The onset of Darcy-Brinkman convection in a porous layer: An asymptotic analysis

In highly porous media boundary (Brinkman) effects are important near impermeable surfaces. We investigate in detail how these effects modify the well-known criterion for the onset of convection of a Boussinesq fluid in a porous medium where Darcy's law applies. It is known that boundary effects serve to raise the critical Darcy-Rayleigh number as D, the Darcy number, increases. For many porous media the value of D is small and this causes severe numerical difficulties in solving the perturbation equations. We extend an earlier numerical study by Walker and Homsy [A.S.M.E. J. Heat Transfer 99 (1977) 338] by performing an asymptotic analysis of the singular perturbation problem which arises in the small-D limit. Excellent agreement is obtained between the asymptotic and numerical results. © 2002 Published by Elsevier Science Ltd.