Thermal and Mechanical Modeling of Metal Foams for Thermal Interface Application

Abstract

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.