Plate fin_and_pin_fin_heat_sinks
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 Plate fin_and_pin_fin_heat_sinks Plate fin_and_pin_fin_heat_sinks Document Transcript

  • International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmtComparison of thermal performances of plate-fin and pin-fin heat sinks subjectto an impinging flowDong-Kwon Kim, Sung Jin Kim *, Jin-Kwon BaeDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Koreaa r t i c l e i n f o a b s t r a c tArticle history: In this paper, we compare thermal performances of two types of heat sinks commonly used in the elec-Received 16 September 2008 tronic equipment industry: plate-fin and pin-fin heat sinks. In particular, heat sinks subject to an imping-Received in revised form 26 February 2009 ing flow are considered. For comparison of the heat sinks, experimental investigations are performed forAccepted 26 February 2009 various flow rates and channel widths. From experimental data, we suggest a model based on the volumeAvailable online 15 April 2009 averaging approach for predicting the pressure drop and the thermal resistance. By using the model, ther- mal resistances of the optimized plate-fin and pin-fin heat sinks are compared. Finally, a contour map,Keywords: which depicts the ratio of the thermal resistances of the optimized plate-fin and pin-fin heat sinks as aHeat sinkImpinging flow function of dimensionless pumping power and dimensionless length, is presented. The contour map indi-Thermal resistance cates that optimized pin-fin heat sinks possess lower thermal resistances than optimized plate-fin heat sinks when dimensionless pumping power is small and the dimensionless length of heat sinks is large. On the contrary, the optimized plate-fin heat sinks have smaller thermal resistances when dimensionless pumping power is large and the dimensionless length of heat sinks is small. Ó 2009 Elsevier Ltd. All rights reserved.1. Introduction ychka [7] also developed a simple semi-empirical model for pre- dicting the heat transfer coefficient of plate-fin heat sinks. Recent advances in semiconductor technology have led to a sig- Meanwhile, many studies have also dealt with the pin-fin heat sinknificant increase in power densities encountered in microelec- subject to an impinging jet. A numerical simulation of the three-tronic equipment [1,2]. Accordingly, effective cooling technology dimensional flow and temperature field was performed by Satheis essential for reliable operation of electronic components [3,4]. et al. [8]. Ledezma et al. [9] presented a simplified numerical modelVarious types of cooling systems have been developed as thermal to obtain correlations for the optimal fin spacing of pin-fin heatsolutions. In this regard, a heat sink is the most widely used type sinks. Kondo et al. [10] suggested a semi-empirical zonal modelof cooling device and has received much attention due to its for a pin-fin heat sink. The flow behavior and heat transfer duecost-effective performance. Two common types of heat sinks to air jet impingement on pin-fin heat sinks was experimentallywhich are widely used in the industry are plate-fin heat sinks studied by Issa and Ortega [11].and pin-fin heat sinks. The former offers simple design and easy As noted above, the plate-fin and pin-fin heat sinks are bothfabrication, while the latter has an advantage of providing higher commonly used and studied as cooling solutions for electronicheat transfer coefficient at the expense of higher production cost. equipment. Then, an obvious question is which type of heat sinkGiven that the two types of heat sinks have respective strengths, has better performance? To date, several researchers have beena considerable body of research has been concentrated on both interested in this question and sought proper answers. Kondoconfigurations. et al. used a zonal approach in optimizing the thermal performance Numerous studies have focused on the plate-fin heat sink sub- of plate-fin and pin-fin heat sinks under the constraint of fixedject to an impinging flow. Biber [5] numerically studied a number pumping power and heat sink size. They showed that optimizedof different combinations of channel parameters and presented a plate-fin heat sinks provide 40% lower thermal resistances com-correlation for the average Nusselt number for a plate-fin heat sink. pared to optimized pin-fin heat sinks [12]. Li et