Keywords Perforated pinned heat sinks, Conjugate heat transfer, Electronic component cooling.

Transcription

1 Eect o Dierent Perorations Shapes on the Thermal-hydraulic Perormance o Perorated Pinned Heat Sinks Amer Al-Damook 1,, J.L. Summers 1, N. Kapur 1, H. Thompson 1 mnajs@leeds.ac.uk, j.l.summers@leeds.ac.uk, n.kapur@leeds.ac.uk, h.m.thompson@leeds.ac.uk 1 School o Mechanical Engineering, University o Leeds, UK Mechanical Engineering Department, University o Anbar, MOHESR, HCED, Iraq Abstract The beneits o using pinned heat sinks (PHSs) with multiple circular, square and elliptic perorations or electronic cooling applications are investigated using Computational Fluid Dynamics (CFD). A conjugate heat transer analysis, using the RANS-based modiied k-ω turbulence model, is used to determine the eect o peroration shape on the cooling and hydraulic perormance o PHSs. The numerical solutions indicate that the optimum design will be a compromise between elliptical perorations, which minimize pressure drop and mechanical an power consumption, and circular perorations, which provide the most eective heat transer. Employing staggered arrangements o perorated pins in PHS is also shown to be highly beneicial and to enable the power consumption required to cool a heat sink to a target temperature to be reduced signiicantly. Keywords Perorated pinned heat sinks, Conjugate heat transer, Electronic component cooling. I. INTRODUCTION Heat sinks with extended suraces, such as plate ins or pins, are widely used in industry to improve heat transer in critical cooling applications, or example the aerospace, automotive and nuclear industries, Sahin & Demir [1]-[]. This requires their designers to achieve the required heat transer levels subject to multiple constraints on their volume, mass, cost etc. The main motivation o the present study is the use o PHSs in the air cooling o electronics, which remains the most common method o reducing the temperature o CPUs below critical values in order to provide acceptable component reliability [3]. A number o recent studies have explored the perormance beneits o perorating plate ins in plate in heat sinks (PFHSs) or perorating the pins in pinned heat sinks (PHSs). These have shown that perorations can increase simultaneously heat transer and reduce the mechanical an power needed to overcome the pressure losses [3]-[4]. The plate ins in PFHSs can be perorated either longitudinally, along the ins, or laterally across them. Shaeri et al [5]-[8] considered the eect o longitudinal perorations or both laminar and turbulent lows and demonstrated that these can enhance heat transer while reducing pressure drop by reducing the size o the recirculation zones (wakes) behind the plate ins. Ismael et al [9]- [11] extended this work to consider the eect o the longitudinal peroration shape (circular, square, triangular and hexagonal) on perormance and ound that both circular and hexagonal perorations provide signiicant enhancements. Lateral plate in perorations in PFHSs have also been considered. Yaghoubi et al [1]-[13] showed that lateral perorations are ineective or laminar airlows but that they do lead to enhanced heat transer or turbulent lows. Ismail et al [14] later considered the eect o lateral peroration shape (circular, square, triangular and hexagonal) or turbulent airlows. They ound that hexagonal perorations yielded the highest heat transer rate while triangular ones minimize the riction coeicient. In comparison with PFHSs, relatively ew studies have considered the eect o pin perorations on the perormance o PHSs. Sahin and Demir [15]-[16], or example, studied the eect o single circular or square perorations or PHSs with in-line pin arrays, while Amol and Farkade [17] considered the eect o staggered arrangements o pins with single perorations o circular cross section. These and other studies have ound consistently that a single peroration leads to an enhancement in heat transer and a reduction in pressure drop compared to equivalent solid pin systems. In addition to the increased area or