nevertheless, this effect fades as theflow rate increases. The secondary flow regime from the micromixer interrupts the main stream flow the increases the pressureloss of MTM as the flow rate increases.

4.2.3. Overall enhancementIt is a general fact that increment of Nuavg always accompanied

by additional pressure drop. The compensation of Nur with f r isverified based on overall enhancement ‘N r ’. The 3D surface plotshows that Nur intensifies progressively with increment of G asshown in Fig. 7.

As the G increases, the improvement of N r for respective micromixer arrangement and flow direction starts to increase at differ-ent acclivity. The most significant improvement observed amonga MTM is for ‘A2, D1’ where N r increases from lowest among theMTM to the highest. In terms of sensitivity of flow direction on

Fig. 7. Variation of N avg and N r with variation of G, flow orientation and micromixer arrangement.

the micro mixer arrangement, A2 is more responsive to the flowdirection where larger difference is observed between the flowdirections at higher G.

Drastically improved of N r at A1, D2 from G = 4 to10 � 10�7 m3/s. This followed by A2, D2 where with slightly lowerN r for a given G. It should be noted that the variation of Nur forboth A1, D2 and A2, D2 with G are almost same but f r of A1, D2was significantly lower compared to A2, D2. This fact leads to sig-nificant improvement of N r at A1, D2.

It is a common fact that with increase of flow rate, the magni-tude of vortex enhances and the thermal boundary layer in theconstant cross-sectional area shrinks. Inclusion of micro mixersin MCHS signifies this effect as vortices are formed in it. The cool-ing fluid temperature in the center of vortex region is higher com-pared to the surrounding vicinity. Fig. 8 portrays the pressurecontour plots and isotherms of micro mixer at A1, D2 atG = 9 � 10�7 m3/s and A2, D1 from G = 4 � 10�7 m3/s. While formerhas a large fluid vortex, the latter has two vortices that are compar-atively smaller where each of them swirls at opposing direction.These inimical whirlpools are formed owing to the repetitive diver-sion of the mainstream fluid into the same channel (upper chan-nel) that makes it very repulsive. It can be observed in Fig. 8(b)that pressure at end of latter mainstream, the pressure at upperchannel is much lower compared lower channel unlike in formerchannel, the exit pressure of both mainstreams are almost same.Thus, the fluid in micro mixer is deterred from entering the chan-nel and it circulates at different stationary focal point in opposingdirection continuously. Unfortunately, such adverse fluid circula-tion impeded the heat transfer and increased the pressure seri-ously. A very high temperature is observed in this proximity andthis can seriously deteriorates the heat transfer.

4.3. Effect of inner angle ‘h’ and outer angle ‘s’ of the micro mixer

Effect of variation in the inner angle ‘h’ and outer angle ‘s’ on thethermal and flow characteristic is studied. These two parametersdetermine the shape of the micro mixer. Even though the highestperformance is obtained from ‘A1, D1’ from the previous analysis,it had higher friction factor compared to the simple atG = 9 � 10�7 m3/s. Since the objective of the study is to attain ther-mal enhancement without additional pressure loss, configuration‘D2, A2’ is selected at G = 9 � 10�7, for this analysis. The width ofthe micro mixer and numbers micro mixers are fixed at 10 lmand 6, respectively.

4.3.1. Heat transfer characteristicNuavg increase greatly with increment of h for all s as shown

Fig. 9(a). While having the baseline value of simple MCHS at

Fig. 8. (a) Pressure contour plot and (b) isotherms in the secondary channel withdifferent flow rate (G), micro mixer arrangement (A) and flow direction (D).

Fig. 9. Variation of Nuavg and Nur with variation of h and s.

Fig. 10. Variation of f avg and f r with variation of h and s.

58 N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62

Nuavg = 10.08, a noticeable relation is also observed f and s. For agiven h, Nuavg accretes with s. Indeed, the accession progressionof f with h has also improved at s = 30�.

