Pressure Drop of Impingement Air Cooled Plate Fin Heat Sinks

Zhipeng Duan Graduate Research Assistant e-mail: zpduan@engr.mun.ca Y. S. Muzychka Associate Professor Mem. ASME e-mail: yuri@engr.mun.ca Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John s, Newfoundland, A1B 3X5, Canada Pressure Drop of Impingement Air Cooled Plate Fin Sinks The performance of impingement air cooled plate fin heat sinks differs significantly from that of parallel flow plate fin heat sinks. A simple impingement flow pressure drop model based on developing laminar flow in rectangular channels is proposed. The model is developed from simple momentum balance and utilizes fundamental solutions from fluid dynamics to predict its constitutive components. To test the validity of the model, experimental measurements of pressure drop are performed with heat sinks of various impingement inlet widths, fin spacings, fin heights, and airflow velocities. The accuracy of the pressure drop model was found to be within 0% of the experimental data taken on four heat sinks and other experimental data from the published literature at channel Reynolds numbers less than 100. The simple model is suitable for impingement air cooled plate fin heat sinks parametric design studies. DOI: 10.1115/1.71094 Keywords: impingement flow, heat sink, pressure drop, plate fin 1 Introduction The heat dissipated in electronic components is increasing with advances in the performance of modern computers. 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 flowstream direction relative to heat flow direction plays a significant role in determining the heat transfer effectiveness of a fin-fluid arrangement. Three basic one-dimensional heat exchanger flow arrangements are counterflow, crossflow, and parallelflow. The counterflow arrangement has the greatest potential to achieve high effectiveness. This requires an airflow direction normal to the heat sink base. 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 objectives are to develop a robust model for predicting pressure drop of plate fin heat sinks for impingement air cooling. To test the validity of the model, experimental measurements of pressure drop are performed with heat sinks of various dimensions and flow velocities. Literature Review Culham and Muzychka proposed a heat sink model in parallel flow using the apparent friction factor model developed by Muzychka and Yovanovich 3. The friction model is asymptotic between a developing and fully developed flow. Muzychka and Yovanovich 3 validated the model with most of the developing flow data and found the estimation error was within ±1% for a wide range of duct shapes but within ±3% for the rectangular channel. Copeland 4 suggested using a laminar flow pressure drop model for parallel flow in isothermal rectangular channels to model the heat sink. The friction factor data for developing laminar flow were taken from Shah and London 5 and fitted to an equation of the Churchill Usagi form. Contributed by the Electrical and Electronic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received March 1, 006; final manuscript received July 6, 006. Review conducted by Bernard Courtois. Paper presented at the Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 004. Although there has been a wide range of research reporting on impingement air cooling, 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. 6 reported experimental results for a TISE design using unique serpentine square pin fins. Sparrow et al. 7 performed heat transfer experiments on an isothermal TISE type single channel passage. A novel laminar-flow heat sink with two sets of triangular or trapezoidal shaped fins on the two inclined faces of a base has been reported by Hilbert et al. 8. The impingement air divides into two streams which flow between the two sets of fins in a direction that is transverse to the direction of heat transport in the fins. 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 frictional pressure drop is decreased. Sathe et al. 9 conducted a numerical and experimental study of a TISE plate fin heat sink that was notched in the center to reduce flow stagnation. It was found that pressure drop is reduced by cutting the fins in the central impingement zone without losing the heat transfer. Copeland 10 performed theoretical, experimental, and 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, and produces significantly lower pressure drop. Kang and Holahan 11 developed a one-dimensional pressure drop model of impingement air cooled plate fin heat sinks to understand how the heat sink performance depends on the different