al. [13] comparedKondo et al. [6] used a semi-empirical zonal approach for deter- thermal resistances of several plate-fin and pin-fin heat sinks withmining the thermal resistance as well as the pressure drop for a various fin heights and Reynolds numbers experimentally usingplate-fin heat sink. In their model, the heat sink was divided into infrared thermography. Contrary to the results presented by Kondosix regions, each of which was solved separately. Duan and Muz- et al., they concluded that the thermal performance of the pin-fin heat sink is superior to that of the plate-fin heat sink. As indicated * Corresponding author. Tel.: +32 350 3043; fax: +32 350 8207. by these contradictory results, the selection between the plate-fin E-mail address: sungjinkim@kaist.ac.kr (S.J. Kim). and pin-fin heat sinks is still not obvious. Furthermore, previous0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijheatmasstransfer.2009.02.041
  • D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 3511 Nomenclature a wetted area per volume Greek symbols c heat capacity of fluid e porosity (wc/(wc + ww)) h heat transfer coefficient based on one-dimensional bulk g similarity variable mean temperature geff fin efficiency H channel height l viscosity k thermal conductivity h dimensionless temperature K permeability q density L length of heat sink (=width of heat sink) W stream function L* dimensionless length of heat sink (L/H) p pressure Subscripts PPump pumping power bm bulk mean PÃPump dimensionless pumping power (PPump =l3 qÀ2 HÀ1 ) f f f fluid q heat transfer rate in inlet R total thermal resistance opt optimized T temperature pin pin-fin heat sink u,v,w velocity plate plate-fin heat sink U,V,W characteristic velocity s solid v0 inlet velocity w wall wc channel width wÃc dimensionless channel width (wc/H) Superscripts ww fin thickness f averaged value over the fluid region x,y,z Cartesian coordinate system s averaged value over the solid region hi averaged value hTib,f one-dimensional bulk mean temperature for the fluid phaseworks did not compare the optimized plate-fin and pin-fin heat connected to a manometer (FCO510, Furness). To measure the tem-sinks systematically for various pumping powers and the heat sink peratures at the base of the fins, seven 30 gauge J-type thermocou-sizes. Kondo et al. did not show the effect of the size, while Li et al. ples (Omega) are mounted through 3 mm deep holes of a basedid not optimize the geometry of the heat sink. The objectives of the present paper are to eliminate ambiguityassociated with the selection of a heat sink type and to comparethe thermal performance of the optimized plate-fin and pin-finheat sinks for various pumping powers and the heat sink sizes.For this comparison, experimental investigations are performedfor various flow rates and channel widths. Then, from experimentaldata, we suggest a model based on the volume averaging methodfor predicting the pressure drop and the thermal resistance. Byusing the model, thermal resistances of the optimized plate-finand pin-fin heat sinks are compared. Finally, a contour map, whichdepicts the ratio of the thermal resistances of the optimized plate-fin and pin-fin heat sinks as a function of dimensionless pumpingpower and dimensionless length, is presented. This study will helpengineers to choose a heat sink with better performance betweenthe two types of heat sinks subject to an impinging jet.2. Experiments In this section, the experimental portion of the present study isdescribed. Two types of fin designs, plate-fin and inline square pin-fin heat sinks, have been tested as shown in Figs. 1(a), 2(a), and 3.The dimensions of the heat sinks are shown in Table 1. The testedheat sinks are made of aluminum alloy 6061 (k = 170 W/m K) andno additional surface treatment is applied. The general layout and a photo of the experimental apparatusare shown in Figs. 4 and 5, respectively. The gas flows into the windtunnel from a pressure tank through a metering valve and a massflow meter. The flow meter is used for measuring the flow rate inthe wind tunnel (D08-8C, Sevenstar electronics). The wind tunnelwalls are made of acrylic (k = 0.86 W/m K). In order to measurethe pressure difference between the inlet and the outlet of the heatsink, a pressure tap is positioned on the wind tunnel wall and is Fig. 1. Schematic diagrams for plate-fin heat sink subject to an impinging flow.
