Forced convection in cellular porous materials: Effect of temperature-dependent conductivity arising from radiative transfer

Forced convection in a channel occupied by a saturated cellular porous medium is investigated. The problem is formulated as a combined conductive–convective–radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics and metals. Special cases in which radiative conductivity is modeled as a power function of temperature as well as the Stefan-Boltzmann case are investigated. Analytical and numerical solutions are obtained; Darcy and clear fluid limits are also studied.