Micro mixer h = 50�, s = 30� exhibits a very poor heat transfer bycause of its sharp diversion angle and confined area. Thus, only asmall amount of fluid from the main stream channel redirect intothe micro mixer. Aside of that, there is no fluid circulation observedin the micro mixer and the cooling fluid directly flow towards thelower main stream channel. It also observed that the micro mixerenvironed with very high fluid temperature. This suggests thatpoor fluid mixing in that region consequently lowered the thermalenhancement.

As h ? 50� and s ? 30�, the convective heat transfer progres-sively improved as illustrated in Fig. 9(b). Besides the changes inthe shape, the size of the micro mixer also enlarged. This hasencouraged more fluid to imping into the micro mixer and engen-dered more vortices that consequently improved the fluid mixingand shorten the thermal boundary layer.

Laminar stagnation has built up in fringe of the mainstream andthe micro mixer outlet due to the sudden reduction cooling fluidvelocity as flow from these two regime consolidates. This laminarstagnation zone has slightly hampers the heat transfer. In spiteof this impediment, the overall heat transfer improved due to sev-eral factors (1) multiple fluid recirculation; (2) redevelopments ofboundary layer; and (3) enlargement in the heat transfer area at

solid–fluid interface. Enormous heat transfer intensification dueto these factors has compensated the minor heat transfer deterio-ration that happened at the pressure stagnation.

4.3.2. Friction factor characteristicA tremendous reduction in f is observed with decline of h espe-

cially for s = 30� as portrayed in Fig. 10. The escalate amplitude of fvaries depending on s where; as s reduces, the reduction of fbecomes more vigorous with increment of h. For instance, fors = 30�, f crosses the simple MCHS with only a small incrementof h (<30�) since the descent scope is very large. This followed bys = 40� at 40� < h < 50�. Whereas for s = 50�, f remains comparedto of simple MCHS for all values of h. From trend of f , it can beinferred that increment in the inner angle and reduction in theouter angle reduces f greatly.

Reduction of s provide smaller diversion angle and ease coolingfluid to impinge from the mainstream channel to mixer section.Likewise, increment of h results in inverse pressure that also toinvades the fluid into the micro mixer section. Besides, the micromixer area enlarged and fluid in mainstream channel slips overthis area. The velocity of fluid decreases and it redirects at brinkof the micro mixer exit and mainstream channel because of thewall stagnation and viscosity of fluid. This results in a bigger area

Fig. 12. (a) Pressure contour plot and (b) isotherms in the secondary channel withdifferent h and s.

N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62 59

of laminar stagnation area in this section that also helps the fluid toslip over this region. These are the two major reasons of significantreduction in friction factor in this analysis.

4.3.3. Overall enhancementFor comparison of tendency of f r and Nur, the variation of N r

with h is plotted at different s. While in one hand, the variationof f is recedes drastically with h, on the other hand, Nuavg improvedconsiderably, an appreciable improvement is noticed in N r . Asshown in Fig. 11, the proclivity is very much similar to Nur but atgreater ratio proportion due to the reason mentioned above.

Fig. 12 shows that the angle of micro mixer is very steep and thesize is very slender. Therefore, only partial amount of fluid enterthis region and directly flow towards the lower main stream chan-nel. No fluid recirculation is observed due to the limited space. Ash ? 50� and s ? 30�, the micro mixer becomes sharper in its shapeand therefore, the pressure gradient becomes much larger. Besides,the micro mixer size is also enlarged and consequently increasesthe solid–fluid interface area. This let the convection heat transferin the micro mixer increase immensely. As more fluid enters themicro mixer, multiple vortices are generated with high intensitydue to the reverse pressure difference across it.

Isotherms in Fig. 12(b) shows that higher cooling fluid temper-ature in core of the vortices in h = 50�, s = 50� implies that greaterheat transfer happens in this micro mixer. The fluid pressure in thesame locality, nevertheless is lower compared to the neighboringregion.

The pressure plot in the micro mixer h = 50�, s = 50� shows thatpressure stagnation formed at the adjoining point of the micromixer and lower main stream channel. A low pressure area is typ-ically formed at the area flow split from the mainstream region andthe high pressure area (pressure stagnation) is normally built whenfluid merge from different directions.