  • 3512 D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 Fig. 3. Heat sinks used for experimental study: (a) plate-fin heat sink, (b) pin-fin heat sink. Table 1 Tested heat sinks. Fig. 2. Schematic diagrams for pin-fin heat sink subject to an impinging flow. Type of heat sink wc (mm) ww (mm) H (mm) L (mm) Plate-fin 1 0.5 1 25 40 Plate-fin 2 0.95plate having 5 mm thickness. The relative positions of thermocou- Plate-fin 3 1.44ples for temperature measurement are shown in Fig. 4. The maxi- Plate-fin 4 2 Plate-fin 5 3.33mum heat sink base temperature is measured from readings of Pin-fin 1 0.5 1 25 40seven thermocouples. An Agilent 34970A DAQ is used to transport Pin-fin 2 0.95data measured by the thermocouples. From the analysis of the Pin-fin 3 1.44experimental uncertainties, maximum uncertainties for measure- Pin-fin 4 2 Pin-fin 5 3.33ment of the pressure drop and the temperature are estimated tobe 5% and 2%, respectively. The heat sinks are heated by electricalheaters fabricated using stainless steel with 0.25 mm thicknesssandwiched by KaptonÒ films. To reduce heat loss, the bottom of 3. Mathematical modeling using the volume averagingthe heater is insulated with Teflon. The heat loss is determined approachfrom a surface temperature measurement of the test section. Tocalculate the net heat flux at the bottom of the heat sink, the esti- In the present study, detailed information, such as velocity andmated heat loss is subtracted from the electric power supplied to temperature distributions, is of secondary importance. Instead wethe heater. The heat supplied from the power supply is calculated are concerned with estimating the macroscopic aspects of a prob-by measuring the voltage drop and the current through the heater. lem such as the pressure drop across a channel and the overallThe maximum heat loss is about 5% of the supplied heat. thermal resistance of a heat sink. Given that our main interest lies A typical test procedure is as follows: Flow rate is set by regu- in the macroscopic quantities, it would be wise to average the gov-lating the metering value. The heater is then powered up to a heat erning equations in the direction normal to the flow. This approachload of 30 W and allowed to stabilize. The temperature distribution can lead to considerable simplification, especially when the origi-at the base of the heat sink is measured until the change in the nal problem requires a great deal of time and money for obtainingtemperature is smaller than ±0.1 °C in a 2 min period. We con- a complete solution. Since a heat transfer device is modeled as aducted experiments in the laminar flow regime with flow rates fluid-saturated porous medium in this technique, it is frequentlyof 50, 100, 150, and 200 Standard Liter per Minute (SLM). The called a porous medium approach. This approach has been success-pumping power is calculated by multiplying the measured flow fully applied in thermal design and optimization of heat transferrate and pressure drop. The range of the pumping power (PPump) devices such as internally finned tubes and microchannel heatfrom 0.00082 to 0.096 W is covered in the present experiment. sinks with a parallel flow [14,15]. In this section, a modeling tech-Each experiment was conducted four times. nique based on the volume averaging approach is proposed.
