Experimental Investigation of Heat Transfer in Impingement Air Cooled Plate Fin Heat Sinks

Transcription

1 Zhipeng Duan Graduate Research Assistant Y. S. Muzychka Associate Professor Member ASME Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John s, Newfoundland, A1B 3X5, Canada Experimental Investigation of Transfer in Impingement Air Cooled Plate Fin Sinks Impingement cooling of plate fin heat sinks is examined. Experimental measurements of thermal performance were performed with four heat sinks of various impingement inlet widths, fin spacings, fin heights, and airflow velocities. The percent uncertainty in the measured thermal resistance was a maximum of 2.6% in the validation tests. Using a simple thermal resistance model based on developing laminar flow in rectangular channels, the actual mean heat transfer coefficients are obtained in order to develop a simple heat transfer model for the impingement plate fin heat sink system. The experimental results are combined into a dimensionless correlation for channel average Nusselt number Nu fl *,Pr. We use a dimensionless thermal developing flow length, L * =L/2/D h RePr, as the independent parameter. Results show that Nu1/ L *, similar to developing flow in parallel channels. The heat transfer model covers the practical operating range of most heat sinks, 0.01L * The accuracy of the heat transfer model was found to be within 11% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than The proposed heat transfer model may be used to predict the thermal performance of impingement air cooled plate fin heat sinks for design purposes. DOI: / Keywords: impingement flow, heat sink, thermal resistance, heat transfer 1 Introduction The heat dissipated in electronic components is increasing with advances in the performance of modern computers. Furthermore, the structure of these components is becoming ever more compact. Therefore, thermal management in the electronics environment is becoming increasingly difficult due to high heat load and dimensional constraints. Impingement air cooling with heat sinks is one attractive solution to these problems. Nottage 1 suggested that the heat sink fin and channel may be thought of as a type of heat exchanger in which the hot fluid stream is replaced with the solid fin. The counterflow arrangement has the greatest potential to achieve high effectiveness. This requires an airflow direction normal to the heat sink base; however, heat sinks with airflow directed normal to the base have received little attention. Since the impingement airflow in a heat sink is intermediate between counterflow and crossflow, its thermal performance is expected to exceed that of a crossflow heat sink. The present work is focused on the impingement flow plate fin geometry. The research objective is to develop a simple model for predicting heat transfer coefficient of plate fin heat sinks for impingement air cooling. Experimental measurements of thermal resistance are performed with heat sinks of various dimensions and airflow velocities to test the validity of the model. 2 Literature Review Teertstra et al. 2 developed an analytical model Eq. 1 to predict the average heat transfer rate for air cooled plate fin heat sinks in parallel flow. The Nusselt number is a function of the heat sink geometry and fluid velocity. The model is asymptotic between two limiting cases fully developed and developing flow in Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received August 17, 2005; final manuscript received November 23, Review conducted by Giulio Lorenzini. Paper presented at the 38th AIAA Thermophysics Conference, parallel plate channels. They validated the model with experiments and found 2.1% rms error and 6% maximum error: Nu b = Re * 3 b Pr * Reb Pr /3 2 where Nu b = h b k a Re b * =Re b b L 3 Reb * Copeland 3 suggested using a laminar flow heat transfer model for parallel flow in isothermal rectangular channels to model the heat sink. The Nusselt number data were taken from Shah and London 4 and fitted to an equation of the Churchill Usagi form. There have been few studies specifically on impingement cooling with heat sinks. The geometry of a heat sink in impingement flow is shown schematically in Fig. 1. In this flow arrangement the air enters at the top and exits out the sides, i.e., top inlet side exit TISE. Biskeborn et al. 5 reported experimental results for a TISE design using unique serpentine square pin fins. Sparrow et al. 6 performed heat transfer experiments on an isothermal TISE type single channel passage. Hilbert et al. 7 reported a novel laminar flow heat sink with two sets of triangular or trapezoidal shaped fins on the two inclined faces of a base. This design is efficient because the downward flow increases the air speed near the base of the fins where the fin temperatures are highest. By having the cool air enter at the center of the heat sink and exit at the sides, the length of the fins in the flow direction is reduced so that the heat transfer coefficient is increased. Sathe et al. 8 conducted a numerical and experimental study of a TISE plate fin heat sink that was notched in the center to reduce flow stagnation. Copeland 9 performed theoretical, experimental, and / Vol. 128, DECEMBER 2006 Copyright 2006 by ASME Transactions of the ASME

