Numerical investigation of heat transfer in extended surface microchannels

International Journal of Heat and Mass Transfer 93 (2016) 612–622

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Numerical investigation of heat transfer in extended surface microchannels Vikas Yadav, Kuldeep Baghel, Ritunesh Kumar ⇑, S.T. Kadam Mechanical Engineering Department, Indian Institute of Technology Indore, MP 453446, India

a r t i c l e

i n f o

Article history: Received 1 June 2015 Received in revised form 16 September 2015 Accepted 11 October 2015

Keywords: Microchannel Single phase flow Extended surface Nusselt number Heat transfer characteristics

a b s t r a c t Microchannel heat sinks (MCHS’s) are currently projected as twenty first century cooling solution. In the present numerical study, heat transfer enhancement in microchannel using extended surface has been carried out. Rectangular microchannel and cylindrical microfins are used in current study. Three different configurations of extended surface microchannel; Case I (upstream finned microchannel), Case II (downstream finned microchannel) and Case III (complete finned microchannel) are compared with plain rectangular microchannel. It is found that heat transfer performance of Case I is better than Case II. Case I even performs better than Case III at low Reynolds number. Average surface temperature is also significantly reduced in case of extended surface microchannels. Optimization of extended surface microchannel has also been successively carried out following univariate search method for number of fins, pitch, diameter and height of fins. Average heat transfer enhancement in optimized case is around 160% with acceptable pressure drop penalty. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Breakthrough in diversified fields is largely dependent on the ability to safely dissipate large amount of heat from extremely small surface area. This urgency has thrown challenge to design compact size efficient heat sink especially for applications; where conventional heat sink cannot be used either due to space constraint or due to high heat flux duty requirement i.e. high speed component [1], laser process equipments [2], fusion related [3] and defense related equipments [4]. Effective thermal management in these applications not only increases their reliability but also helps in achieving next level of miniaturization. With the objective of efficient cooling system for high speed Very Large Scale Integrated (VLSI) circuits, Tuckerman and Pease [5] for the first time fabricated MCHS (w, h) (50 lm, 320 lm), which was capable of removing heat flux up to the rate of 700 W/cm2. Since then MCHS’s have been used as one of the prominent solution for the problems, where electronic devices fail due to excessive heating [6–9]. Major advantages MCHS offer over conventional heat sink are larger surface area to volume ratio, high heat transfer coefficient and very small coolant inventory requirement. MCHS’s are generally fabricated with copper [4,10] or silicon [5,6,11–13] as base material. Copper is an excellent conductor of heat and silicon ⇑ Corresponding author. Tel.: +91 7324 240734; fax: +91 7324 240761. E-mail address: [email protected] (R. Kumar). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.10.023 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

has maintained its popularity as good semiconductor in electronic industry. Due to excellent heat removal capability of MCHS’s, understanding the associated fluid flow and heat transfer characteristics have been topics of intense research in the last decade [14–17]. Surprisingly, the limit to define microchannel has not been unanimously accepted. Different researchers had proposed different criteria for it. Kandlikar and Grande [18,19] suggested the range as (10 lm < dh 6 200 lm), whereas Mehendale et al. [20] projected the range as (1 lm 6 dh 6 100 lm) to distinguish between micro and macrochannel. Cornwell and Kew [21] and Kew and Cornwell [22] advised that macro to micro scale transition criteria should be based on confinement number (Co P 0.5). Recently, Harirchian and Garimella [23] suggested new transition criteria (Bo0.5Re < 160) for distinguishing between micro and macro channels. Exclusive literature review of microchannel is presented by Kadam and Kumar [24], Kandlikar [25–27] and Kandlikar et al. [28]. Lots of work has been carried out on single phase and two phase heat transfer and pressure drop characteristics of microchannel. Due to superior heat transfer characteristic of boiling process major efforts are concentrated on two phase flow studies. However, various associated instabilities such as parallel channel instability [29], pressure fluctuation [12], vapor blocking [30] and flow reversal [31–33], turn two phase flow in microchannel more susceptible against stable performance. Performance fluctuation causes overheating, which induces malfunctioning of the

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

613

Nomenclature AB Ac Asur Bo cp Co dh df g h hf k L Lin N Nu p P DP q00 Re T U ~ V

base area of unit cell (m2) cross-sectional area of channel (m2) surface area (m2) Bond number specific heat (J/kg K) confinement number hydraulic diameter (lm) diameter of fin (mm) gravity (m/s2) height of microchannel (lm) height of fin (mm) thermal conductivity (W/m K) length of microchannel (mm) distance of first fin from inlet (mm) number of fins Nusselt number fin pitch (mm) pressure pressure drop (bar) heat flux (W/cm2) Reynolds number temperature (°C) velocity (m/s) velocity vector

