The effect of inertia on the onset of mixed convection in a porous layer heated from below

A linear stability analysis is presented which determines how the presence of fluid inertia and a mean applied horizontal pressure gradient modifies the familiar Darcy-flow criterion for the onset of convection in the porous-Benard problem. It is found that, when both effects are present, the critical Rayleigh number is raised above 4 pi(2), and increasingly so as either the strength of inertia effects or the magnitude of the pressure gradient or both increase. In general, spanwise periodic vortices are favoured with no change in the critical wavenumber. However, when the flow is restricted to being two-dimensional, the critical wavenumber is also modified. The result of this analysis provides a straightforward qualitative and quantitative means whereby experimental tests can be used to validate or otherwise the Forchheimer model of the effect of fluid inertia. (C) 1997 Elsevier Science Ltd.