2 Fig. 1 Geometry of a plate fin heat sink in impingement flow numerical analyses on a manifold microchannel heat sink with multiple top inlets alternated with top outlets. At a given pumping power, increasing the number of inlet/outlet channels requires an increase in the volume flow rate, but permits higher flow velocity, provides lower thermal resistance. Kang and Holahan 10 developed a one-dimensional thermal resistance model of impingement air cooled plate fin heat sinks to understand how the heat sink performance depends on the different geometry variables. This simple model provides only an order of magnitude estimate of the thermal resistance. Holahan et al. 11 modeled the impingement flow field in the channel between the fins as a Hele Shaw flow. Conduction within the fin is modeled by superposition of a kernel function derived from the method of images. Convective heat transfer coefficients are adapted from existing parallel plate correlations. Kondo et al. 12 completed an experimental study and reported a zonal model of a thermal resistance prediction for impingement cooling heat sinks with plate fins. The impingement flow over the plate fins was divided into six regions. A set of correlations are proposed between the thermal resistance of the heat sink and the geometry of the plate fins. Dividing the heat sink into regions requires a large number of equations and makes the model very complicated. The accuracy of the predicted thermal resistance was found to be within ±25% of the experimental data. Sathe et al. 13 presented a computational analysis for three dimensional flow and heat transfer in the IBM 4381 heat sink. Biber 14 carried out a numerical study to determine the thermal performance of a single isothermal channel with variable width impingement flow. Biber 14 numerically studied many different combinations of channel parameters and presented the correlation Eq. 2 for channel average Nusselt number Re based on impingement inlet velocity Nu = 6.05x 0.22 t 3/ x 1.05 t 3/4 4/3 2 where x t = L D h V ind h 2H s = L D h V chd h = L D h Re Dh Sasao et al. 15 developed a numerical method for simulating impingement airflow and heat transfer in plate fin heat sinks. Saini and Webb 16 presented a modified Biber 14 model and validated this model by experiments. Recently, a simple impingement flow thermal resistance model based on developing laminar flow in rectangular channels has been proposed by the authors 17. Fig. 2 Thermal resistance circuit module surface temperature T s to ambient temperature T amb is depicted in Fig. 2. generated from an electronic module can be approximated as constant heat flux over area A s. The electronic module surface area A s is usually too small to dissipate the heat, so a heat sink is typically required. Since heat sink base area A b is usually larger than A s, thermal spreading resistance R sp occurs when heat leaves a heat source of finite dimensions A s and enters into a larger region A b. flux is assumed uniform over the base of fins. is conducted from the base to the tip of the fins and it is convected from the fin surface R fins. is also convected from the prime surface the exposed portion of the base R bare. The thermal resistance from the fins and prime surface to the ambient air is the total convection resistance of heat sink. The heat sink total convection resistance is usually the dominant thermal resistance in the thermal circuit for the electronic module cooling. Figure 2 illustrates the thermal circuit corresponding to the heat transfer from a plate fin heat sink. One-dimensional transfer in the radial direction is assumed. The total thermal resistance is 3 Theoretical Analysis Sink Thermal Circuit Analysis. sink models typically assume a uniform airflow at the heat sink inlet. The flow in typical plate fin heat sinks used in cooling electronic modules is laminar, because of the small fin spacing and low airflow rates. The thermal resistance circuit for heat flow from the electronic Fig. 3 Schematic showing the effective heat transfer coefficient Journal of Electronic Packaging DECEMBER 2006, Vol. 128 / 413