system or may even lead to permanent damage of the system. Hence, single phase studies are equally important. Peng and Wang [34] in their experimental study on rectangular microchannel observed that single phase heat transfer coefficient was affected by liquid subcooling and flow velocity. Peng and Peterson [35] concluded that heat transfer performance of laminar flow can be augmented by increasing the ratio of hydraulic diameter to centre to centre distance of microchannel. They further showed that increasing aspect ratio also facilitated the performance of MCHS. Harms et al. [11] suggested transition criteria from laminar to turbulent flow in microchannel as Recr = 1500. Low Reynolds number transition in case of microchannel was attributed to sharp inlet, long entrance region and surface roughness. Qu and Mudawar [10] verified that Navier-Stoke and energy equation were capable of predicting heat transfer behavior of the single phase flow in microchannel. They also observed that at constant Reynolds number pressure drop reduced with increase in heat flux, which they attributed to decrease in viscosity of water with increase in temperature. Ergu et al. [36] concluded that single phase pressure drop behavior of rectangular microchannel follows macrochannel theory for laminar flow region. However, Koyuncuoglu et al. [37] found that predicted single phase friction factor by conventional theory was lower than experimental values in case of rectangular microchannel. Wang et al. [38] optimized design parameters of a MCHS using inverse problem approach integrating simplified conjugate-gradient scheme with three dimensional heat transfer and flow model. They found that increasing pumping power is not always cost effective approach for practical heat sink designs. In search of finding suitable heat transfer augmentation technique for single phase flow, researcher have also worked on by choosing among from conventionally proven methods e.g. modification in channel geometry [39–50] and through nanofluids [51– 55]. Gong et al. [39] used wavy microchannel in their numerical study and observed that redevelopment of thermal boundary layer helped in heat transfer enhancement. Sui et al. [40] experimentally verified heat transfer enhancement provided by wavy microchannel as compared to straight microchannel. They accredited it in

vx vy vz

w x y z

velocity component in x direction velocity component in y direction velocity component in z direction microchannel width (lm) Cartesian coordinate Cartesian coordinate Cartesian coordinate

Greek

q l

C

g

density (kg/m3) viscosity (Pa-s) interface thermal performance factor

Subscripts avg average cr critical eff effective f fluid in inlet s solid m mean o plain channel

favor of secondary flow inside the curves of wavy microchannel. Xu et al. [41,42] carried out experimental and numerical study for understanding the effect of combining parallel longitudinal microchannel and transverse microchamber. They observed that presence of microchamber promoted redevelopment of the thermal boundary layer, which augmented heat transfer performance. Yong and Teo [43] numerically investigated heat transfer and pressure drop characteristics of the conversing–diverging microchannel. They observed that heat transfer performance of conversing diverging microchannel was superior to that of straight channel with acceptable pressure drop penalty. Xie et al. [44] proposed double-layer wavy MCHS for improving the heat transfer performance of single layer wavy MCHS. They found lesser pressure drop in case of double-layer wavy MCHS. Xie et al. [45] compared numerically the performance of counter and parallel-flow double-layer plain and wavy MCHS. For better heat dissipation performance, they suggested parallel-flow arrangement for low flow applications and counter-flow arrangement for high flow applications. Overall thermal performance of doubled layer plain MCHS was found to be better than wavy double layer wavy MCHS. Xie et al. [46] suggested partial bifurcation (using straight plates) of exit flow field for improving the performance of straight MCHS. They found increase in heat transfer performance with increase in number of bifurcations. Li et al. [47] numerically compared laminar flow heat transfer characteristics of rectangular straight MCHS and MCHS’s with vertical Y-shaped bifurcation plates with arm angle of 60°, 90°, 120° and 180°. The MCHS with 90° arm angle has highest heat transfer performance. Zhang et al. [48] compared numerically performance of straight and three configurations of entrance region multiple (single and two-stage) bifurcated MCHS. They suggested two-stage bifurcated microchannel with shorter plate at the back of each sub-channel for the best performance. Leng et al. [49] suggested truncation of top channel for improving the performance of double-layer counter-flow MCHS. Optimal truncated length of top channel was found when the coolant temperature in the top channel is approximately equal to the bottom coolant temperature. Leng et al. [50] optimized the design parameters of