heat transer, these enhancement are due to localized jet lows through the perorations which increase local heat transer by shear-induced mixing and reduce pressure drop by alleviating the recirculation zones that orm behind solid pins. Al-Damook et al [3] used complementary experimental and numerical methods to investigate the eect o multiple (up to ive) pin perorations in the perormance o PHSs. They demonstrated that multiple pin perorations can provide signiicantly greater heat transer and pressure drop beneits than or single perorations, and that these beneits increase monotonically as the number o perorations increases, while the location o the perorations has only a relatively minor inluence on perormance. With ive perorations, they demonstrated an 11% increase in heat transer and a 16% reduction in pressure drop compared to an equivalent solid pin PHS. The beneits o using perorations on strip ins where the crosssectional aspect ratio o the ins are between those or plate ins (high aspect ratio) and pins ins (aspect ratio 1) have been investigated recently by Al-Sallami JMESTN

2 et al [18]. They ound that perorating the strip ins provides substantial enhancements in heat transer, with reduced pressure loss and heat sink mass. In This paper presents the irst detailed investigation into the inluence o the shape o pin perorations on the thermal and hydraulic perormance o PHSs. It extends the recent studies o Ismail et al [9]-[11] and Al-Damook et al [3] to compare the eect o pin peroration shape (circular, square and elliptic) or pins with the three perorations shown in Fig.. The paper is organized as ollows. In section the numerical conjugate heat transer model is described while section 3 describes the validation o the numerical method and the results o the numerical investigation. Conclusions are drawn in section 4. II. NUMERICAL METHOD A. Physical Model Thermal airlows over PHSs with a base o 50mm length (L) 50mm width (W) mm thickness (t) and 64 pin ins o height 10mm and diameter mm in an in-line array are considered, Fig. 1. Airlows past PHSs with the pins perorated with three circular, square or elliptical perorations aligned in the direction o the airlow, as shown in Fig., are solved numerically and compared with the benchmark case with solid pins. The inlet air temperature is set to 5 o C while the inlet air velocity is varied rom 6.5m/s to 1m/s, leading to Reynolds numbers in the range based on a length scale given by the hydraulic diameter o the duct Dh=H.W/(H+W), where H and W are the height and width o duct in which the heat sink is located, respectively. The PHS is aluminium, with thermal conductivity k=0 W/m.K. 3PC Circular Holes Fig. : Three perorations shapes or each pin in designs considered, with same numbers and locations o perorations and all dimensions in mm. B. Conjugate Heat Transer Model In the conjugate heat transer model the rate o heat conduction through the aluminium heat sink is balanced by the convective heat transer into the moving air stream, through a coupled boundary condition at the solid/luid interace o the heat sink [14], as illustrated in Fig. 3. The energy equations in the luid and solid domains are given by: For the luid domain c p. T U.. c pt. ( k ) T (1) PrT For the solid domain.( k. T ) 0 () s s d= 1mm h= 1mm, w= 1mm 3PS Square Holes h= 1.5mm, w= 1mm 3PE Elliptical Holes where U is luid (air) velocity; T and T s are luid A Three perorations or each pin in with dierent coniguration shapes and solid temperature, respectively; μ T, Pr T, k and k s are the turbulent viscosity, the turbulent Prandtl number, the thermal conductivity o the luid and solid, respectively. Inlet Flow Pin Fin Heat Sink Conjugate Heat Transer Outlet Flow B Fig. 1: (A) Plan view and (B) side view o the pin ins heat sink being analysed Figure 3: Conjugate heat transer model o pin in heat sink [3] C. Airlow Model Constant Heat Flux Airlow over the PHSs is assumed incompressible, steady state, and turbulent. Several previous studies have used the Reynolds-Averaged Navier-Stokes (RANS) equations to model turbulent airlow through heat sinks successully, see or example [19]-[0]. Time-averaging the continuity, momentum and energy equations with variables decomposed into mean and luctuating components leads to the Reynolds- Averaged Navier-Stokes (RANS) equations, namely: JMESTN