4.4. Effect of depth ‘d’ and number ‘n’ of the micro mixer

Variation in thermal and flow performance with increment indepth (d) and numbers (n) of micro mixer in the micro channelheat sink is analyzed. The analysis is performed by maintaining hand s at 50� and 30�, respectively in micro mixer ‘A1, D2’ atG = 9 � 10�7 m3/s. The range analysis performed is from 0.1 to0.2 lm and 6 to 10 in for d and n respectively. It has to be

Fig. 11. Variation of N avg and N r with variation of h and s.

underlined that, varying of d direct affect the size of the micromixer and combination of d and n will determine the sectionallength of the of constant segment of MTM.

4.4.1. Heat transfer characteristicFig. 13(a) displays that Nuavg increased progressively with incre-

ment of d. Besides that, a visible increment is observed in the vari-ation of n. However, smaller increment is observed at 8 < n < 10compared 6 < n < 10. This trend suggests that increment of num-bers of micro mixer has reached to its maximum potential toenhance the thermal performance. Two possible reasons can pro-pose for the reduced in the ascent scope: (1) the thermal boundarylayer has shrunken sufficiently; (2) the breadth of vortex begins toincrease rather than its quantity. Further increment d and n wouldprobably not improve the heat transfer or deteriorate the thermalperformance in worst case. Nur reached to its peak at d = 0.2 andn = 10 as corollary from increment and reduction of d and n as por-trayed in Fig. 13(b). This trend makes sense as increment of size ofthe micro mixer would provide larger area in micro mixer that con-sequently enhance the fluid diversion from the main stream flowregion and its mixing in the micro mixer. Similarly, increment ofnumbers of micro mixer also results in more fluid quivering andmixing. Aside of that, repetitive boundary layer development inconstant cross sectional area also improves the thermalenhancement.

As discussed earlier, the significance of the forced convection isdependent of fluid recirculation it is directly affected the size andintensity of vortices. Enlargement of the micro mixer augmentsthe peripheral area of vortex that increases the size of vortex andeventually improves the fluid mixing in the bulk flow. As d and nincrease, the numbers of vortex amplified and the thermal bound-ary development shortened that impede the heat transfer rate. Thefluid oscillation, concurrently outweigh heat transfer rate draw-back over the shorter length of total constant cross-sectional area.

4.4.2. Friction factor characteristicOpposing trend is seen in f compared to Nuavg in Fig. 14(a). A

drastic reduction is observed with increment of d. Increment of nalso reduced the friction factor of MTM even though the tendencyof the reduction is found inconsistent. Based on this phenomenon,it is found in Fig. 14(b) that combined effect of d and n weightedbased the simple MCHS had a peak value at d = 0.1 and n = 6 andlowest point at d = 0.2 lm and n = 10. It can be inferred that largerarea between the micro mixer and the mainstream flow couldreduce the flow friction. This could happen possibly due to slip

Fig. 13. Variation of Nuavg and Nur with variation of d and n.

Fig. 14. Variation of f avg and f r with variation of d and n.

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fluid flow over the micro mixer area. Aside of that, the velocity ofcooling fluid abates and the redirects due to the wall stagnation,fluid viscosity and fluid association from mainstream region andmicro mixers. Consequently, a large stagnation area is formed inthis section that enables the fluid to slip over it and diminishesthe friction factor.

4.4.3. Overall enhancementIn previous sections, it can is observed that increment of d and n

has multiplied the benefits of MTM by increasing the Nuavg as wellas reducing f . This has result in tremendous improvement inN r . Asd ? 0.2 lm and n ? 10, N r increased up to 1.53 as shown inFig. 15.

