HEFAT014 10 th International Conerence on Heat Transer, Fluid Mechanics and Thermodynamics 14 6 July 014 Orlando, Florida COMPARISON OF THERMA CHARACTERISTICS BETWEEN THE PATE-FIN AND PIN-FIN HEAT SINKS IN NATURA CONVECTION Younghwan Joo and Sung Jin Kim* *Author or correspondence School o Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute o Science and Technology, Daejeon 305-701, Republic o Korea, E-mail: sungjinim@aist.ac.r ABSTRACT Thermal perormances o optimized plate-in and pin-in heat sins with vertical base plate were compared in natural convection. Comparison is perormed under the same base plate dimensions and in height condition. A Nusselt number correlation or plate-in array was adopted to optimize plate-in heat sins. For pin-in heat sins, a new correlation o heat transer coeicient was developed. With the new correlation, diameter, horizontal spacing, and vertical spacing o pin-in array are optimized. Optimized plate-in and pin-in heat sins are compared analytically. They were compared or various base plate dimensions, in heights, temperature dierences. In most regions, plate-in heat sins show better perormance than pin-in heat sins. INTRODUCTION With the development o technologies, electronic devices have been integrated. Thereore, power dissipation rate per unit area has been increasing. Increased temperature o components caused by high heat dissipation rate leads to perormance reduction and ailure in systems. Thereore, cooling problem became an important issue and development o cooling devices is necessary to advance electronic devices. Heat sin is one o these cooling devices. It increases the area o heat transer using materials with high thermal conductivity. Heat sins are typically divided into orced convection and natural convection heat sins based on the operating conditions. Forced convection heat sins dissipate large amount o heat with additional devices such as an but the reliability is lower than natural convection heat sins because o additional devices. Thereore, natural convection heat sins are widely used or the applications in which high reliability is required and additional devices are not easy to be implemented. Natural convection heat sins have various conigurations to enhance the thermal perormance but typically plate-in and pin-in array are widely used because they are cost-eective. Plate-in array usually has larger surace area than pin-in array because o the area loss caused by cross cut in pin-in array. Pin-in array usually has higher heat transer coeicient because o the depression o growth o the thermal boundary layers. Then, which array type is better? NOMENCATURE A [m ] Surace area c p [J/g-K] Speciic heat d [m] Fin diameter g [m/s ] Standard acceleration o gravity H [m] Fin height h [W/m K] Convective heat transer coeicient K [m ] Permeability [W/m-K] Thermal conductivity [m] Heat sin length n [-] Number o ins Nu [-] Nusselt number Pr [-] Prantl number R th [K/W] Thermal resistance S [m] Spacing o pin-in array T [K] Temperature W [m] Heat sin width w c [m] Fin thicness o plate-in w w [m] Channel spacing o plate-in Special characters α [m /s] Diusion coeicient β [1/K] Volumetric thermal expansion coeicient ε [-] Emissivity η [-] Fin eiciency μ [N-s/m ] Dynamic viscosity ν [m /s] Kinematic viscosity ρ [g/m 3 ] Density σ [W/m K 4 ] Stean-Boltzmann constant φ [-] Porosity Subscripts array base in Array Base Fluid Fin 174
h pin plate ratio v Horizontal Pin-in heat sin Plate-in heat sin Ratio Vertical About the question, there are some previous researches. Sparrow and Vemuri [1] studied the optimal number o pin-in with ixed base plate dimensions and in diameter. With the optimized result, they compared pin-in and plate-in heat sins. However, their comparison was perormed based on the same surace area. Thereore, their results didn t consider the optimal combination o surace area and heat transer coeicient which is dierent or each array type. Iyengar and Bar-Cohen [] tried to compare optimized plate-in and pin-in array with leastmaterial method. In many cases, however, thermal perormance itsel is usually more important than the amount o material. Thereore, there may be other practical constraints to compare plate-in and pin-in heat sins. In the present study, thermal perormances o plate-in and pin-in heat sins with vertical base plate would be compared based on the same base plate dimensions and in height condition. To achieve maximum thermal perormance or the constraints, each array type would be optimized using correlations o convective heat transer coeicient. There have been many researches about plate-in heat sins [3, 4, 5, 6, and 7], so plate-in heat sins would be optimized using correlations suggested by previous researches. For pin-in heat sins, there have been many researches and correlations [1, 8, 9, and 10]. Aihara et al. [9] studied highly populated pin-in heat sins and suggested a Nusselt number correlation. However, their correlation cannot be used or optimization o pin-in array in above constraints. For given horizontal spacing and