Nonlinear Fin Patterns Keep Cold Plates Cooler

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Nonlinear Fin Patterns Keep Cold Plates Cooler By Ralph Remsburg, Chief Engineer, Amulaire Thermal Technology, San Diego Altering the ﬁn geometry of liquid-cooled cold plates improves their thermal efﬁciency.

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pecialists in electronic cooling are focusing more on the problems of the power electronics industry than ever before. Much of this attention is directed at power semiconductor ICs and integrated power electronic modules (IPEMs), such as those based on IGBTs. Built on embedded power technology, IPEMs offer 3-D packaging of electronic components in a small and compact volume, largely replacing the traditional individually packaged ICs in applications such as front-end power factor correction (PFC) and motor drives. Even though IGBTs typically operate with 98% efﬁciency, the 2 kW of waste heat from a 100-kW converter will overwhelm most cooling solutions. The advent of 3-D multilayered packaging of these modules can help achieve better reliability and lower electrical noise and lower costs. However, as the electronic chips are placed closer together, heat ﬂux (W/cm2) and heat density (W/cm3) problems become insurmountable using standard air-cooled solutions. Because the desired junction temperature of an IPEM IC should not normally exceed 120°C, current heat ﬂuxes of 300 W/cm2 are even challenging for most liquid-cooling solutions. To address this challenge, a new cold-plate manufacturing technology allows the creation of nonlinear ﬁn structures that alter ﬂuid-ﬂow patterns and improve the efﬁciency of heat removal from IPEMs.

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Fig. 1. This ﬁgure-of-merit comparison reveals that straight ﬁns become a relative benchmark for the other conﬁgurations shown when heat transfer and pressure drop are critical factors.

Interpreting Previous Research While there have been many studies of single-cooling-ﬁn geometry parameters, the conclusions often conﬂict or can only be applied over a narrow range of variables. A review of the literature reveals that most studies of single-ﬁn geometry neglect the importance of pressure drop, which for most real-world liquid-cooling systems is directly related to the thermal performance of the pump ﬂow curve. Even when applicable, the research on single-ﬁn geometries becomes distorted when multiple identical ﬁn-ﬂow Power Electronics Technology February 2007

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ﬁelds interact within a ﬁn array. For example, research shows that each row of a pin ﬁn array has a lower heat transfer coefﬁcient to about the ﬁfth row; thereafter, the row coefﬁcients are roughly equal. A pin ﬁn’s performance is also greatly affected by the length of the ﬁn. Shorter pins are affected by the velocity distributions caused by the heatsink baseplate. James Marthinuss and George Hall[1] reviewed published 22

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ELECTRONIC COOLING data for air-cooled heatsinks, primarily from Compact Heat Exchangers by William M. Kays and A.L. London[2], and concluded that for identical ﬁn arrays consisting of circular and rectangular passages including circular tubes, tube banks, straight ﬁns, louvered ﬁns, strip or lanced offset ﬁns, wavy ﬁns and pin ﬁns, the optimum heatsink is a compromise among heat transfer, pressure drop, volume, weight and cost. Marthinuss and Hall presented Fig. 1 as a comparison of the published data for straight, louvered, wavy-offset and pin-ﬁn heatsinks when heat transfer and pressure drop are most important. Fig. 2 shows their comparison when heatsink volume, indicated by heat transfer by unit height, is of primary concern. Comparisons and conclusions become even more difﬁcult when nonlinear ﬁn arrays are considered. Nonlinear ﬁn arrays are a recent development resulting out of costeffective nontraditional manufacturing methods such as metal-injection molding. In a nonlinear ﬁn array, each ﬁn is individually designed for maximum performance while simultaneously accounting for the performance ﬂow ﬁelds of the ﬁns adjacent to it in the array.

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A New Direction

Fig. 2. Figures of merit for heat transfer versus heatsink volume, as indicated by unit height, show that straight ﬁns transfer heat relatively inefﬁciently for a given amount of heatsink material.

Further improvements in thermal performance can be achieved by using ﬂow patterns outside the normal cross ﬂow (x-y) plane, such as impingement ﬂow. When a coolant ﬂows parallel to a surface, a nearly stagnant boundary layer of ﬂuid forms on the surface. The thickness of the boundary layer increases as the ﬂuid moves along the plate. There is a velocity boundary layer (V) and a thermal boundary layer (TH). The stagnant ﬂuid within the layer inhibits thermal transport from the solid surface to the ﬂuid. Turbulent ﬂow reduces the thickness of the boundary layer and can result in higher performance. The thickness of the velocity boundary layer can be found by: 5X δV = , where Re X

