Non-Linear Fin Patterns in Cold Plates for Liquid Cooling Ralph Remsburg Chief Engineer Amulaire Thermal Technology 11555 Sorrento Valley Rd. Suite 201 San Diego, CA 92121 (858) 309-4715 email: [email protected] Abstract A thermal study of various linear patterns and a non-linear fin pattern for a liquid-cooled Insulated Gate Bipolar Transistor Integrated Power Electronic Module cold plate. Due to manufacturing costs, fin patterns have been traditionally designed as largely 2D profiles having linear fin spacing. Newer manufacturing process, such as Advanced Molding Technology, allow complete and economical customization of each individual fin’s shape and spacing within the fin array. A series of thermal comparisons will show how cold plate surfaces progress from round tube to non-linear fin arrays for better thermal performance, for a specified 3-chip IGBT module dissipating 1,080W of heat. Nomenclature

three-dimensional packaging of electronic components in a small and compact volume, largely replacing the traditional individual packaged IC technology in applications such as front-end power factor correction and motor drives. Even though IGBTs typically operate with 98% efficiency, the 2kW of waste heat from a 100kW converter will overwhelm most cooling solutions.

⎛ Nu ⎞ 13 ⎟⎟ Pr j = Colburn factor, ⎜⎜ ⎝ Re Pr ⎠

f = Fanning friction factor,

τ0 0.5ρU 2

hc L k ρU L Re = Reynolds Number, Nu = Nusselt number,

The advent of 3D multi-layered packaging of these modules can help achieve better reliability, 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 cooling solutions. Because the desired junction temperature of an IPEM IC should not normally exceed 120oC, current heat fluxes of 300W/cm2 are challenging to even most liquid cooling solutions.

µ

Pr = Prandtl number,

cp µ

k ρ = density (kg/m3) U = velocity (m/s) τ = shear stress (N/m2) hc = heat transfer coefficient (W/m2 K) D = characteristic dimension, length or dia. (m) k = thermal conductivity (W/m K) µ = absolute viscosity (N s/m2) cp = specific heat (J/kg K) δv = velocity boundary layer (m) δth = thermal boundary layer (m)

Literature Review 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 thermal performance by the pump flow curve.

Introduction 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 IC, Integrated Power Electronic Modules (IPEM), such as those based on Insulated Gate Bipolar Transistors (IGBTs). Built on embedded power technology, IPEMs offer

Poulikakos and Bejan (1982) constructed a theorem to determine the optimum fin dimensions for

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Reynolds number, aspect ratio, Nusselt number and the drag coefficient. They found that the circular geometry has the best dimensionless total entropy generation rate for low approach velocities and small wetted surface area. Flat plate fins have the best results for higher approach velocities and large surface areas. Elliptical pins, depending on aspect ratio, could outperform circular pins at medium approach velocities for larger surface areas, but flat plates could outperform elliptical geometries at higher approach velocities for the same areas with high aspect ratios. For small surface areas and low velocities, they concluded that flat plates are not a good selection based on entropy generation rate. Their conclusions are suitable for use in the laminar flow range.

minimum entropy generation in forced convection. They developed and applied an expression for the entropy generation rate of a basic fin to select the optimum dimensions of pin fins, rectangular plate fins, plate fins with trapezoidal cross sections, and triangular plate fins with rectangular cross section. Their study was inconclusive. In two studies (1983 and 1984), Ota et al. experimented with heat transfer and flow around an elliptical cylinder of axes ratios 1:2 and 1:3. Their results showed that the heat transfer coefficient of the elliptical cylinder was higher than that of a circular cylinder having equal circumference, and the pressure drag coefficients of the former were much lower than that of the later.

These findings, while valid for single fin geometries, become distorted when multiple, identical fin flowfields interact within a fin array. Mälhammar (2004) used an alternative formulation of the Reynolds analogy to study the interaction between friction and convection in heat sinks. He found that the analogy was strongly dependant on velocity and only applied directly to flat and moderately curved surfaces. For more complex shapes, an analogy number is introduced to partially compensate for discrepancies.