diameter, their correlation predicts same thermal perormance along the vertical spacing o pin-in array, so optimal vertical spacing cannot be achieved. Thereore, we need a new correlation o convective heat transer coeicient to optimize pin-in heat sins. ANAYTIC EQUATION FOR PIN-FIN HEAT SINK Figure 1 Coniguration o pin-in heat sin Figure imiting cases or pin-in array Figure 1 shows pin-in heat sin. For given W,, and H, coniguration o array is determined with d, S h, S v. Thereore, correlation or convective heat transer coeicient consists o these three parameters. With variations o S h, S v, pin-in array conigurations can be divided into 4 limiting cases as Figure. imiting case 1 means densely positioned pin-ins with small S h and S v. imiting case means vertical single array o pin-ins with large S h and relatively small S v. imiting case 3 means horizontal single array o pin-ins with large S v and relatively small S h. imiting case 4 means isolated horizontal cylinder with large S h and S v. With these limiting cases, we are going to apply asymptotic method to get a new correlation or convective heat transer coeicient o pin-in heat sin. As in the plate-in heat sin, we need to get equations o heat transer coeicient in each limiting case. In limiting case 1, pin-ins are densely positioned, so it can be considered as porous media. By assuming 1-D low, we can start rom ollowing governing equation. P µ 0.55 = u ρ u (1) D 1/ D x K K Brinmann term which considers the eects o wall riction can be ignored because there is no wall or pin-in array. On the other hand, we can assume that exit temperature o air becomes almost same as the temperature o ins when intae low is thermally ully developed immediately. Then, ollowing equation o energy balance can be used. q = mc T T = h A T T () ( ) 1 ( ) p in array in By combining equation (1) and (), we can suggest ollowing equation or limiting case 1. SSc h v p µ µ h1 =. Kρ gβ T (3) 1.1π d K K 4SS h v π d K = (4) 48 In limiting case, horizontal cylinders are arranged in a vertical direction. S h is very large, so it can be considered as an isolated vertical single array o horizontal cylinders. There are previous researches about the situation. Aihara et al. [9] 175
perormed experiments about the heat transer phenomena rom uniormly heated horizontal cylinders and suggested a Nusselt number correlation as ollow. h = 0.311 0.454 ln ( Sv / d ) Gr (5) ( T ) 3 b Gr = (6) ν This correlation is applicable to S v /d=1-4 and Gr =10 6-10 8. Above equation would be used or limiting case. In limiting case 3, horizontal cylinders are arranged in a horizontal direction. S v is large enough to be considered as a vertically isolated horizontal array. To analyse this case, correlation orm o immersed body was employed because it approaches the situation o an isolated horizontal cylinder as S h becomes large. Then, we can postulate ollowing orm o equation or limiting case 3. Sh T ) 1 h3 = (7) d αν d To ind the orm o the unction in the square bracet, we made use o numerical simulation which replaces experiments. For dierent in diameters, heat transer coeicients were evaluated as dimensionless horizontal spacing (S h /d) varies. Then, the results were itted into a single equation as ollow. 1 Sh T ) 1 h3 = 0.59 1.9 exp 0.6111 d αν d (8) Above equation would be used or limiting case 3. imiting case 4 means an isolated horizontal cylinder. There have been many researches about this case. Churchill and Chu [11] suggested a correlation applicable or a wide range o Rayleigh number, so ollowing equation would be used or limiting case 4 by modiying the correlation. 1/6 0.387Rad (9) h4 = 0.60 9/16 8/7 d 1 ( 0.559 / Pr) In asymptotic method, equations or each limiting case should be integrated with proper exponents. The exponents were decided by comparison with experimental results including previous researches. Then, inal orm o average convective heat transer coeicient is obtained. 1 8 8 8 3.5 3.5 3.5 3.5 1 3 4 hm = h ( h h h ) (10) By using above equation, thermal perormance o pin-in heat sin would be predicted. OPTIMIZATION OF HEAT SINK To optimize heat sin or given volume, analytic equations predicting the convective heat transer coeicient and equations to calculate surace area are needed. For plate-in heat sins, we are going to use ollowing equation suggested by Kim et al. [7]. Figure 3 Coniguration o plate-in heat sin hw 0.68 0.813 ( 0.0911 ) ( 0.5170 ) 3.5 3.5 1/3.5 m c Nu in = = El El (10) 4 gβ ) Pr wc El = (11) ν This equation considers the eect o intae low rom the ront side o plate-in heat sins, so it can predict thermal perormance o plate-in heat sin more precisely. Surace area o plate-in heat sin can be expressed with design parameters shown in Figure 3. Aarray = nin ( H wh w w w ) (1) Abase = W n inww (13) W ww n in = (14) wc ww For pin-in heat sins, equation (10) is used to predict convective heat transer coeicient. Surace area o pin-in array can be calculated using equations as ollows. Aarray = nin π d( H d /4) (15) Abase = W n π d (16) in 4 nin = nn v h ( nv 1)( nh 1) (17) nv = ( d) / Sv 1 (18) nh = ( W / d) / Sh 1 (19) For un-inned base plate, ollowing correlation or natural convection rom vertical wall is used. hbase Nu = = 0.59Ra (0) gβ ( T ) 3 b Ra = (1) να With above equations, we can express Q total which means total heat dissipation rom heat sin. Qtotal = ( hbase Abase hin Aarrayη ) T ) () Then, thermal resistance (R th ) which is target dependent variable or thermal perormance comparison is expressed as ollow. 176