614

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

truncated MCHS using multi-parameter optimization algorithm integrating simplified conjugate-gradient method. Jung et al. [51] carried out experiments using aluminum oxide (Al2O3) nanoparticles of 170 nm diameter as heat transfer augmenting agent in rectangular microchannel. They reported 32% increase in heat transfer coefficient (for laminar flow regime) as compared to plain distilled water at 1.8 volume%. Byrne et al. [52] carried out experimental study using CuO (30–50 nm) and water nanofluid (0.005, 0.01, 0.1 volume%) with and without surfactant on parallel microchannels. They reported largest heat transfer gain of around 17% at volume percentage of 0.01%. They also observed that in absence of surfactant nanofluid heat transfer rate was almost similar to plain water. Jang and Choi [53] numerically simulated the performance of rectangular MCHS using diamond nanoparticles (2 nm, 1 volume%) with water as base fluid. They reported 10% improvement in heat transfer as compared to pure water. Wang et al. [54,55] optimized design parameters of MCHS using inverse problem approach integrating simplified conjugate-gradient scheme with three dimensional fluid–solid conjugated cooled by Al2O3 nanofluid. They concluded that use of nanofluid does not always lead to superior performance for MCHS. Surprisingly, extended surface heat transfer enhancement technique has not been explored for microchannel. Only one paper is available in open literature exploring use of extended surface in microchannel. Krishnamurthy and Peles [56] performed experiments on inline pin finned (24 fins of 100 lm diameter) entrenched on microchannel (dh = 222 lm). HFE 7000 was used as a coolant. They reported enhancement in heat transfer coefficient during subcooled boiling for the micro channels with pin fins as compared with plain wall channels. However, heat transfer enhancement in case of single phase flow was reported to be more as compared to two phase flow experiments. Jung et al. [57] experimentally studied the flow field over circular micropillar in rectangular microchannel using Microparticle image velocimetry. They concluded that with the aid of active flow control, design and performance of micropillars can be optimized. In the current investigation, numerical study of single phase heat transfer in upstream finned, downstream finned and complete finned rectangular microchannel has been carried out. Following univariate search method, optimization of number of fins, fins locations, and fins size for rectangular microchannel has also been done. 2. Simulation model MCHS used by [10] has been assumed as the base heat sink in current work. Twenty one microchannels of size (w, h) (231 lm, 713 lm) were etched on copper base substrate and water was used as working fluid [10]. Rather than carrying out simulation of entire heat sink, numerical study has been restricted to the analysis of single microchannel. Hence, single microchannel, fluid flowing across it and neighboring solid surfaces have been taken into account. Fig. 1 shows the cross sectional view of geometry. A and B are top and bottom walls, top wall (A) is assumed to be thermally insulated and uniform heat flux condition upholds at the bottom wall (B). In addition to plain rectangular microchannel, three extended surface (cylindrical fins) configurations have been included in present study. Fig. 2 shows them: (a) Plain microchannel, (b) Case I (upstream finned microchannel), (c) Case II (downstream finned microchannel) and (d) Case III (complete finned microchannel). Dimensions of above are given in Table 1. 2.1. Assumptions Following simplifying assumptions are made in the current numerical study.

Fig. 1. Cross sectional view of geometry.

1. Flow is steady, laminar and Newtonian. 2. No slip boundary condition at wall. 3. Uniform heat flux condition (q00 = Constant) is assumed throughout bottom wall. 4. Radiation heat transfer is neglected. 5. Constant thermo-physical properties for the solid section. Based on the above assumptions, required governing equations for analysis of flow and heat transfer characteristics of fluid side are continuity equation Eq. (1), momentum equation Eq. (2), and energy equation Eq. (3).

VÞ ¼ 0 r  ðqf ~

ð1Þ

r  ðqf ~ V þ qf ~ V  r~ VÞ ¼ rP þ r  lf ½ðr~ V þ r~ V t Þ  2=3r  ~ g ð2Þ VTÞ ¼ r  ðkf rTÞ r:ðqf cp ~

ð3Þ

where, ~ V t is transpose of vector matrix. Correlations for thermodynamic properties of working fluid water have been taken from (http://syeilendrapramuditya.wordpress.com/2011/08/20/ water-thermodynamic-properties/, as of May 29, 2015.). Although, these correlations were developed for 1 bar pressure, they predict thermodynamic properties accurately up to 155 bar (error 1%). For the solid section ~ V ¼ 0. Hence, only energy equation Eq. (4) is required for analysis of heat transfer in the solid region.

ks r2 T ¼ 0

ð4Þ

2.2. Boundary conditions Constant velocity Eq. (5) and constant temperature Eq. (6) boundary conditions are applied at the inlet of the microchannel.

U ¼ U in

ð5Þ

T ¼ T f ;in

ð6Þ

where, Uin = 1.33, 1.99, 2.6, 3.32, 3.98 m/s and Tf,in = 288.1 K. Continuity of heat flux Eq. (7) and temperature Eq. (8) conditions prevail at the interface between solid and fluid.

kf



@T

@T

¼ k s @n
C @n
C

ð7Þ

615

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

Fig. 2. Different configurations of microchannels (a) Plain microchannel, (b) Case I, (c) Case II, (d) Case III.

Table 1 Dimensions of different configurations of microchannels. Microchannel configuration

Plain microchannel Case I (upstream finned microchannel) Case II (downstream finned microchannel) Case III (compete finned microchannel)

Microchannel

Fins dimensions

w, h (lm)

df (mm)

hf (mm)

p (mm)

Lin (mm)

N

231, 231, 231, 231,

– 0.07 0.07 0.07

– 0.4 0.4 0.4

– 4.05 4.05 4.05

– 4.05 24.3 4.05

0 5 5 10

713 713 713 713

T f ;C ¼ T s;C

ð8Þ

~ V¼0

ð9Þ

The flow is assumed to be hydraulic and thermally fully developed at the channel outlet

