Conjugate heat transfer from an electronic module package cooled by air in a rectangular duct

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1 Conjugate heat transfer from an electronic module package cooled by air in a rectangular duct Hideo Yoshino a, Motoo Fujii b, Xing Zhang b, Takuji Takeuchi a, and Souichi Toyomasu a a) Fujitsu Kyushu System Engineering Limited, Fukuoka , Japan b) Institute of Advanced Material Study, Kyushu University, Kasuga , Japan Experimental and numerical studies are carried out for the conjugate heat transfer of an electronic module package cooled by air. Firstly, the heat conduction experiment was conducted to obtain the surface temperature profiles and to estimate the total conductive resistance and natural convection heat transfer rate to air from the outer wall of duct, where the same type two module packages were fixed opposite at the bottom and top inner walls of duct and glass wool was filled inside the gap. The measured temperature profiles were compared with those obtained by the corresponding numerical simulations and the heat transfer coefficient at the outer wall of duct was estimated. Secondly, the convective heat transfer experiment was done for a single module package attached on the bottom wall of the duct by switching three fans on and off in various combinations. As for the surface temperature profiles, the numerical results agree well with the experimental ones. When the thermal conductivity of printed circuit board is varied, however, the heat transfer coefficients based on the conventional definition could not be summarized with a unique correlation due to the effects of conjugate heat transfer. Introducing an effective heat transfer area has solved the problems and a unique correlation is proposed. Numerical simulations also clarified the effect of thermal conductivity ratio on the non-dimensional effective heat transfer area, and further the heat transfer characteristics when two or more module packages are set in the same duct. 1. Introduction Recently, conjugate heat transfer in microelectronic equipment has received considerable attention from heat transfer researchers, because of rapid increase in power dissipation of LSI chips and downsizing of electronic devices. Ramadhyani et al. (1985) and Sugavanam et al. (1994) reported the results of numerical analysis on the conjugate heat transfer from two-dimensional flush-mounted heat sources to laminar flow in the channel. Incropera et al. (1986) and Ortega et al. (1994) did experiments for two-dimensional flush-mounted heat sources. Nakayama and Park (1996) did both the numerical simulations and experiments. They concentrated their attention on the heat transfer from the floor area near the surface-mounted block and discussed how to develop a specific prediction method of the conjugate heat transfer. Zhang et al. (1999) discussed how to define an effective heat transfer area to solve the problems of the conjugate heat transfer from small heat sources mounted on a conductive wall. Fujii et al. (2001) further summarized their experimental results of the conjugate heat transfer behavior of an electronic chip module cooled by air, based on the effective heat transfer area. The present paper describes the experimental and numerical studies on the conjugate heat transfer of a printed circuit board (PCB) with an electronic module packages cooled by air in a rectangular duct. Two experiments, heat conduction and heat convection, and corresponding numerical simulations with a commercial CFD code CFdesign have been performed. For the heat conduction, the surface temperatures of the module package and heat losses to air from the outer walls of duct were measured. From the corresponding numerical simulations, was estimated the value of heat transfer coefficient for the outer walls of duct, which could be used as the boundary conditions for the successive calculations. For the heat convection, the surface temperature profiles were measured at various heat rates and air velocities. The numerical simulations under the corresponding conditions agree well with the experiments as for the temperature profiles. The computational code used was confirmed to be valid, and then several calculations have done with various combinations of thermal conductivities of PCB and fluid. When the conventional definition of heat transfer coefficient was used, however, the heat transfer characteristic could not be summarized with a unique correlation. Then, the effective heat transfer area proposed by Zhang et al. was examined to rearrange the convection heat transfer. After taking into account the effect of thermal conductivity ratio between PCB and fluid, the heat transfer characteristics can be summarized with a unique non-dimensional correlation available not only for a single module package but also

