Penetrative convection in a porous medium with internal heat sources

Abstract

The problem of penetrative convection in a fluid saturated porous medium that is heated internally is analyzed using the methods of linear instability theory and nonlinear energy theory. Critical Rayleigh numbers for the case of a uniform heat source in a layer with two fixed surfaces are obtained numerically. A comparison of the linear and nonlinear results delimit a band of Rayleigh numbers where subcritical instabilities could arise. It is shown that the solution to the initial-boundary value problem for the backward heat equation in a heat-conducting porous medium depends continuously on the internal heat source.