@v x ¼ 0; @x

@v y ¼ 0; @y

@2T ¼0 @x2

@v z ¼0 @z

ð10Þ

ð11Þ

2.3. Solution method Commercial Ansys Fluent software based on finite volume method with coupled algorithm (pressure velocity coupling) is

used to solve governing equations in the solid and fluid domain. Second order discretization scheme is used for the pressure equation. Least square cell based iterative technique has been chosen for solution process. Third order MUSCL (Monotonic UpstreamCentered Scheme for Conservation Laws) scheme has been adopted for discretization of momentum and energy equations. For convergence of solution, residual criteria 1  104 is used for continuity equation, 1  106 for the velocity in x, y and z direction and 1  107 for energy equation. 2.4. Grid independence test Grid independence study has been carried out prior to detailed analysis in order to eliminate the error due to coarseness of grids. Table 2 shows summary of three grid system for all four cases. Complete computational domain has been discretized using unstructured grids of tetrahedral volume elements. Finer meshing

616

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

Table 2 Summary of grid independence study. Grid system

I II III

Number of elements Plain microchannel

Case I

Case II

Case III

684,744 859,536 1,434,220

2,730,727 4,106,159 9,739,031

2,736,175 4,108,917 9,744,097

3,008,239 4,383,438 9,989,021

has been adopted for the finned surface and for the water liquid domain regions, as parameters like temperature, pressure and velocity are more sensitive in these regions. The results obtained for different grid systems have been compared and it is observed that the solutions by the last two grid systems for all cases are very close to each other, outlet temperature and pressure drop variations are less than 0.2%. Hence, in order to save computation time intermediate grid system II has been used for all four cases in final CFD analysis.

3. Results and discussion 3.1. Validation of model Numerical results for the plain microchannel case are first compared with experimental data of [10]. Fig. 3(a) shows comparison of pressure drop data across microchannel for different Reynolds number at heat flux of 100 W/cm2 and 200 W/cm2. It is clear that numerical predictions of pressure drop are in good agreement with experimental observations. Nonlinear behavior of pressure drop

with Reynolds number is due to variation in water viscosity with temperature. Similarly, Fig. 3(b) and (c) compare experimental value of temperature [10] at four different locations along microchannel length and corresponding temperature predictions with numerical model at heat flux of 100 W/cm2 and 200 W/cm2 respectively. Temperature predictions are also in good agreement with experimental values. Hence, the same numerical scheme has been applied for evaluating performance of extended surface microchannels. 3.2. Temperature distribution Fig. 4(a) and (b) show the variation of average interface temperature with Reynolds number at heat flux of 100 W/cm2 and 200 W/cm2. The average interface temperature has been calculated as:

T C;m ¼

1

C

Z C

T C dC

ð12Þ

It is clear that average interface temperature significantly reduces in case of extended surface microchannels as compared to plain microchannel. The same is also highlighted by temperature contour plot (Fig. 5A (a–d)) at heat flux of 100 W/cm2. Fig. 5B (a–d) show the velocity contour plots for all cases at heat flux of 100 W/cm2. Presence of extended surfaces disrupts the temperature profile, and thus the thermal boundary layer cannot reach to fully developed state. Redevelopment of thermal boundary layer and better mixing of fluid due to extended surfaces can be collectively credited for improvement in heat transfer performance.

Fig. 3. Comparison of pressure drop (a), temperature at thermocouple locations (at heat flux (b) 100 W/cm2 (c) 200 W/cm2) with experimental work of Qu and Mudawar [10].

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

617

Fig. 4. Variation of average interface temperature with Reynolds number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

Fig. 5. Temperature (A), velocity (B) contour along the symmetric plane passing through central vertical line of microchannel unit cell at (Re = 400, q00 = 100 W/cm2) (a) Plain microchannel (b) Case I (c) Case II (d) Case III.

Additional heat transfer area also increases heat transfer rate from finned surface. Hence, lower interface temperature is observed in case of extended surface microchannels than plain microchannel. On comparing results for Case I and Case II it is found that average temperature of interface is lower for Case I. As heat transfer poten-

tial is more in the upstream part of the microchannel than downstream part. Thus, proving extended surfaces in upstream part of the microchannel (Case I) ensures lower interface temperature of the heating surface. The similar trends of temperature and velocity contour plots are also observed at heat flux of 200 W/cm2.

618

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

3.3. Heat Transfer characteristic 3.3.1. Nusselt number Heat transfer characteristic of microchannels are estimated in terms of overall Nusselt number for different configurations. The overall Nusselt number is calculated as:

Nu ¼

q00C dh kf ðT C;m  T m Þ

ð13Þ

q00C ¼

q00 AB Asur

ð14Þ

where, Asur is the contact surface area of fluid and solid. AB is area of the bottom wall, where heat is supplied. Tm is the mean temperature of fluid, which has been calculated as volume average temperature for fluid domain and given by Eq. (15).