geometry variables. Holahan et al. 1 modeled the impingement flow field in the channel between the fins as a Hele Shaw flow. Kondo et al. 13 reported on a semi-empirical development of a pressure drop prediction for impingement cooling of heat sinks with plate fins. The flow region is divided into five parts. Each part is modeled by different pressure drop models. These predictions agree with the experimental data within ±30%. Dividing the heat sink into parts requires a large number of equations and makes the model very complicated. Sathe et al. 14 presented a computational analysis for three-dimensional flow and heat transfer in the IBM 4381 heat sink. Biber 15 carried out a numerical study to determine the pressure drop of a single isothermal channel with variable width impingement flow. Biber numerically studied many different com- 190 / Vol. 19, JUNE 007 Copyright 007 by ASME Transactions of the ASME

1 Impingement flow modeling 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 or with small fin spacing, however, this is very unlikely for electronic cooling application heat sinks. The apparent friction factor, f app, for a rectangular channel may be computed using a form of the model developed by Muzychka and Yovanovich 3 for developing laminar flow f app Re Dh = 3.44 1/ + f Re Dh L * Fig. 1 Geometry of a plate fin heat sink in impingement flow binations of channel parameters and presented the correlation for pressure loss coefficient in an impingement flow channel. This model was not validated experimentally. Sasao et al. 16 developed a numerical method for simulating impingement air flow in plate fin heat sinks. Saini and Webb 17 presented a modified Biber 15 model and validated this model by experiments. The predicted pressure drop is 13 31% lower than the experimental data, and underprediction increases with increasing flow rate. 3 Theoretical Analysis The pressure drop model for the impingement flow plate fin heat sink will be based on correlations for laminar duct flows, which are essentially one dimensional. We need only study one half of the heat sink since the flow field and pressure fields on the other half are a mirror image due to symmetry. One half of the impingement cooling heat sink channel is considered as two connected rectangular channels; one is vertical and the other is horizontal. Their effective lengths are L eff1 and L eff, as illustrated in Fig.. This consideration is justifiable if one imagines a typical streamline, for example near the middle of the impingement slot. This streamline length is better approximated by the L-shaped path of height 0.5H and length 0.5L 0.5s after a 90 deg turn. Summing all of the frictional and dynamic losses, the total pressure drop model function is given in terms of Bernoulli s equation L eff1 P = K c + K 90 +4f app1 D h1 4H L eff s +4f app + K D h e 1 V ch Fig. Impingement flow geometric configuration L * L = 3 D h Re Dh The f Re Dh term is the fully developed flow friction factor Reynolds number group and depends on b/h only for laminar flow. A single term from the exact series is suggested by Muzychka and Yovanovich 18 4 f Re Dh = 1+ H b 1 19b 4 H tanh 5 H b They validated the model with most of the available developing flow data and found the estimation error was within ±3% for the rectangular channel. The 90 deg bend pressure loss coefficient data is taken from Idelchik 19 and curve fitted to the following relation for 0 H/s 1.4 10.87 K 90 = 3.64 9.15 H s + H 4.9 s H 5 s 3 If H/s 1.4, The expression of 90 deg bend pressure loss coefficient from Kondo et al. 13 can be used K 90 = 0.5 1+V ch/v ch1 6 For the inlet and exit pressure losses for a heat sink, Kays and London 0 provide loss coefficients in the form P=K V / as a function of the ratio of free-flow area to frontal area =b/ b+t. The graphs for laminar flow in Ref. 0 have been curve fit here for laminar flow K c = 0.4 1 + 0.4 7 4 Experimental Facility K e = 1 0.4 The flow bench was designed to measure the air velocity and pressure drop for different airflow rates. A schematic of the flow bench is presented in Fig. 3. The air was discharged from a blower into the test section. The height of the test section could be varied to allow the use of different fin height heat sinks. Furthermore, the impingement inlet width of the test section could be adjusted from 0% to 100% of the heat sink length. Air entering the test section was first passed through two screens before reaching a plenum chamber. The square crosssection plenum chamber had dimension of 15.4 mm. The screens were employed to rectify the velocity distribution. The channel