3 Fig. 4 Impingement flow geometric configuration R total = T s T amb Q 3 Fig. 5 Proposed solution behaviour of asymptotes The total thermal resistance may be modeled by considering the heat sink as bare plate with effective film coefficient as shown in Fig. 3. The thermal resistance is now R total = R ID + R sp 4 where R 1D is the one-dimensional resistance given by R ID = t b ka b h eff A b The thermal spreading resistance will depend on several geometric and thermal parameters R sp = fl,w,l s,w s,t b,k,h eff 6 The spreading resistance vanishes when the heat flux is distributed uniformily over the entire heat sink base surface. Lee et al. 18 developed an analytical model for predicting thermal spreading resistance in a circular plate with a uniform heat flux on one surface and a convective boundary condition over the other surface. Yovanovich et al. 19 reviewed the previously published spreading resistance models and presented simple correlation equations for ease of computation. Yovanovich et al. 20 presented the thermal spreading resistance of an isoflux, rectangular heat source on a two layer rectangular flux channel with convective or conductive boundary conditions at one boundary. The following expression developed by Yovanovich et al. 20 is only used in the data reduction to account for spreading resistance effects for the present research: 8 R sp = kl 2 s LW m=1 where 8 + kw 2 s LW n=1 sin 2 m L s /2 m kl 2 s W 2 s LW m=1 sin 2 n W s /2 n 3 n=1 m n sin 2 m L s /2sin 2 n W s /2 2 m 2 m,n n m,n 7 = e2t b +1 1 e 2t b h eff /k e 2t b 1 1+e 2t b 8 h eff /k In all summations is evaluated in each series using = m, n, and m,n. The general expression for spreading resistance consists of three terms. The single summations account for twodimensional spreading in the x and y directions, respectively, and the double summation term accounts for three-dimensional spreading from the rectangular heat source. The eigenvalues are m =2m/L, n =2n/W, m,n = m 2 + n 2 1/2. The eigenvalues m and n, corresponding to the two strip solutions, depend on the flux channel dimensions and the indices m and n, respectively. The eigenvalues m,n for the rectangular solution are functions of the other two eigenvalues. Spreading resistance is important in heat sink applications. The value of the effective heat transfer coefficient h eff accounts for both the heat transfer coefficient on the fin surface and the increased surface area, as shown in Fig. 3 1 h eff = A b R sin k The overall heat sink resistance is given by R sin k = 1 Nf R fin + hnf 1bL + h rad A rad Thus, the total heat resistance can be expressed as 9 10 R total = R sp + R base + R sin k 11 Then, the actual heat sink channel mean heat transfer coefficient, h, in Eq. 10 is solved numerically from the experimental measurements for R total. The data are then plotted versus a dimensionless length in the form of an isothermal Nusselt number. These results are then compared with an approximate analytical model and existing models in the literature. Approximate Transfer Analysis. We need only study one half of a single channel of the heat sink since the flow field and temperature contours on the other half are a mirror image due to symmetry, as illustrated in Fig. 4. The R total is known from experimental measurements, therefore, the actual heat sink channel heat transfer coefficient, h, can be obtained from Eq. 11. We can use a dimensionless thermal developing flow length, L * =L/2/D h Re Pr, as the independent parameter. For fully developed flow L *, the air temperature rise nearly equals the channel wall temperature rise. For this condition, it can be shown that from energy balance q = ṁc p T s T i =2V ch bhc p T s T i 12 where q is the total heat transfer rate from a single channel. The Nusselt number obeys a relationship of the type 414 / Vol. 128, DECEMBER 2006 Transactions of the ASME

4 Fig. 6 Flow field at midplane of interfin channel for s/l\0 qd h Nu Dh k a 2HLT s T i 1 L/2 4 Re Dh Pr D h 1 4L * 13 This approximate asymptotic limit is valid for heat sinks with very small fin to fin spacing and/or very long channels when the impingement jet is narrow. In the case of a heat sink with full impingement coverage, the effect of sink length becomes much less an issue since fresh cooling air is always entering the system along channel length. Clearly, fin spacing becomes more of an issue in this case. For narrow jets, both flow length and channel spacing are important in determining if fully developed flow results, i.e., bulk temperature reaching sink base temperature. For very small distances from the rectangular duct inlet, the effect of curvature on the boundary layer development is negligible. Thus, it should approach the classical isothermal flat plate solution for developing flow in the entrance region of rectangular ducts L * 0 Nu L Re 1/2 Pr 1/3 14 The Nusselt number obeys a relationship of