R

v x TdAc v x dAc A

T m ¼ RAc

ð15Þ

c

Fig. 6(a) and (b) show the variation of Nusselt number for different values of Reynolds number at heat flux of 100 W/cm2 and 200 W/cm2. As expected Nusselt number increases (better heat transfer performance) with increase in Reynolds number for all

cases. Nusselt number in case of extended surface microchannels are much higher as compared to plain microchannel. This is due to induced mixing offered by extended surfaces, redevelopment of boundary layer near each cylindrical fin (Fig. 5(B)), and additional heat transfer area. It is also clear that upstream finned microchannel (Case I) performs better than downstream finned microchannel (Case II). The reason for the above is already explained in Section 3.2. One very interesting thing is observed that at low Reynolds number, upstream finned microchannel (Case I) performs better as compared to complete finned microchannel (Case III). At low Reynolds number, less number of fins in the inlet region (Case I) are sufficient for transferring heat transfer potential, if number of fins are increased as in Case III, additional flow resistance offered by extended surface brings down heat transfer performance. 3.4. Pressure drop characteristics Fig. 7(a) and (b) compare pressure drop characteristics of plain microchannel and three extended surface microchannels for different values of Reynolds number at heat flux of 100 W/cm2 and 200 W/cm2 respectively. As expected, pressure drop increases in case of extended microchannels as compared to plain microchannel.

Fig. 6. Variation of Nusselt number with Reynolds number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

Fig. 7. Variation of pressure drop with Reynolds number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

Pressure drop increases due to additional flow resistance offered by extended surface in fluid flow path. Pressure drop even decreases slightly with increase in heat flux, this is due to decrease in water viscosity with increase in temperature. One more interesting observation is noted down, pressure drop in Case I is slightly higher than Case II. As extended surface introduction in lower temperature region (where viscosity of water is high) aggravates pressure drop. The pressure drop is highest in case of Case III. 3.5. Overall thermal performance Extended surface microchannel improves heat transfer performance of plain microchannel but pressure drop also increases. Hence, overall thermal performance of extended surface microchannels have been computed and compared with plain microchannel. Overall thermal performance in the current case has been calculated following [47] and is given by Eq. (16).

g¼

Nu=Nuo ðDP=DP o Þ

ð16Þ

1=3

Fig. 8(a) and (b) show the variation of overall thermal performance factor with Reynolds number at heat flux of 100 W/cm2 and 200 W/cm2 respectively. Overall thermal performance factor is found to be greater than one for all the cases of extended surface microchannels, which proves importance of extended surface microchannel for improving the performance plain microchannel. Overall thermal performance for the Case I is better than Case II and Case III for the entire range of the study but it deteriorates at high Reynolds number. This can be accredited to overriding increase in pressure drop characteristics of Case I in comparison to Nusselt number improvement with increase in Reynolds number. For the Case II and Case III overall thermal performance increase initially then starts decreasing at high Reynolds number. As at low Reynolds number, Nusselt number increase is more dominant, which is superseded by pressure drop increase at high Reynolds number. 3.6. Optimization of extended surface It is clear from above discussion that design optimization i.e. number of fins, pitch, diameter of fins and height of fins can further enhance heat transfer performance. Hence, through univariate search method, optimization of number of fins, fins locations, and fins size for rectangular microchannel have been carried out.

619

3.6.1. Effect of number of fins Fig. 9(a) and (b) show the effect of increase in number of fins (Lin = Lin, Case I) on overall Nusselt number. It is observed that with increase in number of fins, heat transfer performance first increases, attains maximum value and then starts decreasing with further increase in number of fins. Decrease in heat transfer characteristic after optimum number of fins can be attributed to additional flow resistance offered by extended surfaces, which subsides liquid velocity to larger extent than enhancement in heat transfer due to additional heat transfer area. At higher Reynolds number (Re = 1000) heat transfer performance slightly decreases afterwards (N > 6) at heat flux of 100 W/cm2 and first decreases slightly then increases slightly at 200 W/cm2. The above behavior can be attributed to the two counter influencing effects; formation of strong eddies at high Reynolds number in the wake of each extended surfaces and high heat transfer potential at high heat flux. 3.6.2. Effect of pitch of fins Fig. 10(a) and (b) show the effect of increase in pitch of fins on overall Nusselt number, while keeping number of fins optimized (N = 6, as found in the last section). The Nusselt number increases as pitch of fins decreases. This could be attributed to combined effect of enhanced mixing due to shorter distance between fins and earlier redevelopment of thermal boundary layers near each cylindrical fin. 3.6.3. Effect of diameter of fins Fig. 11(a) and (b) show the effect of diameter of fins on overall Nusselt number, while keeping number of fins and pitch at optimized condition (as per result of last two sections). Nusselt number first increases with increase in diameter of fins, attain maximum value, then starts discreasing with further increase in diameter of fins. In the current configuration optimum diameter is found to be 80 lm. This can be explained by two contradictory effects. As fin diameter increases more area is available for heat transfer. However it is clear from velocity contour plot (Fig. 12) that accordingly size of the wake also increases, which reduces convective heat transfer rate. Additional flow resistance offered by large size fin can be other possible reason for reduction in heat transfer characteristics after optimum size. 3.6.4. Effect of fin height Fig. 13(a) and (b) show the variation in overall Nusselt number as a function of fins height for enhanced surface microchannel

Fig. 8. Variation of overall thermal performance factor with Reynolds number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

620

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

Fig. 9. Effect of number of fins on overall Nusselt number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

Fig. 10. Effect of pitch of fins on overall Nusselt number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

Fig. 11. Effect of diameter of fins on overall Nusselt number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

621

Fig. 12. Velocity contour plots near the cylindrical fin for three different diameters of fin. (Re = 400, q00 = 100 W/cm2).