cross-sectional area was divided into nine equal areas. The TSI air velocity transducer, with % uncertainty in velocity measurement, was utilized to measure airflow velocities at the centroids of the nine equal areas. The mean velocity in the plenum chamber was represented as the average of the nine readings in order to reduce the measurement error of the flow velocity. The impingement inlet velocity V inlet and outlet velocity V outlet can be calculated from mass conservation. The exit air from the plenum chamber passes through an inverted trapezoid duct which can be used to adjust impingement inlet width and impinges onto the heat sink. The pressure difference between the impingement inlet static pressure P inlet and the heat sink outlet static pressure P outlet is measured with a calibrated differential pressure transmitter. 8 Journal of Electronic Packaging JUNE 007, Vol. 19 / 191

Fig. 3 test Schematic of experimental facility for impingement flow Fig. 4 Pressure drop comparison for Sink #1 The experimental total air pressure drop for impingement flow can be found in terms of Bernoulli s equation P = P inlet P outlet + 1 V inlet V outlet Tests were conducted for four heat sink geometries for impingement flow. sink pressure drop 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 m/s, 0.5 m/s, 0.6 m/s, 0.7 m/s, 0.8 m/s, 0.9 m/s, and 1.0 m/s, and six different impingement inlet widths, 5% L, 10% L, 5% L, 50%L, 75%L, and 100%L, respectively. 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 1 and Holman. The uncertainties in pressure drop measurement were 19% for minimum P=1.8 Pa and 0.7% for maximum P =60.18 Pa, respectively. Further details on uncertainty analysis and experimental data can be found in Duan 3. 9 Figure 8 shows the comparison between the Saini and Webb 17 experimental data and the analytical model predictions of total pressure drop. These test data are consistently lower than the predictions. Overall, the trend is very good. Figure 9 demonstrates the comparison between the Holahan et al. 1 experimental data and the analytical model predictions of total pressure drop. The experimental data and predictions are in excellent agreement. It was found that all experimental data errors are within ±0% with a rms error of 11.5%. Although the pressure drop 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 pressure drop measurements, the model is reasonably well validated. 6 Conclusion This paper investigated pressure drop of impingement air cooled plate fin heat sinks for a variety of impingement inlet 5 Results and Discussion The model is validated with the experimental data taken on four heat sinks and other experimental data from the published literature. Figures 4 7 show the measured and model predicted air pressure drop of Sinks #1 #4 for different impingement inlet widths. The highest Reynolds number in the experimental data was 170, which is in the laminar regime. The differences between predictions and test results increase slightly with increasing flow rate. Table 1 Geometry of the heat sinks used in the experiments Dimension Sink #1 Sink # Sink #3 Sink #4 L mm 17 17 17 17 W mm 1 1 116 116 t b mm 1.7 1.7 1.7 1.7 t mm 1. 1. 1. 1. b mm.5.5 4.7 4.7 H mm 6.5 50.0 34.0 50.0 N f 36 36 Fig. 5 Pressure drop comparison for Sink # 19 / Vol. 19, JUNE 007 Transactions of the ASME

Fig. 6 Pressure drop comparison for Sink #3 Fig. 8 data Pressure drop comparison for Saini and Webb 17 test widths, fin spacings, and fin heights. The analytic model is developed for the low Reynolds number laminar flow 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 Re 100. The accuracy range of the analytical model was established by comparison with experimental measurements of four actual heat sinks and other published experimental data. The analytical pressure drop model predictions agree with experimentally measured values within ±0% and 11.5% rms over a Reynolds number range 300 Re 100. The pressure drop increases with a decrease in impingement inlet width for the same flow rate. The pressure drop model developed may be suitable for impingement air cooled plate fin heat sinks parametric design studies. 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 b fin spacing, m D h hydraulic diameter, m f, f app friction factor and apparent friction factor, respectively H fin height, m K c,k e contraction and expansion loss coefficient, respectively K 90 loss coefficient due to 90 deg bend in airflow L length of heat sink base, m Fig. 7 Pressure drop comparison for Sink #4 Fig. 9 data Pressure drop comparison for Holahan et al. 1 test Journal of Electronic Packaging JUNE 007, Vol. 19 / 193