the type for developing flow Nu Dh V chl Assuming Pr=0.707 for air 1/2 Pr 1/3D h L 2Pr 1/6 Re 1/2 D h Pr D h L/2 Nu Dh L * 1 2 L * Figure 5 shows the behavior of two asymptotes for fully developed and developing flow. From the proposed solution behavior, we can predict a smooth transition region. The flow fields at midplane of interfin channel for s/l 0 and s/l are illustrated in Figs. 6 and 7, respectively. Impingement flow in a plate fin heat sink is essentially a simultaneously developing hydraulic and thermal boundary layer problem in rectangular ducts. The flow may become fully developed if the heat sink channel is sufficiently long in the flow direction for narrow jets or in heat sinks with with small fin spacings. However, this is very unlikely for most electronic cooling applications. Fig. 8 Schematic of the thermal tester 4 Experimental Facility Figure 8 shows a schematic of the thermal tester. Two electrical heaters were used to simulate an electronic module. These electrical heaters were put into a 76.2 mm square cross section 12 mm high copper block. Insulation was applied to the bottom and the periphery of the copper block. The heat loss was estimated to be less than 5% of the heat input, and a correction was applied in the data reduction. The heat input to the heat sink was determined at the time of test by the product of measured voltage and current UI corrected for ambient heat loss Q loss. Five copper-constantan thermocouples were attached to the upper surface of the copper block to measure the upper surface average temperature. Another five thermocouples were attached to the lower surface of copper block to measure the lower surface average temperature. The upper and lower surfaces are divided into four equal areas. The five thermocouples are placed at the centroids of the four equal areas and the center of the whole surface, respectively. The mean temperature of the heat source was represented as the average of the ten readings of thermocouples. The ambient temperature was measured with three other thermocouples. The three thermocouple readings were averaged to give the average ambient temperature. The measurement includes the spreading resistance. Tests were conducted for four heat sink geometries for impingement flow. The dimensions of the apparatus are based on heat sink length and width. sink thermal resistance data were taken for different flow rate conditions and different impingement inlet widths. For each heat sink, the experimental measurements were carried out at seven different velocities in the plenum chamber V d, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 m/s, and six different impingement inlet widths, 5% L, 10% L, 25% L, 50% L, 75% L, 100% L, respectively. In total, 168 data points were collected for thermal resistance. The details of the heat sinks used for the tests are summarized in Table 1. The uncertainty analysis for the test data was conducted using the root sum square method described in Moffat 21 and Holman 22. The uncertainty in the total measured thermal resistance Table 1 Geometry of the heat sinks used in the experiments Dimension sink No. 1 sink No. 2 sink No. 3 sink No. 4 Fig. 7 Flow field at midplane of interfin channel for s/l\1 L mm W mm t b mm t mm b mm H mm N f Journal of Electronic Packaging DECEMBER 2006, Vol. 128 / 415

5 Fig. 9 Experimental Nusselt number data and model R total was a maximum of 2.6% for the validation test data. Further details on uncertainty analysis, thermal resistance analysis and experimental data can be found in Duan Results and Discussion The R total is calculated from Eq. 3 based on experimental measurements; therefore, the actual heat sink channel mean heat transfer coefficient, h, can be obtained from Eq. 11. The experimental data points of four actual heat sinks and other published experimental data points are fitted to a simple correlation to account for s/l effect s L Nu Dh = 17 L * which assumes air as the working fluid. The model fits the experimental data within 11%. Higher order fits, i.e., s/l 2 do not provide further improvement. We may also use a simpler form which is not dependent on s/l Nu Dh = L * The simpler model fits the experimental data within 18%. This model is also very close to Eq. 16, which supports the belief that heat transfer rates in impingement flow are controlled by boundary layer type behavior. The data and model are shown in Fig. 9. The developed heat transfer model covers the practical operating range of this type heat sinks. It is possible to develop an asymptotic model for fully developed and developing flow if further experimental data points in fully developed region are obtained. However, this is not practical for impingement flow cooling of parallel plate heat sinks, since it is