Chapman et al. (1994) experimentally compared parallel plate fins, cross-cut pin fins, and elliptical pin fins in low air flow environments. For equal volumes, they found that the overall thermal resistance of parallel plate fins was lower than crosscut pins or elliptical pins, but the heat transfer coefficient was higher for elliptical pin fins than the other two designs. Li et al. (1998) experimentally compared circular and elliptical pin fins. They found that elliptical pin fins have a better rate of heat transfer than circular pin fins, and the resistance of elliptical pins is lower than circular pins within the Reynolds number range from 1000 to 10000.

Other research shows that each row of a pin fin array has a lower heat transfer coefficient to about the 10th row. Pin fins performance is also are greatly affected by the length of the fin. Shorter pins are affected by the velocity distributions caused by the heat sink base plate.

Behnia et al. (1998) numerically investigated the heat transfer performance of circular, square, rectangular and elliptical fins. They fixed the fin cross-sectional area per unit base area, the wetted surface area per unit base area, and the flow passage area for all geometries. They concluded that circular pin fins outperform square pin fins and elliptical fins outperform plate fins. They also found that elliptical fins work best at lower values of pressure drop, but round pin fins have better performance at higher values.

Marthinuss and Hall (2003) reviewed published data for air-cooled heat sinks, primarily from Kays & London's “Compact Heat Exchangers”, 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 heat sink is a compromise among heat transfer, pressure drop, volume, weight, and cost.

McIntyre et al. (2001?) compared the performance of three pin fins (cylindrical, square, and elliptical) on the merits of only thermal resistance. For identical frontal area, they concluded that optimized elliptical pins outperform square pins, which outperform circular pins.

Analysis Marthinuss and Hall presented Figure 1 as a comparison of the published data for straight, louvered, wavy offset and pin fin heat sinks when heat transfer and pressure drop are most important.

Khan et al. (2003) numerically evaluated rectangular, square, circular and elliptical pin fins, having equal surface area by developing a dimensionless entropy generation rate based on

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considered. Non-linear fin arrays are a recent development allowed by cost effective nontraditional manufacturing methods such as metal injection molding. In a non-linear fin array, each fin is individually designed for maximum performance while simultaneously accounting for the performance flowfields of the fins adjacent to it in the array. Further improvements in thermal performance can be achieved by using flow patterns outside the normal crossflow (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: 5x δv = Re x

Figure 1 - Heat Transfer/Pressure Drop Figure of Merit Figure 2 shows their comparison when heat sink volume, indicated by heat transfer by unit height, is of primary concern.

and the thermal boundary layer thickness is found by: ⎛ δ ⎞ δ th = 0.975⎜⎜ v1 ⎟⎟ ⎝ Pr 3 ⎠ 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 form again. 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. Figure 3 shows the IGBT layout of the subject study. Three 300W IGBT chips, 16mm x 12.7mm, and three 60W diodes, 8.8mm x 12.7mm, are attached to a 50mm x 50mm cold plate, 13mm thick. Non-conducting geometries were added to the cold plate to simulate fluid entrance and exit effects as shown in Figure 4. The heat source stack up and thermal resistance chain is detailed in Table 1 and

Figure 2 - Size Figures of Merit Comparisons and conclusions become even more difficult when non-linear fin arrays are

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Figure 5. The values do not include the effects of heat spreading.

IGBT 1-D Thermal Resistance

Silicon, 3.65E-03, 7%

Solder, 1.67E-02, 31%

Solder, 1.04E-02, 19%

Copper, 3.85E-03, 7%

Copper, 3.85E-03, 7%

AlN, 1.56E-02, 29%

Figure 5 – IGBT Material Thermal Resistance Chain

For each simulation, the ambient air temperature and the water inlet temperature is 80oC. Radiation effects are not included in the analysis. The steady-state temperature distribution was recorded as the volumetric flow rate was increased from 1 liter/minute to 12 liters/minute. The results for the simulations are shown in Table 2 and Figure 6.