  • D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 3513 The momentum and energy equations are given as follows.   ! @u @u @u @p @2u @2u @2u q u þv þw ¼À þl þ þ ð1Þ @x @y @z @x @x2 @y2 @z2   ! @v @v @v @p @2v @2v @2v q u þv þw ¼À þl þ þ ð2Þ @x @y @z @y @x2 @y2 @z2   ! @T @T @T @2T @2T @2T qc u þ v þ w ¼k þ þ ð3Þ @x @y @z @x2 @y2 @z2 In the volume averaging approach, the governing equations for the averaged velocity and temperature are established by the averaging momentum equations and energy equation. Before averaging these equations, it is necessary to define the quantities to be averaged. Since the present system has a periodic structure in the z direction, the representative elementary volume (REV) for averaging can be visualized as a rectangular parallelepiped aligned parallel to the z-axis, as shown in Fig. 1(b). The averaged quantities over the fluid and solid phases of the REV are then defined, respectively, as follows: Z wc Z wc þww 1 1 h/if ¼ /dz; h/is ¼ /dz ð4Þ wc 0 ww wc For the averaged fluid temperature, the one-dimensional bulk mean temperature is more suitable than the mean temperature to calcu- late the thermal performance of the heat sinks. The one-dimen- sional bulk mean temperature is defined as Fig. 4. Layout of the experimental apparatus. R wc Tudz hTif ;b ¼ R wc 0 ð5Þ 0 udz As pointed out by Slattery [16], some information is lost when gov- erning equations are averaged: in the present case, the dependence of the velocity and temperature distributions in the averaging direc- tion is lost. For the present configuration, the lost information is recovered with an approximation. For this, it is assumed that the velocity and temperature profiles for the fluid in the averaging direction are similar to those of a Poiseuille flow between two infi- nite parallel plates. This assumption is similar to the assumption made for the profile shape function in obtaining integral solutions for a laminar boundary layer flow [17]. The velocity and tempera- ture distributions for the Poiseuille flow in this configuration can be easily determined to be   z z u ¼ 6huif Á 1À ð6Þ wc wc  4  3  ! 420 1 z 1 z 1 z T¼ ðhTib;f À hTis Þ À þ þ hTis ð7Þ 17 6 wc 3 wc 6 wc Fig. 5. Photo of the experimental apparatus. The governing equations for the averaged velocity and temperature are established by averaging the momentum and energy equations with Eqs. (6) and (7). x directional momentum equation:3.1. Plate-fin heat sink ! 6 @huif @huif @hpif qf huif þ hv if þ The problem under consideration is an impinging flow through 5 @x @y @x !a plate-fin heat sink as shown in Fig. 1(a) and (b). The bottom elf @ 2 huif @ 2 huifsurface is kept constant at a high temperature. Air impinges on ¼À huif þ l þ ð8Þ K @x2 @y2the heat sink along the y-axis and then flows parallel to x-axis.Air, employed as a coolant, passes through the heat sink, thusremoving the heat generated by the component attached at the y directional momentum equation:bottom of the heat sink substrate. In analyzing this problem, ! 6 @hv if @hv if @hpifthe flow is assumed to be steady and laminar. In addition, all qf huif þ hv if þ 5 @x @y @ythermal properties are evaluated at the film temperature of fluid. !In addition, it is assumed that the aspect ratio of the channel is el 2 @ hv if @ hv if 2higher than 1 and the solid conductivity is higher than the fluid ¼À hv if þ l þ ð9Þ K @x2 @y2conductivity.