essentially a developing flow problem. Figure 10 demonstrates the comparison between the proposed model and Biber 14 model. The differences between proposed model and Biber model increase with decrease of L *. The Biber model does not consider the effects of impingement inlet width s/ L. That means Nusselt number is constant when impingement inlet width changes 0%s/L100% for the same flow rate. Figure 11 shows the comparison between the proposed model and Teertstra et al. 2 model for parallel flow. The differences between proposed model and Teertstra et al. model increase with Fig. 10 Comparison for Biber see Ref. 14 model Fig. 11 Comparison for Teertstra et al. see Ref. 2 model 416 / Vol. 128, DECEMBER 2006 Transactions of the ASME

6 increase of L *. They should converge at lower values of L *.As shown in Fig. 11, the impingement flow transition point to fully developed flow is larger than normal duct parallel flow transition point L * In addition, although the impingement zone is small relative to fin surface area, impingement zone is associated with enhanced heat transfer rates. Therefore, the thermal performance of air cooled plate fin heat sinks in impingement flow exceeds that of similar heat sinks in parallel flow. Although the heat transfer prediction algorithm is based on a very simple model, it succeeds in representing the trends of the experimental values fairly well. The agreement is quite satisfying in view of the simplicity of the model. Given the uncertainties of thermal resistance measurements, the model is validated reasonably well. 6 Conclusion This paper investigated thermal resistance and heat transfer of impingement air cooled plate fin heat sinks for a variety of impingement inlet widths, fin spacings, and fin heights. The simple heat transfer model is developed for the low Reynolds number laminar flow and heat transfer in the interfin channels of impingement flow plate fin heat sinks, since the expected practical operating range of this type of high performance heat sink would typically produce flows in the range of Re1200. The accuracy range of the simple model was established by comparison with experimental measurements of four actual heat sinks and other published experimental data. The heat transfer model covers the practical operating range of this type heat sink, 0.01L * The accuracy of the heat transfer model was found to be within 11% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than The developed heat transfer model may be used to predict the thermal performance of impingement air cooled plate fin heat sink for design purposes. The present model provides an accurate means to predict the mean heat transfer coefficient for systems utilizing impingement flow. Whereas current models for parallel flow only provide accuracy in the limit of narrow impingement zones, while models for wide impingement zones fail to capture the effect of jet width. Acknowledgment The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada NSERC, and R-Theta Inc. for providing heat sinks for the present study. Nomenclature A b base plate area, m 2 A s heat source area, m 2 b fin spacing, m c p specific heat at constant pressure, J/kg K H fin height, m h heat transfer coefficient, W/m 2 K h eff effective heat transfer coefficient, W/m 2 K h rad radiation heat transfer coefficient, W/m 2 K I current, A k thermal conductivity of heat sink, W/m K k a thermal conductivity of air, W/m K L length of heat sink base, m L s length of heat source, m L * dimensionless thermal developing flow length N f number of fins Nu Nusselt number Pr Prandtl number q total heat transfer rate over a single channel, W Q total electrical power input, W Q loss ambient heat loss, W R thermal resistance, K/W Re Dh channel Reynolds number, =D h V ch / R 1D one-dimensional thermal resistance, K/W R bare prime surface thermal resistance, K/W R base conduction thermal resistance of heat sink base, K/W R fins fin surface thermal resistance, K/W R rad radiation thermal resistance, K/W R sink overall heat sink thermal resistance, K/W R sp thermal spreading resistance, K/W R total total thermal resistance, K/W s impingement inlet width, m t fin thickness, m t b base plate thickness, m T temperature rise, K T amb ambient temperature, K T s heat source temperature, K T i inlet air temperature, K T source mean heat source temperature, K T base mean heat sink base temperature, K U voltage, V V ch channel average velocity, m/s V in impingement inlet velocity, m/s W width of heat sink base, m W s width of heat source, m Greek Symbols m,n eigenvalues, = 2 m + 2 n 1/2 m eigenvalues, =m/c dummy variable, m 1 n eigenvalues, =n/d density of air, kg/m 3 spreading function References 1 Nottage, H. 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