On Rayleigh Bènard Convection with Porous Boundaries

Abstract

In this paper, we utilize a combination of analytical and computational techniques to study the onset of Rayleigh Benard convection in a horizontal layer of fluid heated from below. It is established mathematically that the principle of exchange of stabilities is valid. The characteristic value problem is solved and results are computed numerically for a wide range of values of the boundary parameters characterizing the nature of porous boundaries. Under a situation where in the value of the parameter characterizing the nature of the permeability of the upper boundary varies inversely to the value of parameter that characterize the nature of the lower boundary, we find a specific range of values of the permeability parameter of the lower boundary in which the increasing values of this parameter has destabilizing effect. In addition, existing results are obtained as the limiting cases of the boundary parameters, namely when both the bounding surfaces are either dynamically free or rigid, and either one of them is dynamically free while the other one is rigid.