The onset of Darcy-Brinkman convection in a porous layer using a thermal nonequlibrium model?part I:stress-free boundaries

Abstract

The paper deals with the onset of convection in a porous layer heated from below, by considering the case when the fluid and solid phases are not in local thermal equilibrium and when form-drag and boundary effects are included in the analysis. Analytical progress is facilitated by taking stress-free boundaries conditions. Asymptotic solutions for both small and large values of the scaled inter-phase heat transfer coeffcient, H, are presented and comparisons with the numerical solutions are performed. Excellent agreement is obtained between the asymptotic and the numerical results.