Fig. 13. Effect of height of fins on overall Nusselt number at heat flux (a) 100 W/cm2 (b) 200 W/cm2.

optimized for number of fins, pitch and diameter. Nusselt number increases with increase in fins height. This is basically due to increase in heat transfer area, which improves heat transfer performance of enhanced surface microchannel. 4. Conclusion In the present investigation three dimensional CFD analysis of extended surface (cylindrical fins) rectangular microchannels and plain rectangular microchannel have been carried out and compared. Parametric variations of number of fins, pitch of fins, diameter of fins and height of fins have also been carried out in order to optimize the performance of enhanced surface microchannel. Following are main findings of current study. 1. Significant temperature reduction in bottom wall temperature has been observed in case of extended surface microchannels as compared to plain microchannel. Temperature reduction in case of upstream finned microchannel (Case I) is higher than temperature reduction in case of downstream finned microchannel (Case II).

2. Heat transfer performance of plain microchannel is significantly improved by extended surface microchannels. Performance of upstream finned microchannel (Case I) is better than other extended surface microchannels at low Reynolds number, but at high Reynolds number heat transfer performance of complete finned microchannel (Case III) is the best. Heat transfer performance of upstream finned microchannel (Case I) is always better than downstream finned microchannel (Case II). 3. Pressure drop in case of extended surface microchannels is higher as compared to plain microchannel. However pressure drop penalty is lower in comparison to heat transfer gain. Overall thermal performance of extended surfaces are found to be much superior in comparison to plain microchannel. 4. Performance of enhanced surface microchannel increases with decrease in pitch of fins and increase in height of fins. There is optimum number of fins at which heat transfer performance of enhanced surface microchannel is found to be optimum. Similarly, performance of enhanced surface microchannel is maximum corresponding to optimum diameter of fins. These parameters are optimized successively and average enhancement in Nusselt number is 160% as compared to plain microchannel.

