Effect of radiative transfer on the onset of convection in a porous medium

The effect of radiative transfer on thermal convection of a thin fluid-saturated densely packed porous layer bounded by stress-free radiating horizontal planes heated from below is studied using linear theory. The coefficients of absorption, emission and scattering are computed from packed bed properties using a two-flux model. The Milne-Eddington approximation is employed to determine approximate solutions valid for optically thin (transparent) and optically thick (opaque) gray media which absorb and emit thermal radiation. The effect of radiation parameters on the cell size and on the onset of convection are studied in detail using the Galerkin approximation. It is shown that the effect of radiation is to inhibit the onset of convection in a porous medium. The physical explanation for this is given, taking into account the increase in thermal conductivity due to the combined effects of the porosity of the medium and radiation