COMPARISON OF THERMA PERFORMANCE Figure 4 Optimization o plate-in heat sin Figure 6 Region map o R th,ratio at W=0.1 m, T b -T =50K (a) In the present study, thermal perormances o plate-in and pin-in heat sins are compared analytically. The constraints or the comparison are 1) same base plate dimensions, ) same in height. Based on the optimization process, region maps o thermal resistance ratio are obtained as Figure 6. The deinition o thermal resistance ratio is as ollow. Rth, pin Rth, ratio = (4) Rth, plate In above equation, each thermal resistance is minimum thermal resistance or a given volume o heat sin. According to the deinition o R th,ratio, plate-in heat sins have better perormance when R th,ratio is larger than 1. From the region map, we can see that thermal perormance o plate-in heat sins is superior to that o pin-in heat sins when is larger than 0.03 m. When is larger than 0.03 m, plate-in heat sins become superior with large H. However, the eect o is more dominant than that o H on the thermal perormance. CONCUSION R (b) Figure 5 Optimization o pin-in heat sin ( T T ) 1 b th = = total base base in array Q h A h A η (3) Figure 4 shows optimization o plate-in heat sin. Optimal coniguration seems to have small in thicness and optimal channel spacing is about 7-8 mm. Figure 5 shows optimization o pin-in heat sin. Two graphs are shown because there are three main parameters (S h, S v, d) or pin-in heat sins. Figure 5 (a) shows a contour o R -1 th or a ixed diameter (d=4 mm). Figure 5 (b) means collection o optimized results or dierent diameters. Thereore, the optimal perormance in Figure 5 (a) is expressed as a point on Figure 5 (b). Above results are gained rom =0.1 m, W=0.1 m, H=0.03 m, T b -T =50K. In the present study, thermal perormances o plate-in and pin-in heat sins were compared or the ixed base plate dimensions and in height. To compare the optimized heat sins, each heat sin type was optimized based on the correlations or convective heat transer coeicient o in array. For the pin-in heat sin with staggered circular in, however, we couldn t ind appropriate correlation which is available or optimization in our constraints. Thereore, a new correlation or convective heat transer coeicient o pin-in heat sin was suggested. Using the correlations or both types o heat sins, thermal perormances were compared and a region map was suggested. According to the region map, we can conclude that plate-in heat sins show better thermal perormance in most practical regions. REFERENCES [1] E. M. Sparrow and S. B. Vemuri, Orientation eects on natural convection/radiation heat transer rom pin-in arrays, International journal o heat and mass transer 9.3 (1986) 359-368. 177
[] M. Iyengar and A. Bar-Cohen, east-material optimization o vertical pin-in, plate-in, and triangular-in heat sins in natural convective heat transer, Thermal and Thermomechanical Phenomena in Electronic Systems, 1998, ITHERM'98, The Sixth Intersociety Conerence on, IEEE, (1998) 95-30. [3] W. Elenbaas, Heat dissipation o parallel plates by ree convection, Physica 9 (194) 1-8. [4] D. W. Van de Pol and J. K. Tierney, Free convection Nusselt number or vertical U-shaped channels, Journal o Heat Transer 95 (1973) 54. [5] J. R. Culham, M. M. Yovanovich, and S. ee, Thermal modeling o isothermal cuboids and rectangular heat sins cooled by natural convection, Components, Pacaging, and Manuacturing Technology, Part A, IEEE Transactions on, 18 (1995) 559-566. [6] A. Bar-Cohen and W. M. Rohsenow, Thermally optimum spacing o vertical, natural convection cooled, parallel plates, Journal o Heat Transer 106 (1984) 116-13. [7] T. H. Kim, D. K. Kim, and K. H. Do, Correlation or the in Nusselt number o natural convective heat sins with vertically oriented plate-ins, Heat and Mass Transer 49 (013) 413-45. [8] A. I. Zograos and J. E. Sunderland, Natural convection rom pin in arrays, Experimental Thermal and Fluid Science 3.4 (1990) 440-449. [9] T. Aihara, S. Maruyama, and S. Kobayaawa, Free convective/radiative heat transer rom pin-in arrays with a vertical base plate (general representation o heat transer perormance), International journal o heat and mass transer 33.6 (1990) 13-13. [10] A. Bejan, A. J. Fowler, and G. Stanescu, The optimal spacing between horizontal cylinders in a ixed volume cooled by natural convection, International journal o heat and mass transer 38.11 (1995) 047-055. [11] S. W. Churchill and H. H. Chu, Correlating equations or laminar and turbulent ree convection rom a horizontal cylinder, International Journal o Heat and Mass Transer 18.9 (1975) 1049-1053. 178