Figure 3 – 1,080W IGBT Layout

Layer 1

Material x (mm)

y (mm)

z (mm)

k (W/m K) 120

θ (oC/W)

Silicon

12.7

16.0

0.089

0.00365

2

Solder

12.7

16.0

0.127

60

0.0104

3

Copper

12.7

16.0

0.305

390

0.00385

4

AlN

12.7

16.0

0.635

200

0.0156

5

Copper

127

16.0

0.305

390

0.00385

6

Solder

12.7

16.0

0.203

60

0.0167

7

Cu Base

12.7

16.0

3.962

390

0.0500

IGBT Fin Comparison 200

o

Maximum Temperature ( C)

180

0.104

Table 1 – IGBT Material Stack Thermal Resistance

160

140

120 Copper Tube (10.0D) Machined Copper Fins (1.5) Stacked Copper Fins (0.2) Square Copper Fins (0.786) Round Copper Fins (1.0D) Elliptical Copper Fins (0.5D 1:4) Non-Linear Impingement

100

80 0

2

4

6

8

10

12

Volumetric Water Flow Rate (l/min)

Figure 6 – Comparison of IGBT Cold Plate Fin Configurations.

Type Round Tube Machined Fins Stacked Fins Square Pins Round Pins Elliptical Pins Non-Linear Pins

Figure 4 – Flow Through a Machined Fin Cold Plate

# Fins 20 41 798 798 798 782

D (mm) 10 1 0.2 0.786 1 0.5 0.5

A (cm2) 15.7 225 435 275 275 275 194

Table 2 – Fin Geometry Comparison Figure 7 shows an impingement design utilizing a non-linear fin array. Each fin is individually designed to take advantage of the

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2. Ota, T., Aiba, S., Tsuruta, T., and Kaga, M., 1983, “Forced Convection Heat Transfer from an Elliptical Cylinder,” Bulletin of the JSME, Vol. 26, No. 212, pp. 262 - 267.

existing direction of fluid flow, minimizing pressure drop, while offering a larger heat transfer surface area.

3. Ota, T., Nishiyama, H., and Taoka, Y., 1984, “Heat Transfer and Flow Around an Elliptical Cylinder,” International Journal of Heat and Mass Transfer, Vol. 27, No. 10, pp. 1771 - 1779. 4. Chapman, C. L., Lee, S., and Schmidt, B. L., 1994,“Thermal Performance of an Elliptical Pin Fin Heat Sink,” Proceedings of the Tenth IEEE SemiTherm Symposium, pp. 24-31. 5. Li, Q., Chen, Z., Flechtner, U., and Warnecke, H. J., 1998, “Heat Transfer and Pressure Drop Characteristics in Rectangular Channels with Elliptical Pin Fins,” International Journal of Heat and Fluid Flow, V 19, pp. 245 - 250.

Figure 7 – Non-Linear Fin Pattern Optimized for Impingement Flow Conclusion A three IGBT/three diode model dissipating 1,080W was constructed. Liquid cooling with water at 80oC was simulated. The heat from the sources was transferred to the water coolant through a round tube, machined plate fins, stacked fins, machined square pins, round pins, elliptical pins, and a unique nonlinear fin array using impingement.

6. Behnia, M., Copeland, D., and Soodphadakee, D., 1998, “A Comparison of Heat Sink Geometries for Laminar Forced Convection,” Proceedings of The Sixth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, Seattle, Washington, USA, May 27 - 30, pp. 310-315.

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 heat sink 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 heat sink.

7. Khan, W. A., Culham J. R., and Yovanovich, M. M., 2003, “The Role of Fin Geometry in Heat Sink Performance,” Proceedings of InterPACK03, International Electronic Packaging Technical Conference and Exhibition, Maui, Hawaii, USA, July 6-11. 8. Mälhammar, Å., 2004, “A Method for Comparing Heat Sinks based on Reynolds Analogy,” 10th International Workshop on Thermal Investigations of ICs and Systems, Côte d'Azur, France, September 29 - October 1.

The non-linear 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.

9. Marthinuss, J., and Hall, G., 2003, “Air Cooled Compact Heat Exchanger Design for Avionics Thermal Management Using Published Test Data,” Proceedings of InterPACK03, International Electronic Packaging Technical Conference and Exhibition, Maui, Hawaii, USA, July 6-11.

References 1. Poulikakos, A. and Bejan, A., 1982, “Fin Geometry for Minimum Entropy Generation in Forced Convection,” Journal of Heat Transfer, Vol. 104, pp. 616-623.

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