  • 3514 D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517Energy equation for the fluid phase: Partial differential governing equations (Eqs. (11) and (23)–(25)) ! can be transformed into an ordinary differential equation with a b;f b;f @hTi @hTi similarity variable. The similarity variable g, the stream functioneqf cf huif þ hv if @x @y W, and the dimensionless temperatures are defined as ! sffiffiffiffiffiffiffiffiffiffiffi s b;f @hTib;f @hTib;f v 0 qf ¼ haðhTi À hTi Þ þ ekf þ ð10Þ g¼y ð26Þ @x2 @y2 Hlf sffiffiffiffiffiffiffiffiffiffiffiEnergy equation for the solid phase: v 0 lf   W¼ FðgÞx ð27Þ @hTis @hTis H qfð1 À eÞks 2 þ 2 þ haðhTib;f À hTis Þ ¼ 0 ð11Þ @x @y hTib;f À T w hb;f ðgÞ ¼ ð28Þwhere e, K, h, and a are the porosity, permeability, heat transfer T in À T wcoefficient, and wetted area per volume, respectively. hTis À T w hs ðgÞ ¼ ð29Þ wc T in À T we¼ ð12Þ ww þ wc With Eqs. (26)–(29), the governing equations (Eqs. (11) and (23)– 2 (25)) and the boundary conditions (Eqs. (16) and (17)) are given asa¼ ð13Þ ww þ wc
  • !À1 6 00 6 e H lf FF þ ð1 À F 0 F 0 Þ þ ð1 À F 0 Þ ¼ 0 ð30Þ @u
  • @u
  • ew2 5 5 K v 0 qfK ¼ Àewc huif
  • À
  • ¼ c ð14Þ v  @z z¼wc @z z¼0 12 0 0
  • ! À eqf cf Fhb;f ¼ haðhs À hb;f Þ ð31Þ H kf @T
  • @T
  • 70kf !h¼ À
  • Á ðhTis À hTib;f ÞÀ1 ¼ ð15Þ v 0 qf 2 @z
  • z¼wc @z
  • z¼0 17wc ð1 À eÞks 00 hs þ haðhb;f À hs Þ ¼ 0 ð32Þ HlfBoundary conditions are given as F ¼ 0; hs ¼ 0 for g ¼ 0 ð33Þ f f f s sffiffiffiffiffiffiffiffiffiffiffiffiffiffihui ¼ hv i ¼ 0; hTi ¼ hTi ¼ T w for y ¼ 0 ð16Þ 0 v 0 Hqf F 0 ¼ 1; hb;f ¼ 1; hs ¼ 0 for g ¼ ð34Þ f f @hTis lfhv i ¼ À v 0 ; hTi ¼ T in ; ¼ 0 for y ¼ H ð17Þ @y By solving Eq. (30), the following equations for the velocity distribu-Eqs. (8)–(10) can be further simplified. For this, it is assumed that tion are obtained.the aspect ratio of the channel is much higher than 1 and the solidconductivity is higher than the fluid conductivity. F¼g ð35Þ @W v 0 @W v0H; L ) wc ; ks ) kf ð18Þ u¼ ¼ x; v ¼À ¼À y ð36Þ @y H @x HEstimating the order of magnitude of each term appearing on the In general, Eqs. (31) and (32) cannot be solved analytically. How-right-hand side of Eqs. (8) and (9), we have ever, when we assume the fin efficiency is 1, the following equa- Uf Uf Uf tions for the temperature distribution can be obtained.lf ) lf ; lf ð19Þ   w2 c L2 H2 0 1eqhac H Vf Vf Vf f f v0lf ) lf ; lf 2 ð20Þ B g C w2 c L2 H hs ¼ 0; hb;f ¼ @qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA ð37ÞCombining Eqs. (10) and (11), we have v 0 Hqf =lf   !  y eqhac H @hTib;f f @hTib;f @hTis s b;f f f v0eqf cf hui þ hv if ¼ ð1 À eÞks hTi ¼ T w ; hTi ¼ ðT in À T w Þ þ Tw ð38Þ @x @y @x2 H @hTib;f @hTis @hTib;f Finally, the pressure drop between the inlet and the outlet of the þ ekf 2 þ ð1 À eÞks 2 þ ekf ð21Þ heat sink and the thermal resistance are obtained, respectively, @x @y @y2 from Eqs. (36) and (38).Estimating the order of magnitude of each term appearing on the Z L=2 Zright-hand side of Eq. (21), it follows that 1 1 H f Dpplate ¼ hpify¼H dx À hpix¼L=2 dy LÀL=2 H 0ks T kf T ks T kf T ! ! 2 ) 2 ; 2 ) ð22Þ 1 L2 2 elf H 1 L2 1L L H H2 ¼ qv 02 À þ v0 þ ð39Þ 10 H2 5 K 12 H2 3From the relations shown in Eqs. (19), (20), and (22), the simplified 0 0 !À1 11À1forms of Eqs. (8)–(10) are given as T w À T in @ 2@ haH AA Rplate ¼ ¼ eqf cf v 0 L 1 À 1 þ ð40Þ ! q eqf cf v 0 f f f6 @hui @hui @hpi elf f q huif þ hv if þ ¼À hui ð23Þ5 f @x @y @x K When the fin efficiency is not 1, the approximate value of the ther- ! mal resistance is given from Eq. (40) by using the fin model as f f f6 @hv i @hv i @hpi el q huif þ hv if þ ¼ À hv if ð24Þ follows:5 f @x @y @y K 0 0 ! !À1 11À1 @hTi b;f @hTi b;f geff haHeqf cf huif þ hv if ¼ haðhTis À hTib;f Þ ð25Þ Rplate ¼ @eqf cf v 0 L2 @1 À 1 þ AA ð41Þ @x @y eqf cf v 0