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ρUL Fig. 3. This diagram shows the physical layout of larger IGBTs and , µ smaller diodes on the water-cooled cold plate, as well as the thermal where X is the linear distance of ﬂuid ﬂow along the contours. heatsink surface,  is the density of the ﬂuid (kg/m3) Thermal and µ is the absolute viscosity (Ns/m2). The thermal x y z R conductivity Layer Material boundary layer thickness is found by: (m) (m) (m) (°C/W) (W/m K)  δV  1 Silicon 0.016 0.0127 0.0000889 120 3.65E-03 δ TH = 0.975  1 / 3  ,  Pr  2 Solder 0.016 0.0127 0.000127 60 1.04E-02 C µ where the Prandtl number (Pr) is Pr= r= P , 3 Copper 0.016 0.0127 0.0003048 390 3.85E-03 k with CP being the speciﬁc heat of the ﬂuid (J/kg K) 4 AlN 0.016 0.0127 0.000635 200 1.56E-02 and k being the thermal conductivity (W/m K). 5 Copper 0.016 0.0127 0.0003048 390 3.85E-03 When turbulent coolant ﬂow impinges on a surface 6 Solder 0.016 0.0127 0.0002032 60 1.67E-02 that is perpendicular to the ﬂow, the boundary layer is 7 Cu Base 0.016 0.0127 0.0039624 390 5.00E-02 minimized. The highest values for single-phase heat1.04E-01 transfer coefﬁcient can be achieved by impingement, Total Table 1. IGBT material stack thermal resistance. directing ﬂow in the Z axis, thereby breaking down the Re X =

Power Electronics Technology February 2007

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ELECTRONIC COOLING ��

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Type Round tube Machined ﬁns Stacked ﬁns Square ﬁns Round ﬁns Elliptical ﬁns Nonlinear ﬁns

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Fin count —

Characteristic dimension (mm) 10

Total surface area (cm2) 15.7

20

1

225

41 798 798 798

0.2 0.786 1 0.5

435 275 275 275

782

0.5

194

Table 2. Fin geometry comparison.

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Fig. 6. This comparison of IGBT cold-plate ﬁn conﬁgurations indicates the relatively superior thermal performance of nonlinear impingement water cooling.

injection molding, impingement cold plates with optimized ﬁn patterns can be molded that allow the coolant to extract the maximum amount of heat from all the surfaces in the ﬂow path. Fig. 3 shows a model of an IGBT layout to which thermal cooling will be applied. Three 300-W IGBT chips, each being 16 mm  12.7 mm, and three 60-W diodes, with the dimensions of 8.8 mm  12.7 mm, are attached to a 50-mm  50-mm cold plate, 13 mm thick. The various material layers and thermal resistance chain of the complete assembly is detailed in Table 1 and Fig. 4. However, the values do not include the effects of heat spreading. Thermally insulated virtual partitions were added to the cold-plate model to demonstrate entrance and exit effects of lateral ﬂuid ﬂow, as shown in curved traces in Fig. 5. For each simulation, the ambient-air temperature and the water-inlet temperature is 80oC. Radiation effects are not included in the analysis. The heat from the 1080-W IGBT/ diode assembly was transferred to the water coolant through multiple heatsink structures. These included a round tube, machined plate ﬁns, stacked ﬁns, machined square pins, round pins, elliptical pins and a unique nonlinear ﬁn array using impingement. The steady-state temperature distribution for each conﬁguration was recorded as the volumetric

Fig. 4. A comparison of the thermal-resistance layers in the IGBT cold plate reveals copper baseplate is the greatest contributor to the overall thermal resistance of the stack. ��

Fig. 5. The ﬂuid ﬂow through a machined-ﬁn cold plate includes thermally insulated structures that simulate entrance and exit effects.

boundary layer almost completely. Outside this impingement zone, the coolant contacts the surface and ﬂows away from the impingement point parallel to the surface, allowing the boundary layer to reform. With a process such as metalPower Electronics Technology February 2007

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ELECTRONIC COOLING for attachment. The performance of the machined-plate ﬁn heatsink was restricted by the limits of the machining operation. The square, round and elliptical pins had similar performance at low velocities. As the velocity increased, the elliptical pins outperformed the round pins, and the square pin performance fell to roughly the level of the machinedplate ﬁn heatsink. Fig. 7 shows an impingement design using a nonlinear ﬁn array. Each ﬁn is individually designed to take advantage of the existing direction of ﬂuid ﬂow, minimizing pressure drop while offering a larger heat-transfer surface area. The nonlinear design, while having less surface area, beneﬁted from the physics of impingement ﬂow and a combination of round and elliptical ﬁns having optimized aspect ratios and orientation. As shown in Fig. 6 and Table 2, these advantages gave the nonlinear design the greatest thermal performance among the several heatsink conﬁgurations tested. PETech

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Fig. 7. This nonlinear ﬁn pattern is optimized for impingement ﬂow.

References

ﬂow rate was increased from 1 liter per minute (LPM) to 12 LPM. The results for the simulations are shown in Table 2 and Fig. 6. The round tube, having signiﬁcantly less surface area, and a low heat transfer coefﬁcient yielded high die temperatures, indicating failure of the electronics. The performance of thin-stacked ﬁns, while having a large surface area, was signiﬁcantly degraded due to the solder layer, which is required

1. Marthinuss, James, and Hall, George, “Air Cooled Compact Heat Exchanger Design for Avionics Thermal Management Using Published Test Data,” Proceedings of InterPACK03, International Electronic Packaging Technical Conference and Exhibition, July 6-11, 2003. 2. Kays, William M., and London, A.L., Compact Heat Exchangers, Krieger Publishing Co., 3rd edition, January 1998.

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Power Electronics Technology February 2007

Non-Linear Fin Patterns in Cold Plates for Liquid Cooling