2 for two or more ones. The experimental results can also be summarized with the same correlation as obtained by numerical simulations. 2. Heat conduction experiments and simulations 2.1 Experimental setup Figure 1 shows the geometry of the experimental setup. The same type two PCBs with electronic module packages are fixed opposite at the bottom and top inner walls of duct with mm in length, 200 mm in width, and mm in height shown in the figure. Each PCB (its thermal conductivity λ p =0.3 W/m/K) having 1 mm square and 1.2mm thick is set at the center about 0 mm away from inlet of the duct. The module package consists of a heat spreader (λ hs =398 W/m/K), a heater (λ h =45 W/m/K) and a package substrate (λ ps =16 W/m/K). The heat spreader is 28 mm square, and 0.5 mm thick, and is attached to the heater with 13.4 mm square and 0.4 mm thick. The heat spreader and the heater are tightly adhered to the package substrate with 45 mm square and 2.4 mm thick. The package substrate is connected with ball grid array to the center of the PCB. Glass wool (λ gw =0.05 W/m/K) was filled inside the gap to prevent natural convection. Figure 2 shows the location of the thermocouples. Six T-type thermocouples with 50 m diameter are installed on the module package to measure the surface temperature, T s. The thermocouples numbered from 1 to 4 are located on the heat spreader surface, and the other two, No.5 and No.6, are located on the package substrate surface. A built-in diode is installed in the center of the heater, and enable to measure junction temperature, T d. The heater is energized with a DC power supply in a variable voltage range and the maximum power dissipation of the heater is about 5 watts Package substrate Heater 45 x 45 x x 13.4 x :Thermocouple No B Heat spreader 28 x 28 x 0.5 B Package substrate Heat spreader PCB 3.0 PCB 1 x 1 x 1.2 Fan 35 x 35 x 5.0 Heat spreader Package substrate PCB.0 B-B Package substrate (Symmetrical arrangement) Fan Heater Fig. 2 Location of six thermocouples Table Package substrate Fig. 1 Schematic of module package 2.2 Simulation model The simulation model has been developed based on the corresponding experimental setup described above. The dimensions and thermophysical properties of the duct and module package for the present simulations are the same as the experimental ones. On the other hand, the complicated internal structures of the package substrate

3 and PCB were simplified and they were replaced with two blocks with uniform but different thermal conductivities to save computational time. A volumetrically uniform heat generation was assumed in the heater. Natural convection boundary conditions are employed at the outer surfaces of the duct. The heat transfer coefficient was estimated to be 7.46 W/m 2 /K by fitting the surface temperatures obtained numerically with those measured for various heating rates. 2.3 Heat conduction results Figure 3 compares the measured temperature profiles with numerical ones. The temperature profiles for typical heating rates are plotted. The solid and broken lines represent the results of the experiments and the simulations, respectively. The ordinate is the temperature difference between T s and the room temperature, T o. The abscissa indicates the thermocouple number corresponding to the locations shown in Fig. 2. As the results of setting the heat transfer coefficient 7.46 W/m 2 /K, the temperature profiles of the simulation are in good agreement with the experimental results except for the position of package substrate edge (No.6), where the numerical values show higher than those measured. The temperatures on the package substrate of the experiments are lower than those at the heat spreader surface. On the T s -T o [K] 0.0 other hand, the temperatures on the package substrate of the simulations are relatively flat compared with the experimental results. These slight differences can be attributed to the simplification of the simulation model. From the results of heat conduction experiments, the heat conducted through the package substrate and PCB, and convected away from the outer walls of the duct was estimated. The heat conduction rate, Q loss, is proportional to the temperature difference (T d - T o ), and can be expressed by Q loss = 2.79 x -2 (T d - T o ) x -2 (1) Equation (1) can be used to estimate the natural convection heat losses at the same temperature difference, (T d - T o ), for forced convection experiments. 3. Forced convection experiments and simulations 3.1 Experimental setup The geometry and dimensions of the experimental setup are those used in the same as the heat conduction experiment except that there are no more the PCB at the top inner wall of duct and glass wool filled inside. The three fans with 35 mm square and 5.0 mm high are attached on the downstream most of the duct. Switching three fans on and off in various combinations can change the flow rate. The average velocity at the inlet was measured with an accurate hot-wire anemometer. 3.2 Simulation model The simulation model is also almost the same as the heat conduction case except that the convection boundary conditions inside the duct must be considered. The uniform pressure and the uniform velocity are assumed at the inlet and the outlet of the duct, respectively. 3.3 Convection heat transfer results The average velocities at the duct inlet were measured for the three operation modes. The average values were 0.33, 0.66, and 1.0 m/s for one, two, and three fans, respectively. The temperature profiles at the module package surface were measured at three heat dissipation rates, 1.00, 2.19 and 3.71 W, while the three fans ran together. Figure 4 shows a comparison of temperature profiles between experiments and simulations at U=1.00 m/s, and Experiments Q t =2.09 W Q t =1.50 W Q t =0.989 W Q t =0.506 W Simulations Location of thermocouples Fig. 3 Temperature profiles