  • D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 3515 geff haHwhere geff is the fin efficiency. On the other hand, when eqf cf v 0 ( 1, Eq. (47) becomes  qffiffiffiffiffiffiffiffiffiffiffi ha tanh H ks ð1ÀeÞ T w À T in Rpin ¼ ¼ ðgeff haHpR2 ÞÀ1 0 ð51bÞgeff ¼ qffiffiffiffiffiffiffiffiffiffiffi ð42Þ q ha H ks ð1ÀeÞ Eqs. (51a) and (51b) correspond to low and high pumping-powerWhen geff haH ) 1, Eq. (41) becomes conditions, respectively. eqf cf v 0 The value of the present model lies in its simplicity. The pres-Rplate ¼ ðeqf cf v 0 L2 ÞÀ1 ð43aÞ sure drop and thermal resistance for the plate-fin heat sink are eas- geff haH ily obtained by solving Eqs. (39) and (41), respectively, togetherOn the other hand, when eqf cf v 0 ( 1, Eq. (41) becomes with Eqs. (44) and (45). On the contrary, the model suggested by 2 À1 Kondo et al. [6] consists of dozens of equations and requires te-Rplate ¼ ðgeff haHL Þ ð43bÞ dious calculation process. However, the applicability of the sug-Eqs. (43a) and (43b) correspond to low and high pumping-power gested model is limited because the permeability K and the heatconditions, respectively. transfer coefficient h are obtained from experimental data. The Eqs. (39) and (41) are derived without adopting correlations for present model is applicable forthe friction factor and the Nusselt number for a parallel flow. In-stead, it is assumed that the velocity and temperature profiles for 5  109 Pà Pump 1011 ; 1 Là 2 ð52Þthe fluid in the averaging direction are similar to those of a Poiseu- for which the experiment is conducted.ille flow between two infinite parallel plates, as shown in Eqs. (6)and (7). This assumption is reasonable but is not exact, because 4. Results and discussionthe velocity and temperature profiles for an impinging flow arenot exactly the same as those for the flow between two infinite The pressure drop and the thermal resistance obtained fromparallel plates. Therefore, the permeability K and the heat transfer experiments are compared with those from the proposed model.coefficient h presented in Eqs. (14) and (15) should be modified in As shown in Fig. 6, the experimental results of the pressure droporder to better predict the pressure drop and the thermal resis-tance. In the present study, the appropriate values for K and h 100are determined from the experimental data for the pressure dropand the thermal resistance with Eqs. (39) and (41), respectively. Fi-nally, the modified parameters obtained from experimental inves-tigations are given as follows. 10 Pressure drop (Pa) ew2 cK¼ ð44Þ 12ðð0:289 þ 16:0wÃ Þ þ ð0:00263 þ 0:133wà ÞRewc Þ c c 70kf à 2 À3h¼ ðð17:4wc À 63:4ðwc Þ Þ þ ð7:67  10 Þwà Rewc Þ Ã c ð45Þ 1 17wc Experimental data From the model wc=3.3mm3.2. Pin-fin heat sink wc=2.0mm 0.1 wc=1.44mm The fluid flow in the pin-fin heat sink is axisymmetric in nature wc=0.95mmrather than two-dimensional. In the present study, the pin-fin heat wc=0.50mmsink is modeled as an equivalent porous cylinder which has the 0.001 0.002 0.003same porosity, wetted surface, and base area. The top view for 3 Flow rate (m /s)the equivalent porous cylinder is shown in Fig. 2(b). By solvingEqs. (11) and (23)–(25) in cylindrical coordinates, the pressure (a) Plate-fin heat sinksdrop between the inlet and the outlet of the heat sink and the ther-mal resistance are given, respectively, as 100 ! ! 3 R2 2 elf H 1 R2 1Dppin ¼ qv 2 0 0 À þ v0 0 þ ð46Þ 40 H2 5 K 8 H2 3 0 0 10 !