3 U. 0 (3) U. U t 1 U U. U' ' T pi U U T ' t U U 3( k I) where (4) and U' U are the Newtonian and Reynolds Stress tensors respectively, μ is the air viscosity, ρ its density, U and U ' the average and turbulent luctuation velocity vectors respectively, p is the pressure and I the unit tensor. The incompressible RANS equations are solved with the energy equation or the temperature ield in the luid, T, with a heat source Watts, using the ollowing equation T t U T t Pr Prt. Q T C (5) p where C p is the speciic heat capacity o the air, Pr and ν are the Prandtl number and kinematic viscosity o the air respectively and the subscript t indicates their turbulent counterparts. Following Zhou & Catton [19] and Leung & Probert [0], the thermal airlow through the heat sink is modelled using the k-ω SST model with automatic wall unction treatment. As discussed above and ollowing Al-Damook at al [3], who ound that with maximum temperature dierences o 6 o C or polished aluminium ins, the radiative heat loss is only 1% o the total heat transer rate, radiative heat transer is neglected. Air density and viscosity are assumed to be constant and equal to those at the inlet temperature o 5 o C. This model combines the accurate ormulation o the k-ω model in the near-wall region with the ree-stream independence o the k-ε one in the ar ield, and has been shown to predict highly separated lows accurately in a number o previous validation studies [19]-[1]. The equations or the SST model are: ( k) ~ * ( k. U) Pk k. ( k t) k t (6) ( ) (. U) S. ( t ) t 1 (1 F1 ) k. (7) where the blending unction F 1 is deined by 4 k k F1 tanh min max,, * y y C Dk y in which 1 10 C D k max k.,10 The turbulent eddy viscosity is computed rom a1k t max( a1, S F ) (8) where S is the invariant measure o the strain rate and F is a second blending unction deined by k 500 F tanh max, * y y To limit the growth o turbulence in stagnation regions, a production limiter is used in the SST model. u u u j i P i ~ * k t Pk min Pk,10 k x j x j x i The constants or this model are *.09, 0.555, 0.075, 0.85, 0.5, 0.44, k , k 1, D. Solver Settings The grid is composed o dense tetrahedral mesh elements to improve the quality o the numerical prediction near curved pin suraces. A commercial inite volume method (FVM)-based code, ANSYS FLUENT [] is used to solve the ully coupled momentum and energy equations, using second order upwinding, while continuity is satisied using the SIMPLE method in which the velocity components are irst calculated rom the Navier Stokes equations using a guessed pressure ield. Computation is started irst by solving the continuity, momentum, k and ω equations to determine the low ield and then the energy equation to ind the temperature ield in the computational region. The procedure continues until the sum o the residuals o the continuity and momentum equations in each cell is less than 10-4 and the residuals o the energy equations are smaller than E. Boundary Conditions The computational problem is reduced in size by exploiting the symmetry o the PHS to apply symmetry boundary conditions along the sides o the channel (Fig. 4). This inlet and outlets o the domain should be ar enough rom the entrance and exit regions o the heat sinks to avoid boundary eects such as reverse low at the exit. To avoid these problems, the entrance and exit regions are a distance o 1.5d rom the heat sink. The luid and thermal conditions are: 1- At the inlet: 6.5m/s U =1m/s, T air =5 o C - At the PHS suraces: dt dt U=0m/s, s k. ks. dn dn 3- At the bottom base wall o the heat sink: U=0m/s, =0000W/m 4- At the outlet: P=P guage = 0 Pa, dt 0 dx JMESTN

