Research Papers: Thermal Systems

Thermal and Mechanical Modeling of Metal Foams for Thermal Interface Application

[+] Author and Article Information
Ninad Trifale

School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: ntrifale@purdue.edu

Eric Nauman

School of Mechanical Engineering,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: enauman@purdue.edu

Kazuaki Yazawa

Birck Nanotechnology Center,
Purdue University,
585 Purdue Mall,
West Lafayette, IN 47907
e-mail: kyazawa@purdue.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 18, 2015; final manuscript received February 23, 2016; published online April 5, 2016. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 138(7), 072801 (Apr 05, 2016) (12 pages) Paper No: HT-15-1426; doi: 10.1115/1.4032957 History: Received June 18, 2015; Revised February 23, 2016

We present a study on the apparent thermal resistance of metal foams as a thermal interface in electronics cooling applications. Metal foams are considered beneficial for several applications due to its significantly large surface area for a given volume. Porous heat sinks made of aluminum foam have been well studied in the past. It is not only cost effective due to the unique production process but also appealing for the theoretical modeling study to determine the performance. Instead of allowing the refrigerant flow through the open cell porous medium, we instead consider the foam as a thermal conductive network for thermal interfaces. The porous structure of metal foams is moderately compliant providing a good contact and a lower thermal resistance. We consider foam filled with stagnant air. The major heat transport is through the metal struts connecting the two interfaces with high thermally conductive paths. We study the effect of both porosity and pore density on the observed thermal resistance. Lower porosity and lower pore density yield smaller bulk thermal resistance but also make the metal foam stiffer. To understand this tradeoff and find the optimum, we developed analytic models to predict intrinsic thermal resistance as well as the contact thermal resistance based on microdeformation at the contact surfaces. The variants of these geometries are also analyzed to achieve an optimum design corresponding to maximum compliance. Experiments are carried out in accordance with ASTM D5470 standard. A thermal resistance between the range 17 and 5 K cm2/W is observed for a 0.125 in. thick foam sample tested over a pressure range of 1–3 MPa. The results verify the calculation based on the model consisting the intrinsic thermal conductivity and the correlation of constriction resistance to the actual area of contact. The area of contact is evaluated analytically as a function of pore size (5–40 PPI), porosity (0.88–0.95), orientation of struts, and the cut plane location of idealized tetrakaidecahedron (TKDH) structure. The model is developed based on assumptions of elastic deformations and TKDH structures which are applicable in the high porosity range of 0.85–0.95. An optimum value of porosity for minimizing the overall interface thermal resistance was determined with the model and experimentally validated.

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Fig. 1

Foam sample used for experimentation, 10PPI 0.93 porosity

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Fig. 2

TKDH structure with six squares and eight hexagons

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Fig. 3

Schematic representation of different components of total thermal resistance

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Fig. 4

(a) Schematic representation of experimentation setup and (b) actual experimentation setup

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Fig. 6

Resistance network analogy, individual struts as part of resistance network

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Fig. 7

Effective thermal conductivity, comparison of multiple methods

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Fig. 8

(a) Bottom layer in contact initially, adjacent layer struts deform to come in contact with the surface and (b) contact area patch for struts

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Fig. 9

(a) Normalized area against orientation angle and porosity and (b) normalized area of contact as a function of PPI and pressure

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Fig. 10

(a) Width of contact patch for two layers sharp peak marks initiation of second layer contact and (b) length of contact patch for layer 2. The second layer deforms but only higher porosity foams have deformation large enough to make contact.

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Fig. 11

Trends for 1/√(area) against pressure—similar to the contact resistance trend

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Fig. 12

(a) Contact resistance as a function of pressure for 10, 20, and 40 PPI and (b) contact resistance for 0.87 and 0.93 porosity

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Fig. 13

Thermal resistance extrapolation using multiple thicknesses for various pressures

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Fig. 14

(a) Experimental results for 0.87 porosity foams, (b) experimental results for 0.93 porosity foams, and (c) experimental results for 0.95 porosity foams

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Fig. 15

Comparison of thermal resistance for various porosity ranges of 0.88–0.9, 0.91–0.93, and 0.94–0.96

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Fig. 16

(a) Thermal resistance for 10 PPI foams (0.89 porosity), (b) thermal resistance for 20 PPI foams (0.89 porosity), and (c) thermal resistance for 40 PPI foams (0.89 porosity)

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Fig. 17

Repeatability data for 10 PPI, 0.25 in. 0.89 porosity samples

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Fig. 18

Variation of thermal resistance against porosity for multiple pressures

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Fig. 19

Total resistance against PPI for 0.25 in. 0.89 porosity samples

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Fig. 20

Total resistance against PPI for 0.5 in. 0.89 porosity sample



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