À1 11À1 Pressure drop (Pa) geff haH AARpin ¼ @eqf cf v 0 pR0 1 À 1 þ 2@ ð47Þ eqf cf v 0 1where  2 qffiffiffiffiffiffiffiffiffiffiffi Experimental data From the model ww 4ww wc=3.3mme¼1À ; ; R0 ¼ L2 =p a¼ ð48Þ wc=2.0mm ww þ wc ðww þ wc Þ2 0.1 wc=1.44mm ew2 c wc=0.95mmK¼ ð49Þ wc=0.50mm 12ðð0:232 þ 10:4wcÃ Þ þ ð0:000376 þ 0:0840wà ÞRe Þ c wc 70kf 0.001 0.002 0.003h¼ ðð9:96wà À 28:3ðwà Þ2 Þ þ ð6:41  10À4 ÞRewc Þ c c ð50Þ 3 17wc Flow rate (m /s) geff haHWhen eqf cf v 0 ) 1, Eq. (47) becomes (b) Pin-fin heat sinksRpin ¼ ðeqf cf v 0 pR2 ÞÀ1 0 ð51aÞ Fig. 6. Pressure drop (L = 40 mm, H = 25 mm, ww = 1 mm).
  • 3516 D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517are in close agreement with the predictions from the present mod- sults for the thermal resistance obtained from the experiments andel within a maximum error of 31% for the plate-fin heat sinks and the model match well within a maximum error of 20% for the22% for the pin-fin heat sinks, respectively. As shown in Fig. 7, re- plate-fin heat sinks and 13% for the pin-fin heat sinks, respectively. The close agreement between experiment and prediction is be- 10 cause the permeability and heat transfer coefficient are deter- Experimental data From the model mined from the experimental side of the work. From Figs. 6 and wc=3.3mm 7, it is concluded that Eqs. (44), (45), (49), and (50) are reasonable wc=2.0mm choices for the permeability and the heat transfer coefficient. wc=1.44mm Using the models for the plate-fin and pin-fin heat sinks, their Thermal resistance ( C/W) wc=0.95mm thermal resistances are calculated. Then, we numerically optimize wc=0.50mm o the dimensions for the plate-fin and pin-fin heat sinks by using the gradient descent algorithm. The optimized structures for which the thermal resistances are minimized under the fixed pumping power are then obtained, as listed in Table 2. The constraint for the fixed pumping power physically means that the power required to drive 1 the coolant through the heat sinks is fixed. Finally, by comparing the thermal resistances of the optimized plate-fin and pin-fin heat sinks, a contour map for an impinging flow configuration is pre- sented in Fig. 8. Fig. 8 depicts the ratio of the thermal resistances of the optimized plate-fin and pin-fin heat sinks Ropt,plate/Ropt,pin as 0.001 0.002 0.003 a function of dimensionless pumping power and dimensionless 3 length. This ratio was successfully used for comparing thermal per- Flow rate (m /s) formances of plate-fin and pin-fin heat sinks with parallel-flow (a) Plate-fin heat sinks configuration [18]. In Fig. 8, in the region where the ratio is above 1, the thermal resistance of the optimized pin-fin heat sink is smal- 10 ler than that of the optimized plate-fin heat sink. On the other Experimental data From the model hand, the thermal resistance of the optimized plate-fin heat sink wc=3.3mm is smaller than that of the optimized plate-fin heat sink when wc=2.0mm the ratio is below 1. wc=1.44mm The contour map for an impinging flow configuration indicates Thermal resistance ( C/W) wc=0.95mm the following: Optimized pin-fin heat sinks have lower thermal wc=0.50mm resistances than optimized plate-fin heat sinks only when the o dimensionless pumping power is small and the dimensionless length of heat sinks is large. In other words, the pin-fin heat sink shows better performance than the plate-fin heat sink as the pumping power per unit of heat sink volume decreases. It is worth 1 mentioning that Fig. 8, which