4 Inlet 5- At the other suraces: U=0m/s, dt 0 dz 6- At the symmetry boundaries: du 0, dt dy dy 0 Symmetry let side surace Perorated Pin Fins Adiabatic other walls Outlet Symmetry right side surace Perorated Pinned Heat Sink Constant Heat Flux Fig. 4: Schematic diagram o the low domain used in the CFD analyses, shown eight perorated pin ins F. Post Processing The CFD analysis is used to determine the velocity and temperature ields as well as the Nusselt number (Nu T ), based on the total surace area, pressure drop (ΔP), an power (P an ) and CPU temperature (T case ), as ollows [3]. The heat transer rate is represented by Nusselt number: Nu T = h.l/k air (9) where h is the heat transer coeicient (W/K.m ), L the length o the heat sink in the low direction (m) and k air the thermal conductivity o the air (W/m.K). Now h T = (10) where is the power applied to the base (W), A T is the total surace area including the pin and peroration surace areas (m ), T s is the pin heat sink surace temperature and T m is the average bulk mean temperature T m =(T in +T out )/. The an power required to drive the luid through the heat sink can be evaluated as [4]-[5], P an =U.A p.δp (11) where U: inlet air velocity (m/s), A p (m ): crosssectional area o the low passage o the heat sink=h.s.(n-1). III. RESULTS AND DISCUSSION A. Grid Independence CFD solutions are obtained on a range o grids, where the number o cells varies between 98,000 and 10,000. The eect o grid resolution on Nu T, T case and ΔP is shown in Table 1, which demonstrates that increasing the number o cells beyond 10,000 results in typically a % change in these parameters. All numerical results reported below have been obtained using 150,000 cells. Table 1: Grid independence study data or dierent perorated pin in heat sinks Square Perorated Pins () Cells Nu T T case ( o C) P (Pa) Circular Perorated Pins () Cells Nu T T case ( o C) P (Pa) Elliptic Perorated Pins () Cells Nu T T case ( o C) P (Pa) B. Validation against Previous Studies It is important that any numerical model should be careully validated beore it is used or design purposes. The experimental data o Yang et al [6] provides a useul validation case or predictions o the heat transer coeicient (h T ) and the pressure drop (ΔP) over solid PHSs. Fig. 5 indicates that the % error between predicted the experimental and numerical results is less than %, and 5%, respectively. It is clear that the heat transer coeicient and the pressure drop measurement rom the previous experimental study are in good agreement with those present predicted CFD. Other validations o the numerical approach used here can be ound in Al-Damook et al [3]-[4]. The numerical model is now used to explore the eect o employing the perorated pins shown in Fig. on the thermal and hydraulic perormance o PHSs. C. Eect o Peroration Shape on Pressure Drop and Mechanical Power Consumption Fig. 6 explores the eect o perorations shape and inlet air velocity 6.5m/s U 1m/s on the pressure drop, ΔP, over a PHS with the 8x8 array o pins shown in Fig. 1. The elliptically-perorated pins () have the lowest pressure drops, which are typically around 1% lower than or the solid pins (). The an power required to drive the air through the heat sink, ignoring losses due to an ineiciency, is deined by JMESTN

5 P (Pa) Fan Power (W) h (W/K.m ) P (Pa) P an =UA ΔP, where U is the inlet air velocity and A is the cross-sectional area o the low passage o the heat sink. Fig. 7 shows the corresponding data or the eect on an power, P an : power consumption or the square, circular and elliptical perorations is approximately 7%, 9%, and 1% lower than or solid pins. The reductions in pressure drop and power consumption increase with the peroration volume and hence the porosity o pins increases, providing less resistance to air low through them Exp. Yang's Data CFD Present Study Fig. 6: Eect o peroration shapes on the pressure drop with various inlet air velocities Exp. Yang's Data CFD Present Study Fig. 7: Eect o peroration shapes on the an power o pinned heat sinks Fig. 5: Comparison between CFD predictions and the experimental data o Yang et al [6] o heat transer coeicient and pressure drop. D. Eect o Peroration Shape on Heat Transer Fig. 8 shows the eect o the peroration shape on the Nusselt number, Nu T, or Reynolds numbers in the range 3500 Re The data show that the perorations increase Nu T in all cases, and that the largest enhancement compared to the solid pin cases () is or circular perorations (~9%) while the square and elliptical perorations lead to typical enhancements o between 4%. Fig. 9 shows the mean air velocity through each pin in the heat sink or the three perorated pin cases with U=1m/s. The inding that the circular perorations have the largest velocities is consistent with previous studies which have suggested JMESTN