4 three heat dissipation rates. The temperature profiles obtained from simulations agree well with those measured. The numerical results for the other two operation modes are also in good agreement with the experimental data as shown in Fig. 5, where the heat dissipation rate is kept at 1.00 W. These results confirm that the present CFD code is valid and can be used for the calculations of the conjugate heat transfer with high accuracy. T S -T o [K] Experiments Q t = 3.71 W Q t = 2.19 W Q t = 1.00 W Simulations U=1.00 m/s Location of thermocouples Fig. 4 Temperature profiles for three fans in operation 4. Parametric study on single module package 4.1 Non-dimensional correlation with conventional method Based on the validity of the present simulations, some parametric calculations were carried out with various inlet air velocities and thermal conductivities of PCB. Figure 6 shows the non-dimensional relationship between the heat transfer coefficient and air velocity. The ordinate and abscissa are the Nusselt and Reynolds numbers, respectively, which are defined as: Nu = h t L hs /λ a (2) Re = U D H /ν a (3) Here, U is the average velocity of the duct inlet, and D H is the hydraulic diameter of the duct, and L hs is the length of the heat spreader, and ν a and λ a represent the kinematic viscosity and thermal conductivity of air, respectively. The heat transfer coefficient, h t, in Eq. (2) is defined by following conventional method as: h t = Q net /A ref /(T max -T o ) (4) T s -T o [K] Experiment U=0.33 m/s, Q t = 1.00 W U=0.66 m/s, Q t = 1.00 W Simulations Location of thermocouples Fig. 5 Temperature profiles for single and two fans in operation λ p /λ a : Re ( = U D H /ν) Where, Q net is the net heat transfer rate, Q t -Q loss. Q t is the total heat dissipated, Q loss is the heat loss convected away from the outer walls of the duct, A ref is the surface area of the heat spreader, and T max represents the maximum temperature at the heat spreader surface. As shown in Fig. 6, the Nusselt number in conjugate heat transfer depends not only on the Reynolds number but also on the thermal conductivity ratio of PCB and air. The numerical results, therefore, could not be summarized with a unique non-dimensional correlation when the conventional definition of heat transfer coefficient is used. In the following discussion, the concept of effective heat transfer area is introduced to deal with such a complicated conjugate heat transfer phenomenon and to derive a unique correlation. Nu ( = h L hs / λ a ) 3 Fig. 6 Nu number versus Re number (Based on the conventional heat transfer coefficient)

5 4.2 Non-dimensional correlation with effective heat transfer area To introduce the effective heat transfer area, a uniform heat flux is assumed as an average even for the non-uniform heat flux over a heat transfer surface. At first, the convective heat flux at the heat spreader surface must be defined as q = Q conv /A ref (5) Here, Q conv is the convective heat actually transferred to air from the heat spreader surface, which can only be obtained from the simulation. The effective heat transfer area is, then, defined as A eff = Q net /q = (Q net / Q conv )A ref (6) Using effective surface area, the heat transfer coefficient is newly defined as h = Q net /A eff /(T max -T o ) (7) Therefore, the average Nusselt number can be defined with A eff 0.5 as the reference length by Nu = h A eff 0.5 /λ a (8) Figure 7 shows the relationship between the effective heat transfer area and the thermal conductivity ratio, λ p /λ a. For the region of relatively lower thermal conductivity ratio, the non-dimensional heat transfer area increases with an increase in Reynolds number. This tendency disappears in the region of higher thermal conductivity ratio. At λ p /λ a =780, the effective heat transfer area is almost independent of the Reynolds number. Figure 8 shows the relationship between Nusselt and Reynolds numbers. The numerical results can be expressed by a unique non-dimensional correlation by introducing another parameter, the thermal conductivity ratio. Nu/(λ P /λ a ) = 1.6 Re 0.4 (9).0 A eff /A ref Re number : λ P /λ a Fig. 7 Relationship between A eff /A ref and λ P /λ a Nu/(λ P /λ a ) Nu/(λ P /λ a ) = 1.6 Re 0.4 λp/λa : Experiments Re (=U D H /ν a ) Fig. 8 Nu number versus Re number based on effective heat transfer area According to the above definitions, the present experimental results are rearranged. The results agree well with Eq. (9) as shown with the symbol in Fig. 8. Practically, the effective heat transfer area for a board with known thermal conductivity can be determined from such numerical results as shown in Fig. 7. Then the Nu can be calculated by using Eq. (9) for a given inlet velocity and the duct geometry. Further, the heat transfer coefficient can be obtained from Eq. (8). Finally, the maximum temperature, that is, the most important parameter for thermal design can be predicted by the definition of heat transfer coefficient Eq. (7). Conclusively, the present method can provide two important parameters for thermal design, one is the maximum temperature, T max, and the other is the effective surface area. The latter is particularly important for the case of arrangement with multiple heat sources. 5. Multiple module packages Further calculations are carried out for the two cases of multiple arrangements of module packages, that is, the series and parallel arrangements. The concept of the effective heat transfer area can also be applied to these systems. Figure 9 shows the relationship between Nu and Re for the series arrangement. The heat transfer characteristic of the upstream package shown by the solid line is almost the same as that for a single module