622

V. Yadav et al. / International Journal of Heat and Mass Transfer 93 (2016) 612–622

References [1] T.W. Kenny, K.E. Goodson, J.G. Santiago, E. Wang, J.M. Koo, L. Jiang, E. Pop, S. Sinha, L. Zhang, D. Fogg, S. Yao, R. Flynn, C.H. Chang, C.H. Hidrovo, Advanced cooling technologies for microprocessor, Int. J. High Speed Electron. Syst. 16 (1) (2006) 301–313. [2] R.J. Phillips, Microchannel heat sinks, Lincoln Lab. J. 1 (1988) 31–47. [3] R.D. Boyd, Subcooled flow boiling critical heat flux (CHF) and its application to fusion energy components. Part 1. A review of fundamentals of CHF and related data base, Fusion Technol. 7 (1985) 7–30. [4] J. Lee, I. Mudawar, Low-temperature two-phase microchannel cooling for high heat-flux thermal management of defence electronics, IEEE Trans. Compon. Package. Technol. 32 (2) (2009) 453–465. [5] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE Electron Device Lett. 2 (5) (1981) 126–129. [6] E.G. Colgan, B. Furman, M. Gaynes, W.S. Graham, N.C. LaBianca, J.H. Magerlein, R.J. Polastre, M.B. Rothwell, R.J. Bezama, R. Choudhary, K.C. Marston, H. Toy, J. Wakil, J.A. Zitz, R.R. Schmidt, A practical implementation of silicon microchannel coolers for high power chips, IEEE Trans. Compon. Packag. Technol. 30 (2) (2007) 218–225. [7] L.M. Collin, L.G. Frechette, A. Souifi, S. Lhostis, F. de Crecy, S. Cheramy, J.P. Colonna, V. Fiori, Impact of integrating microchannel cooling within 3D microelectronic packages for portable applications, in: Microelectronics Packaging Conference European, Grenoble, France, 2013, pp. 1–8. [8] Y. Madhour, J. Olivier, E. Costa-Patry, S. Paredes, B. Michel, J.R. Thome, Flow boiling of R134a in a multi-microchannel heat sink with hotspot heaters for energy-efficient microelectronic CPU cooling applications, IEEE Trans. Compon. Packag. Manuf. Technol. 1 (6) (2011) 873–883. [9] T. Kishimoto, T. Ohsaki, VLSI packaging technique using liquid-cooled channels, IEEE Trans. Compon. Hybrids Manuf. Technol. 9 (4) (1986) 328–335. [10] W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink, Int. J. Heat Mass Transfer 45 (12) (2002) 2549–2565. [11] T.M. Harms, M.J. Kazmierczak, F.M. Cerner, A. Holke, H.T. Henderson, J. Pilchowski, K. Baker, Experimental investigation of heat transfer and pressure drop through deep microchannels in a (100) silicon substarte, Proc. ASME Heat Transfer Division HTD-351 (1997) 347–357. [12] H.Y. Wu, P. Cheng, Visualization and measurements of periodic boiling in silicon microchannels, Int. J. Heat Mass Transfer 46 (14) (2003) 2603–2614. [13] J. Zhang, P.T. Lin, Y. Jaluria, Design and optimization of multiple microchannel heat transfer systems, J. Therm. Sci. Eng. Appl. 6 (1) (2014), http://dx.doi.org/ 10.1115/1.4024706. [14] H.C. Chiu, J.H. Jang, H.W. Yeh, M.S. Wu, The heat transfer characteristics of liquid cooling heat sink containing microchannels, Int. J. Heat Mass Transfer 54 (1–3) (2011) 34–42. [15] S.T. Kadam, K. Baghel, R. Kumar, Simplified model for prediction of bubble growth at nucleation site in microchannels, J. Heat Transfer 136 (6) (2014), http://dx.doi.org/10.1115/1.4026609. [16] S.M. Kim, I. Mudawar, Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks, Int. J. Heat Mass Transfer 55 (13–14) (2012) 3720– 3731. [17] M.K. Steinke, S.G. Kandlikar, Single-phase heat transfer enhancement techniques in microchannel and minichannel flows, in: 2nd ASME International Conference on Microchannels and Minichannels, Rochester, New York, USA, 2004, pp. 141–148. [18] S.G. Kandlikar, W.J. Grande, Evolution of microchannel flow passage thermohydraulic performance and fabrication technology, Heat Transfer Eng. 24 (1) (2003) 3–17. [19] S.G. Kandlikar, W.J. Grande, Evolution of microchannel flow passages – thermohydraulic performance and fabrication technology, in: ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, 2002. [20] S.S. Mehendale, A.M. Jacobi, R.K. Shah, Fluid flow and heat transfer at microand meso-scales with applications to heat exchanger design, Appl. Mech. Rev. 53 (7) (2000) 175–193. [21] K. Cornwell, P.A. Kew, Boiling in small parallel channels, Proc. Energy Effic. Process Technol. (1993) 624–638. [22] P.A. Kew, K. Cornwell, Correlation for prediction of boiling heat transfer in small diameter channel, Appl. Therm. Eng. 17 (8–10) (1997) 705–715. [23] T. Harirchian, S.V. Garimella, A comprehensive flow regime map for microchannel flow boiling with quantitative transition criteria, Int. J. Heat Mass Transfer 53 (13–14) (2010) 2694–2702. [24] S.T. Kadam, R. Kumar, Twenty first century cooling solution: microchannel heat sinks, Int. J. Therm. Sci. 85 (2014) 73–93. [25] S.G. Kandlikar, History, advances and challenges in liquid flow and flow boiling heat transfer in microchannels: a critical review, J. Heat Transfer 134 (3) (2012), http://dx.doi.org/10.1115/1.4005126. [26] S.G. Kandlikar, High flux heat removal with microchannels – a roadmap of challenges and opportunities, Heat Transfer Eng. 26 (8) (2005) 5–14. [27] S.G. Kandlikar, Fundamental issues related to flow boiling in minichannels and microchannels, Exp. Therm. Fluid Sci. 26 (2–4) (2002) 389–407. [28] S.G. Kandlikar, S. Colin, Y. Peles, S. Garimella, R.F. Pease, J.J. Brandner, D.B. Tuckerman, Heat transfer in microchannels – 2012 status and research needs, J. Heat Transfer 135 (9) (2012), http://dx.doi.org/10.1115/1.4024354.