The detailed study of the flow and thermal field in Fig. 16 showsthat multiple vortices are developed in both micro mixers. In virtueof large impinging area, the fluid flows into the micro mixer andthen whirls up creating recirculation due to converse pressure dif-ference across the micro mixer. It has also noted that, the laminarpressure stagnation at verge of main stream and the micro mixeroutlet becomes larger with increment of d and n. The streamlines,temperature and pressure plot for both micro mixers (d = 0.2 lm,

n = 10 and d = 0.1 lm, n = 10) are observed to be similar (exceptfor numbers and size of vortices).

The isotherms shows the cooling fluid temperature is muchhigher in MTM with d = 0.2 lm and n = 10 that suggest higher heattransfer compared to d = 0.1 lm and n = 6. Even though vorticesare observed in both micro mixers, more vortices is seen in the for-mer at larger size in three different position; one at the entry sec-tion and two at the exit section. Higher temperature is observed inthe focal vicinity of the vortices as in previous analysis. The coolingfluid pressure in the same locale, on the other hand, is lower com-pared to the neighboring region. Thus, it can be reckoned that themore vortices are generated, the greater heat absorption inducedin the micro mixer.

As mentioned above, increment of d directly reflects incrementof the size of micro mixers. The significance of the forced convec-tion is dependent on fluid recirculation and it is directly affectedby the size and intensity of vortices. Enlargement of the micromixer augments the peripheral area of vortex that increases thequantity and size of vortices. Increase of n the also increased thenumber of vortices and these eventually improves the fluid mixing

Fig. 15. Variation of N avg and N r with variation of d and n.

Fig. 16. (a) Pressure contour plot and (b) isotherms in the secondary channel withdifferent d and n.

N.R. Kuppusamy et al. / International Journal of Heat and Mass Transfer 91 (2015) 52–62 61

in the bulk flow tremendously. Besides the size and numbers ofvortices, the solid–fluid interface area and repetitive developmentof boundary layer also increase as corollary of increment of d and n.Increase of d and n might shorten the thermal boundary develop-ment that could impede the heat transfer rate. The fluid oscillation,concurrently outweigh heat transfer rate drawback against theshorter entire length of constant. Excessive increase of d couldshorten the step-wise constant cross-sectional length that wouldimpede the thermal boundary layer redevelopment and reducethe intensity of the vortices as mentioned previously. It can beinferred that moderate increase of d and n can improve heat trans-fer, but if done overly, the thermal performance is deteriorated.

5. Conclusion

A newly designed micro channel heat sink with micro mixer(MTM) is proposed in the present study. The primary objective thisnumerical study is to obtain the appropriate flow rate, micro mixerangle and its size in order to achieve highest thermal enhancementpossible without additional pressure drop. From the data obtainedin the study, the following conclusion can be deduced:

1. There is an optimum flow rate, appropriate flow direction andmicro mixer arrangement to achieve thermal enhancementwithout additional pressure loss that is A1, D2 atG = 9 � 10�7 m3/s.

2. Reduction of the outer angle and increment of the inner angle ofmicro mixer also improves thermal enhancement and reducesthe pressure loss significantly.

3. Increment in number of micro mixer and enlargement of itsdepth improve the performance of the MTM as well.

4. In virtue of repetitive alternating flow, large and intense vor-tices are generated in the micro mixer. Besides, the thermalboundary layer is shortened and thickened. Therefore, thermalperformance of MTM intensified exceptionally.

5. The slip of main stream flows over the micro mixer and laminarstagnation zone are the prime reason of drastic reduction offriction factor in MTM. Ultimately, the overall performancehas escalated tremendously by virtue of these reasons.

6. There are numerous methods to improve the convection heattransfer. However, researchers and thermal engineers shouldcritically address the drawback of increased of pressure dropi.e. pumping power that would increase the capital cost.Fortunately, for the present study, the enhancement in heattransfer together with reduction in pressure drop is observed.This is double winning factor that would be very useful forresearchers and heat transfer engineers.

Conflict of interest

None declared.

Acknowledgements

The authors would like to acknowledge the Ministry of HigherEducation of Malaysia and the University of Malaya, KualaLumpur, Malaysia for the financial support under the projectUM.C/HIR/MOHE/ENG/40.

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