Experimental and analytic investigations for effective thermal conductivity in high porosity metallic foams

To demonstrate a totally analytic model of effective thermal conductivity in high porosity open-cell metallic foams, a 3D tetrakaidecahedron configuration is selected as the representative unit cell for the metal foam. By solving 1D steady-state Fourier's equation for the representative volume, a purely analytic model without requiring any fitting or empirical coefficient is obtained. Coinciding well with the present measurements and experimental data from literature, this model suggests a linear dependence of effective thermal conductivity upon porosity, where the proportionality coefficient is the reciprocal of thermal tortuosity. The heat transfer in fluid phase is negligible due to large thermal conductivity ratio between solid ligaments and fluid phase (e.g., air-saturating Al foam), 1D heat conduction along the tortuous ligaments thus dominates. Neglecting natural convection and radiation of thermal energy, the topological parameters, such as pore density (PPI) and ligament cross-sectional shape, exert little influence on effective thermal conductivity. Furthermore, the effective conductivity remains constant within the experimental temperature range.