Power Electronics

Nonlinear Fin Patterns Keep Cold Plates Cooler

Altering the fin geometry of liquid-cooled cold plates improves their thermal efficiency.

Specialists 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.

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 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 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 cost-effective 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.

A New Direction

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 (δV) and a thermal boundary layer (δTH). 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:

where X is the linear distance of fluid flow along the heatsink surface, is the density of the fluid (kg/m3) and µ is the absolute viscosity (Ns/m2). The thermal boundary layer thickness is found by:

with CP being the specific heat of the fluid (J/kg K) and k being the thermal conductivity (W/m K).

When turbulent coolant flow impinges on a surface that is perpendicular to the flow, the boundary layer is minimized. The highest values for single-phase heat-transfer coefficient can be achieved by impingement, directing flow in the Z axis, thereby breaking down the 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 metal-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 80°C. 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 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 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 machined-plate 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.

References

  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.

Table 1. IGBT material stack thermal resistance.
Layer Material x (m) y (m) z (m) Thermal conductivity (W/m K) Ru (°C/W)
1 Silicon 0.016 0.0127 0.0000889 120 3.65E-03
2 Solder 0.016 0.0127 0.000127 60 1.04E-02
3 Copper 0.016 0.0127 0.0003048 390 3.85E-03
4 AlN 0.016 0.0127 0.000635 200 1.56E-02
5 Copper 0.016 0.0127 0.0003048 390 3.85E-03
6 Solder 0.016 0.0127 0.0002032 60 1.67E-02
7 Cu Base 0.016 0.0127 0.0039624 390 5.00E-02
Total 1.04E-01
Table 2. Fin geometry comparison.
Type Fin count Characteristic dimension (mm) Total surface area (cm2)
Round tube 10 15.7
Machined fins 20 1 225
Stacked fins 41 0.2 435
Square fins 798 0.786 275
Round fins 798 1 275
Elliptical fins 798 0.5 275
Nonlinear fins 782 0.5 194
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