6 that the increased heat transer with perorations is due to the ormation o air jets lowing through the perorations which enhance convective heat transer around them, see Sara et al. [7]. NuT Ux (m/s) perorated pins at an inlet airlow at 10m/s (Re= 5393). For the solid pins, the base plate temperatures vary between approximately 58.5 o C and 71 o C, whereas pins with circular, square and elliptical perorations temperatures range between 5 o C to 66.5 o C, 5.5 o C to 67 o C and 53 o C to 67 o C, respectively. Tcase ( o C) Re Fig. 8: Nusselt number or solid and dierent peroration shapes with various Re Number o Pins Fig. 9: Variation o mean local air velocity through the dierent pin perorations shapes In electronics cooling the principal role o the heat sink is to remove heat in order to restrict the temperature o the CPU below critical temperatures to ensure perormance reliability. Fig. 10 shows the eect o peroration shape on the average heat sink base plate temperature, T case, or inlet air velocities 6.5m/s U 1m/s. The improved heat transer with the circular perorations results in values o T case that are typically 8% smaller than or a PHS with solid pins, whereas those or the square and elliptical perorations are roughly 6% smaller than with solid pins. Fig. 11 compares the surace temperature distribution o a PHS with solid pins () and those obtained with the Fig. 10: Heat sink base temperature with peroration shapes and inlet air velocity Fig. 11: Temperature distribution through perorated pinned heat sinks:,, and models at Re=5393 E. Eect o Pin Arrangement The eects o employing the staggered arrangement o pins ins, shown in Fig. 1, are now investigated. Fig. 13 compares the pressure drop, ΔP, across a PHS or both an in-line and a staggered array o solid () and perorated () pins. The pressure JMESTN

7 P (Pa) drop across the staggered array is approximately 30% greater than the corresponding in-line array or both the solid and perorated pins. The main reason or this is that the staggered arrangement increases the low blockage in the airlow direction. Fig. 14 shows the eect o a staggered pin arrangement or both solid and perorated pins () on the resultant CPU temperature as a unction o an power consumption. It shows that the staggered arrangement enables as lower CPU temperature to be achieved or a given mechanical power consumption. At the higher power consumptions, the CPU temperature o the staggered array o perorated pins is approximately 5 o C lower than or the in-line arrangement while those o the solid pins are approximately 4 o C lower. The improved heat transer with the staggered arrangement o pins is due to increased turbulent mixing and convection rom the PHS, Yang et al [6]. The perormance o the in-line and staggered arrays o pins are compared in Table 3. A elliptical perorated pin ins these lead to reductions in mass o the pins o 15%, 19% and % respectively. The total weight o the PHS, W T, is given by the expressions (1) (13) where V Base is the volume o the base o the PHS, V Pins the total volume o its pins, V T the total volume o the PHS and W T its total weight, where the density o aluminium. Thus, the total weight reduction is approximately 4% or circular perorated pins () and 5% or both square perorated pin ins () and elliptic perorated pin ins () Staggered Array In-line Array Staggered Array In-line Array B Fig. 13: Eect pins array on pressure drop with variation Reynolds number or solid () and perorated () PHSs models Staggered Array In-line Array Staggered Array In-line Array 75 Tcase( o C) 70 Fig. 1: Schematic diagram o pinned heat sink with (A) in-line and (B) staggered [18] arrays F. Eect o Perorations on Heat Sink Weight Minimizing the weight o consumer electronics is a key design goal and a number o studies have attempted to either maximize the heat transer rate or a given in weight or minimize the weight or a speciied heat transer rate [11]. Perorations reduce the mass o the pins and or the circular, square and Fan Power (W) Fig. 14: Eect pins array on T case and P an or solid () and perorated () PHSs models JMESTN

8 These igures demonstrate that the perorated ins investigated here can provide substantial improvements in heat transer with signiicant reductions in power consumption and heat sink mass. IV. CONCLUSIONS Pinned Heat Sinks (PHSs) provide the cooling required in many critical applications. The present study demonstrates that perorating the pin ins in a PHS can provide substantial improvements in heat transer, power consumption and weight, at the price o increased manuacturing complexity. It has been shown that the shape o the perorations can also have an important inluence on heat sink perormance. Circular perorations provide the greatest enhancement in heat transer, since they maximize the speed o the air jets lowing through the perorations, while the elliptical perorations considered provide the greatest reduction in pressure drop since they oer the least resistance to air lowing through them. Further perormance enhancements can be achieved by staggering the pins, which enhances turbulent mixing around the pins at the price o a larger pressure drop. However, results have shown that the enhancement in heat transer is dominant in the sense that this approach enables the heat sink base temperature to be cooled to a target temperature or a signiicantly lower power consumption. Table : Enhancement o Nu T, P an, and T case or perorated pin Heat Sinks Designs Circular Perorated Pins () Square Perorated Pins () Elliptic Perorated Pins () A T Parameter Studies Nu T P an (W) T case ( o C) 15% 9% 9% 8% 18% 4% 7% 5% 17% 4% 1% 5% Table 3: The reduction o T case and the increase in P an o the staggered array o pins compared with the in-line array or and PHSs Heat Sinks Designs Staggered array o solid Pins () Staggered array o perorated Pins (3P) ACKNOWLEDGEMENTS Parameter Studies P an (W) T case ( o C) 30% 10% 30% 1% The authors would like to thank the Higher Committee or Education Development in Iraq (HCED), Iraqi Ministry o Higher Education and Scientiic Research (MOHE), and Mechanical Engineering Department University o Anbar, Iraq or inancial support o this work. REFERENCES [1] Shaeri, M.R. and M. Yaghoubi, Thermal enhancement rom heat sinks by using perorated ins. Energy Conversion and Management, (5): p [] Shaeri, M.R. and M. Yaghoubi, Numerical analysis o turbulent convection heat transer rom an array o perorated ins. International Journal o Heat and Fluid Flow, (): p [3] Amer Al-damook, Kapur N., Summers J.L., Thompson H.M., An experimental and computational investigation o thermal airlows through perorated pin heat sinks, in progressing o Applied Thermal Engineering Journal, 89 (015) [4] Amer Al-damook, Kapur N., Summers J.L., Thompson H.M., Computational design and optimisation o pin in heat sinks with rectangular perorations, Applied Thermal Engineering Journal, (016). [5] Shaeri, M.R. and M. Yaghoubi, Thermal enhancement rom heat sinks by using perorated ins. Energy Conversion and Management, (5): p [6] Shaeri, M.R. and M. Yaghoubi, Numerical analysis o turbulent convection heat transer rom an array o perorated ins. International Journal o Heat and Fluid Flow, (): p [7] Shaeri, M.R. and T.C. Jen, The eects o peroration sizes on laminar heat transer characteristics o an array o perorated ins. Energy Conversion and Management, : p [8] Shaeri, M.R. and T.C. Jen, Turbulent Heat Transer Analysis o a Three-Dimensional Array o Perorated Fins Due to Changes in Peroration Sizes. Numerical