Analytical considerations of thermal radiation in cellular metal foams with open cells

An analytical model is developed to characterize the radiative transport process in highly porous, open-celled metal foams having idealized cellular morphologies in terms of fundamental radiative parameters such as emissivity, reflectivity and configuration factors. In comparison with the conventional two-flux approach or the diffusion approximation utilizing the Rosseland mean coefficient, the present model is explicit and yet relatively simple. Overall, the predicted effective radiative conductivity as a function of pore size and relative density (defined as the ratio of foam density to solid density) agrees well with that measured using a guarded-hot-plate apparatus for steel alloy foams. A systematic parametric study is subsequently carried out. The contribution of reflectance to thermal radiation is found to be significant, up to 50%, but the effect of temperature gradient is relatively small. The equivalent radiative conductivity increases linearly with increasing cell size for a fixed relative density, whilst for a given cell size the variation of relative density only has a small effect on radiation due to the mixed effects of increased emission and extinction.