Influence of Darcy number on the onset of convection in a porous layer with a uniform heat source

This note considers the effect of different Darcy numbers on the onset of natural convection in a horizontal, fluid-saturated porous layer with uniform internal heating. It is assumed that the two bounding surfaces are maintained at constant but equal temperatures and that the fluid and porous matrix are in local thermal equilibrium. Linear stability theory is applied to the problem, and numerical solutions obtained using compact fourth order finite differences are presented for all Darcy numbers between Da=0 (Darcian porous medium) and Da→∞ (the clear fluid limit). The numerical work is supplemented by an asymptotic analysis for small values Da.