Radiation and non-darcy effects on convection in porous media

Abstract

Combined conduction, convection and radiation heat transfer in a gray fluid-saturated sparsely packed porous medium is examined analytically for marginal convection using linear stability analysis. The effects of boundary and inertia which were absent in the usual Darcy model are considered. The Milne-Eddington approximation is employed to determine the solutions valid for transparent and opaque media which absorbs and emits thermal radiation. It is shown that the nature of the bounding surfaces and radiation significantly influence the critical Rayleigh and wave numbers. The mechanism for suppressing or augmenting convection is discussed in detail. The results obtained using Galerkin technique are compared with the existing results of Darcy model and of non-radiating systems and agreement is found.