L * dimensionless flow length L eff effective length, m N f number of fins P inlet static pressure of heat sink impingement inlet, Pa P outlet static pressure of heat sink outlet, Pa P pressure drop, Pa Re Dh channel Reynolds number, D h V ch / s impingement inlet width, m t fin thickness, m t b base plate thickness, m V ch channel average velocity, m/s V d velocity in the plenum chamber, m/s V inlet heat sink impingement inlet velocity, m/s V outlet heat sink outlet velocity, m/s W width of heat sink base, m Greek symbols density of air, kg/m 3 fraction of frontal free flow area Subscripts 1 based upon vertical channel based upon horizontal channel ch channel References 1 Nottage, H. B., 1945, Efficiency of Extended Surface, Trans. ASME, 67, pp. 61 631. Culham, J. R., and Muzychka, Y. S., 001, Optimization of Plate Fin Sinks Using Entropy Generation Minimization, IEEE Trans. Compon. Packag. Technol., 4, pp. 159 165. 3 Muzychka, Y. S., and Yovanovich, M. M., 1998, Modelling Friction Factors in Non-Circular Ducts for Developing Laminar Flow, Proceedings nd AIAA Theoretical Fluid Mechanics Meetings, Albuquerque, NM, Paper No. AIAA 98-49. 4 Copeland, D., 000, Optimization of Parallel Plate Sinks for Forced Convection, Proceedings 16th Semi-Therm Symposium, San Jose, CA, pp. 66 7. 5 Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic, New York. 6 Biskeborn, R. G., Horvath, J. L., and Hultmark, E. B., 1984, Integral Cap Sink Assembly for IBM 4381 Processor, Proceedings International Electronics Packaging Conference, Baltimore, MD, pp. 468 474. 7 Sparrow, E. M., Stryker, P. C., and Altemani, A. C., 1985, Transfer and Pressure Drop in Flow Passages That Are Open Along Their Lateral Edges, Int. J. Mass Transfer, 8 4, pp. 731 740. 8 Hilbert, C., Sommerfeldt, S., Gupta, O., and Herrell, D. J., 1990, High Performance Micro-Channel Air Cooling, Proceedings 6th IEEE Semiconductor Thermal and Temperature Measurement Symposium, Scottsdale, AZ, pp. 108 113. 9 Sathe, S. B., Sammakia, B. G., Wong, A. C., and Mahaney, H. V., 1995, A Numerical Study of A High Performance Air Cooled Impingement Sink, Proceedings ASME HTD-Vol. 303, National Transfer Conference, Portland, OR, Vol. 1, pp. 43 54. 10 Copeland, D., 1995, Manifold Microchannel Sinks: Numerical Analysis, Proceedings ASME HTD. 319/EEP Cooling and Thermal Design of Electronic Systems, San Francisco, CA, Vol. 15, pp. 111 116. 11 Kang, S. S., and Holahan, M. F., 1995, Impingement Sinks for Air Cooled High Power Electronic Modules, Proceedings ASME HTD- National Transfer Conference, Portland, OR, Vol. 1, pp. 139 146. 1 Holahan, M. F., Kang, S. S., and Bar-Cohen, A. 1996, A Flowstream Based Analytical Model for Design of Parallel Plate sinks, Proceedings ASME HTD-Vol. 39, National Transfer Conference, Houston, TX, Vol. 7, pp. 63 71. 13 Kondo, Y., and Matsuhima, H., 1995, Prediction Algorithm of Pressure Drop for Impingement Cooling of Sinks With Longitudinal Fins, Transfer-Jpn. Res., 4 4, pp. 315 37. 14 Sathe, S. B., Kelkar, K. M., Karki, K. C., Tai, C., Lami, C., and Patankar, S. V., 1997, Numerical Prediction of Flow and Transfer in an Impingement Sink, J. Electron. Packag., 119 1, pp. 58 63. 15 Biber, C. R., 1997. Pressure Drop and Transfer in an Isothermal Channel With Impinging Flow, IEEE Trans. Compon., Packag. Manuf. Technol., Part A, 0 4, pp. 458 46. 16 Sasao, K., Honma, M., Nishihara, A., and Atarashi, T., 1999, Numerical Analysis of Impinging Air Flow and Transfer in Plate Fin Type Sinks, Proceedings ASME EEP-Vol. 6-1, Advances in Electronic Packaging, Maui, HI, Vol. 1, pp. 493 499. 17 Saini, M., and Webb, R. L., 00, Validation of Models for Air Cooled Plane Fin Sinks Used in Computer Cooling, Proceedings 8th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, San Diego, CA, pp. 43 50. 18 Muzychka, Y. S., and Yovanovich, M. M., 00, Laminar Flow Friction and Transfer in Non-Circular Ducts and Channels: Part I-Hydrodynamic Problem, Compact Exchangers, A Festschrift on the 60th Birthday of Ramesh K. Shah, Grenoble, France, pp. 13 130. 19 Idelchik, I. E., 1993, Handbook of Hydraulic Resistance, 3rd ed., CRC, Boca Raton, FL. 0 Kays, W. M., and London, A. L., 1984, Compact Exchangers, 3rd ed., McGraw Hill, New York. 1 Moffat, R. J., 1988, Describing the Uncertainties in Experimental Results, Exp. Therm. Fluid Sci., 1, pp. 3 17. Holman, J. P., 1994, Experimental Methods for Engineers, 6th ed., McGraw Hill, New York. 3 Duan, Z. P., 003, Impingement Air Cooled Plate Fin Sinks, M.Eng. thesis, Memorial University of Newfoundland, St. John s, Newfoundland. 194 / Vol. 19, JUNE 007 Transactions of the ASME