[29] W. Qu, I. Mudawar, Measurement and prediction of pressure drop in twophase micro-channel heat sinks, Int. J. Heat Mass Transfer 46 (15) (2003) 2737–2753. [30] S.L. Qi, P. Zhang, R.Z. Wang, L.X. Xu, Flow boiling of liquid nitrogen in microtubes: Part I – the onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop, Int. J. Heat Mass Transfer 50 (25–26) (2007) 4999–5016. [31] A.E. Bergles, S.G. Kandlikar, On the nature of critical heat flux in microchannels, J. Heat Transfer 127 (1) (2005) 101–107. [32] S.G. Kandlikar, Nucleation characteristics and stability considerations during flow boiling in microchannels, Exp. Therm. Fluid Sci. 30 (5) (2006) 441–447. [33] W. Qu, I. Mudawar, Measurement and correlation of critical heat flux in twophase micro-channel heat sinks, Int. J. Heat Mass Transfer 47 (10–11) (2004) 2045–2059. [34] X.F. Peng, B.X. Wang, Forced convection and flow boiling heat transfer for liquid flowing through microchannels, Int. J. Heat Transfer 36 (14) (1993) 3421–3427. [35] X.F. Peng, G.P. Peterson, Convective heat transfer and flow friction for water flow in microchannel structures, Int. J. Heat Mass Transfer 39 (12) (1996) 2599–2608. [36] O.B. Ergu, O.N. Sara, S. Yapici, M.E. Arzutug, Pressure drop and point mass transfer in a rectangular microchannel, Int. Commun. Heat Mass Transfer 36 (6) (2009) 618–623. [37] A. Koyuncuoglu, R. Jafari, T.O. Ozyurt, H. Kulah, Heat transfer and pressure drop experiments on CMOS compatible microchannel heat sinks for monolithic chip cooling applications, Int. J. Therm. Sci. 56 (2012) 77–85. [38] Z.H. Wang, X.D. Wang, W.M. Yan, Y.Y. Duan, D.J. Lee, J.L. Xu, Multi-parameters optimization for microchannel heat sink using inverse problem method, Int. J. Heat Mass Transfer 54 (13–14) (2011) 2811–2819. [39] L. Gong, K. Kota, W. Tao, Y. Joshi, Parametric numerical study of flow and heat transfer in microchannels with wavy walls, J. Heat Transfer 133 (5) (2011), http://dx.doi.org/10.1115/1.4003284. [40] Y. Sui, P.S. Lee, C.J. Teo, An experimental study of flow friction and heat transfer in wavy microchannels with rectangular cross section, Int. J. Therm. Sci. 50 (12) (2011) 2473–2482. [41] J.L. Xu, Y.H. Gan, D.C. Zhang, X.H. Li, Microscale heat transfer enhancement using thermal boundary layer redeveloping concept, Int. J. Heat Mass Transfer 48 (9) (2005) 1662–1674. [42] J. Xu, Y. Song, W. Zhang, H. Zhang, Y. Gan, Numerical simulations of interrupted and conventional microchannel heat sinks, Int. J. Heat Mass Transfer 51 (25–26) (2008) 5906–5917. [43] J.Q. Yong, C.J. Teo, Mixing and heat transfer enhancement in microchannels containing converging–diverging passages, J. Heat Transfer 136 (4) (2014), http://dx.doi.org/10.1115/1.4026090. [44] G. Xie, Z. Chen, B. Sunden, W. Zhang, Numerical predictions of flow and thermal performance of water-cooled single-layer and double-layer wavy microchannel heat sinks, Numer. Heat Transfer A 63 (3) (2013) 201–225. [45] G. Xie, Z. Chen, B. Sunden, W. Zhang, Comparative study of flow and thermal performance of liquid-cooling parallel-flow and counter-flow double-layer wavy microchannel heat sinks, Numer. Heat Transfer A 64 (1) (2013) 30–55. [46] G. Xie, F. Zhang, B. Sunden, W. Zhang, Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow, Appl. Therm. Eng. 62 (2) (2014) 791–802. [47] Y. Li, F. Zhang, B. Sunden, G. Xie, Laminar thermal performance of microchannel heat sinks with constructal vertical Y-shaped bifurcation plates, Appl. Therm. Eng. 73 (1) (2014) 185–195. [48] R. Zhang, Z. Chen, G. Xie, B. Sunden, Numerical analysis of constructal watercooled microchannel heat sinks with multiple bifurcations in the entrance region, Numer. Heat Transfer A 67 (6) (2015) 632–650. [49] C. Leng, X.D. Wang, T.H. Wang, An improved design of double-layered microchannel heat sink with truncated top channels, Appl. Therm. Eng. 79 (2015) 54–62. [50] C. Leng, X.D. Wang, T.H. Wang, W.M. Yan, Multi-parameter optimization of flow and heat transfer for a novel double-layered microchannel heat sink, Int. J. Heat Mass Transfer 84 (2015) 359–369. [51] J.Y. Jung, H.S. Oh, H.Y. Kwak, Forced convective heat transfer of nanofluids in microchannels, Int. J. Heat Mass Transfer 52 (1–2) (2009) 466–472. [52] M.D. Byrne, R.A. Hart, A.K. Silva, Experimental thermal-hydraulic evaluation of CuO nanofluids in microchannels at various concentrations with and without suspension enhancers, Int. J. Heat Mass Transfer 55 (9–10) (2012) 2684–2691. [53] S.P. Jang, S.U.S. Choi, Cooling performance of a microchannel heat sink with nanofluids, Appl. Therm. Eng. 26 (17–18) (2006) 2457–2463. [54] X.D. Wang, B. An, L. Lin, D.J. Lee, Inverse geometric optimization for geometry of nanofluid-cooled microchannel heat sink, Appl. Therm. Eng. 55 (1–2) (2013) 87–94. [55] X.D. Wang, B. An, J.L. Xu, Optimal geometric structure for nanofluid-cooled microchannel heat sink under various constraint conditions, Energy Convers. Manage. 65 (2013) 528–538. [56] S. Krishnamurthy, Y. Peles, Flow boiling heat transfer on micro pin fins entrenched in a microchannel, J. Heat Transfer 132 (4) (2010), http://dx.doi. org/10.1115/1.4000878. [57] J. Jung, C.J. Kuo, Y. Peles, M. Amitay, The flow field around a micropillar confined in a microchannel, Int. J. Heat Fluid Flow 36 (2012) 118–132. , (29/05/2015).