Convection in a porous medium with internal heat source and variable gravity effects

Abstract

The problem is studied of convection in a fluid saturated porous layer which is heated internally and where the gravitational field varies with distance through the layer. For this problem it is not known whether exchange of stabilities holds. We here find critical Rayleigh numbers for both linear instability and nonlinear energy stability, and numerical findings indicate that for the heat sources and gravity fields chosen, the growth rate of linear theory is real at criticality.