6 package, while that of the second package shown by the dashed line is about 20 % lower, due to the thermal wake effect. Figure is the case of the parallel arrangement where four module packages are considered. When the thermal conductivity of PCB is high, the heat transfer characteristics of both upstream and downstream arrays of packages are almost the same as those for the series arrangement as shown by the solid and dashed lines. The Nusselt numbers become around % higher than those when the thermal conductivity is low. Νu/(λ P /λ a ) Air L hs 2L hs Nu/(λ P /λ a ) = 1.6 Re 0.4 λp/λa & position 11.7, Upstream 11.7, Downstream 780.3, Upstream 780.3, Downstream Νu/(λ P /λ a ) Air L hs 2L hs Nu/(λ P /λ a ) = 1.6 Re 0.4 λ p /λ a & position 11.7, Upstream 11.7, Downstream 780.3, Upstream 780.3, Downstream Nu/(λ P /λ a ) = 1.3 Re 0.4 Nu/(λ P /λ a ) = 1.3 Re 0.4 Re ( = U D H /ν a ) Re ( = U D H /ν a ) Fig. 9 Nu number versus Re number Fig. Nu number versus Re number (Series arrangement) (Parallel arrangement) 6. Conclusions Both the experiments and simulations for the conjugate heat transfer of an electronic module package cooled by air have been carried out. The main conclusions are as follows. 1. Experimental results have shown that the present code CFdesign can accurately predict the heat transfer characteristics of the conjugate heat transfer problems. 2. Based on the concept of effective heat transfer area, a unique non-dimensional correlation is proposed, which can predict the maximum temperature at the module package surface and can estimate the spreading of surface area. The present method is confirmed to be available for the series and parallel arrangements of multiple module packages. References journal article M. Fujii, M. Behnia, X. Zhang, S. Gima and K. Hamano, Conjugate heat transfer behavior of an electronic chip module cooled by air, Proc. of IPACK 01, IPACK (CD-ROM), F.P Incropera, J.S. Kerby, D.F. Moffatt, and S. Ramadhyani, Convection heat transfer from discrete heat sources in a rectangular channel, Int. J. Heat Mass Transfer, vol. 29, pp , W. Nakayama and S. -H. Park, Conjugate heat transfer from a single surface-mounted block to forced convective air flow in a channel, J. Heat Transfer, vol. 118, pp , A. Ortega, U.S. Wirth, and S.J Kim, Conjugate forced convection from a discrete heat source on a plane conducting surface, Heat Transfer in Electronic Systems, ASME HTD, vol. 292, pp , S. Ramadhyani, D.F. Moffatt, and F. P. Incropera, Conjugate heat transfer from small isothermal heat souces embedded in a large substrate, Int. J. Heat Mass Transfer, vol. 28, pp , R. Sugavanam, A. Ortega, and C.Y. Choi, A numerical investigation of conjugate heat transfer from a flush heat source on a conductive board in lamina channel flow, Proc. of Intersociety Conference on Thermal Phenomena in Electronic Systems (I-THERM IV), pp , X. Zhang, T. Imamura, and M. Fujii, Conjugate heat transfer from small heat sources mounted on a conductive wall, Proc. of Int. Intersociety Electronic Packaging Conf. - INTERpack '99, vol.1, pp , 1999.

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