Analytical and Numerical Modeling of Conductive and Convective Heat Transfer Through Open-Cell Metal Foams

In this paper, a comprehensive analytical and numerical study of conductive and convective heat transfer through high porosity metal foams is presented. In the first part a novel theoretical model for determination of effective thermal conductivity of metal foams is introduced. This general analysis can be applied to any complex array of interconnected foam cells. Assuming dodecahedron unit cell for modeling the structure of metal foams, an approximate equation for evaluation of effective thermal conductivity of foam with a known porosity is obtained. In this approximation method, unlike the previous two-dimensional (2D) models, porosity is the only geometric input parameter used for evaluation of effective thermal conductivity, while its predictions of effective thermal conductivity are in excellent agreement with the previous models. In the second part a 3D numerical model for conduction in metal foam is constructed. The foam has a square cross section and is exposed to constant temperature at both ends and constant heat flux from the sides. We assume local thermal equilibrium (LTE), i.e., the solid and fluid temperatures are to be locally equal. Comparison of the 3D numerical results to the experiments shows very good agreement. The last part of the study is concerned with the 3D numerical modeling of convective heat transfer through metal foams. Experimentally determined values of permeability and Forchheimer coefficient for 10 pores per inch (PPI) nickel foam are applied to the Brinkman-Forchheimer equation to calculate fluid flow through the foam. Local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) methods were both employed for heat transfer simulations. While LTE method resulted in faster calculations and also did not need surface area to volume ratio (α_sf) and internal convective coefficient (h_sf) as its input, it was not accurate for high temperatures. LTNE should be used to obtain distinct local solid and fluid temperatures.