Heat Transer, Part A: Applications, (11): p. 16. [9] Ismail, F., M.O. Reza, M.A. Zobaer, and Mohammad Ali, Numerical investigation o turbulent heat convection rom solid and longitudinally perorated rectangular ins. IEEE 5th BSME International Conerence on Thermal Engineering, 013. p [10] Ismail, F., Eects o Perorations on the Thermal and Fluid Dynamic Perormance o a Heat Exchanger. IEEE Transaction on Component, Packaging and Manuacturing Technology, 013. p.1-8 [11] Ismail, M. F., Hasan M. N., & Ali M., Numerical simulation o turbulent heat transer rom perorated plate-in heat sinks. Heat and Mass Transer, (4), p [1] Yaghoubi M., Shaeri M. R., & Jaarpur K., Three-dimensional numerical laminar convection heat transer around lateral perorated ins. Computational Thermal Sciences: An International Journal, (3): p [13] Yaghoubi M., Shaeri M. R., & Jaarpur K., Heat transer analysis o lateral perorated in heat sinks. Applied Energy, (10): p JMESTN

9 [14] Ismail, M. F., Hasan M. N., & Saha S. C., Numerical study o turbulent luid low and heat transer in lateral perorated extended suraces. Energy, : p [15] Sahin, B. and A. Demir, Thermal perormance analysis and optimum design parameters o heat exchanger having perorated pin ins. Energy Conversion and Management, 008a. 49(6): p [16] Sahin, B. and A. Demir, Perormance analysis o a heat exchanger having perorated square ins. Applied Thermal Engineering, 008b. 8(5-6): p [17] Amol B. Dhumme and Hemant S. Farkade, Heat Transer Analysis o Cylindrical Perorated Fins in Staggered Arrangement. International Journal o Innovative Technology and Exploring Engineering (IJITEE), 013. (5): p [18] Waleed Al-Sallami, Amer Al-damook, Thompson H.M., A Numerical Investigation o Thermal Airlows over Strip Fin Heat Sinks, International Communications in Heat and Mass Transer, (016). [19] Zhou, F. and I. Catton, Numerical Evaluation o Flow and Heat Transer in Plate-Pin Fin Heat Sinks with Various Pin Cross-Sections. Numerical Heat Transer, Part A: Applications, (): p [0] Leung, C. W., & Probert, S. D., Heatexchanger perormance: eect o orientation. Applied energy, (4), [1] Menter, F. R., Zonal Two Equation k-ω Turbulence Models or Aerodynamic Flows, AIAA 1993, p [] ANSYS FLUENT User's Guide, 011. [3] Holman, J. P., Experimental Methods or Engineers, McGraw Hill Book Company, 10971, 8th edition, 011. [4] Sparrow, E. M., Ramsey, J. W., & Altemani, C. A. C., Experiments on in-line pin in arrays and perormance comparisons with staggered arrays, Journal o heat transer, (1): p [5] Yang, Y. T., & Peng, H. S., Investigation o planted pin ins or heat transer enhancement in plate in heat sink. Microelectronics Reliability, (): p [6] Yang, K.S., Chu, W.H., Chen, Y. and Wang, C.C.. A comparative study o the airside perormance o heat sinks having pin in conigurations. International Journal o Heat and Mass Transer, (3), pp [7] Sara, O. N., Pekdemir, T., Yapici, S. and Ersahan, H., Thermal Perormance Analysis or Solid and Perorated Blocks Attached on a Flat Surace in Duct Flow. Energy Conversion & Management, (10): p V. NOMENCLATURE A p D D D h F H H K N N L Nu P an P Pr Pr t Q S y S Re T T U α α,β,β* ϕ μ μt ρ Ν ν t ε σ k σ ω σ cross-sectional area o the low passage o the heat sink, m pin diameter o the pin in heat sink, mm peroration diameter o the pin in, mm hydraulic diameter, m riction actor pin in height, mm heat transer coeicient, W/m.K turbulence kinetic energy number o perorations number o pins heat sink length, mm Nusselt number an power, W pressure drop, Pa Prandtl number turbulent Prandtl number power applied on the base, W pin pitch in streamwise direction, mm an invariant measure o the strain rate Reynolds number temperature, o C temperature dierence, K air velocity inlet, m/s luid thermal diusivity (m /s) turbulence model constant porosity V void =V luid viscosity (Pa s) turbulent eddy viscosity, Pa/s luid density (kg/m 3 ) kinematic viscosity, m /s turbulent kinematic viscosity, m /s k-ε turbulence model constant turbulence model constant or the k-equation k-ω turbulence model constant JMESTN