describes the comparison of the ther- mal performance of the optimized plate-fin and pin-fin heat sinks, is helpful in determining the best designs for heat sinks. For the plate-fin heat sink, impinging air flows out only along the y-axis. On the contrary, air can flow out in every direction for 0.001 0.002 0.003 the pin-fin heat sink. Hence, the flow impedance of the optimized 3 pin-fin heat sink is typically lower than that of the optimized plate- Flow rate (m /s) fin heat sink, and the inlet velocity of the optimized pin-fin heat (b) Pin-fin heat sinks sink is higher than that of the optimized plate-fin heat sink under the fixed pumping-power condition, as shown in Fig. 9. From Eqs. Fig. 7. Thermal resistance (L = 40 mm, H = 25 mm, ww = 1 mm). (43a) and (51a), it can be shown that Ropt,plate/Ropt,pin is proportionalTable 2Comparison of geometries and thermal resistances for optimized heat sinks.Dimensionless Dimensionless Type of Optimum channel Optimum fin Optimum thermalpumping power length heat sink width (mm) thickness (mm) resistance (K/W) P pump Ll3 qÀ2 HÀ1 H wc,opt ww,opt Ropt3 Â 1010 1 Plate-fin 0.763 0.202 1.76 Pin-fin 0.716 0.807 1.936 Â 1010 1 Plate-fin 0.639 0.185 1.48 Pin-fin 0.578 0.677 1.65 109 Â 10 1 Plate-fin 0.576 0.175 1.34 Pin-fin 0.511 0.614 1.50 103 Â 10 2 Plate-fin 1.15 0.233 0.747 Pin-fin 1.09 1.10 0.7346 Â 1010 2 Plate-fin 0.977 0.217 0.617 Pin-fin 0.881 0.917 0.6209 Â 1010 2 Plate-fin 0.884 0.207 0.553 Pin-fin 0.779 0.830 0.562H = 25 mm, qf = 1.1774 kg/m3, lf = 1.8462 Â 10À5 kg/m s, cf = 1.0057 Â 103 J/kg K, kf = 0.02624 W/m K, ks = 171 W/m K.
  • D.-K. Kim et al. / International Journal of Heat and Mass Transfer 52 (2009) 3510–3517 3517 5. Conclusion In this paper, we compared thermal performances of plate-fin and pin-fin heat sinks subject to an impinging flow. Experimental investigations were performed for various flow rates and channel widths. From experimental data, we suggested a model based on the volume averaging method for predicting the pressure drop and the thermal resistance. Using the proposed model, thermal resistances of the optimized plate-fin and pin-fin heat sinks were compared under fixed pumping-power conditions. It was shown that optimized pin-fin heat sinks possess lower thermal resistances than optimized plate-fin heat sinks when dimensionless pumping power is small and the dimensionless length of heat sinks is large. On the contrary, the optimized plate-fin heat sinks have smaller thermal resistances when dimensionless pumping power is large and the dimensionless length of heat sinks is small. Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the National Research Lab. Program funded by the Ministry of Science and Technology (No.Fig. 8. Ratios of the thermal resistances of the optimized plate-fin and pin-fin heat M1060000022406J000022410).sinks (ks/kf = 6.4 Â 103, Pr = 0.707). References [1] S. Oktay, R.J. Hannemann, A. Bar-Cohen, High heat from a small package, Mech. Eng. 108 (3) (1986) 36–42. [2] A. Bar-Cohen, Thermal management of electric components with dielectric liquids, in: J.R. Lloyd, Y. Kurosaki (Eds.), Proceedings of ASME/JSME Thermal Engineering Joint Conference, vol. 2, 1996, pp. 15–39. [3] F.P. Incropera, Convection heat transfer in electronic equipment cooling, J. Heat Transfer 110 (1988) 1097–1111. [4] W. Nakayama, Thermal management of electronic equipment: a review of technology and research topics, Appl. Mech. Rev. 39 (12) (1986) 1847–1868. [5] C.R. 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