Das. Rees, THE EFFECT OF INERTIA ON THE ONSET OF MIXED CONVECTION IN A POROUS LAYER HEATED FROM BELOW, International communications in heat and mass transfer, 24(2), 1997, pp. 277-283
A linear stability analysis is presented which determines how the pres
ence 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 in
creasingly so as either the strength of inertia effects or the magnitu
de of the pressure gradient or both increase. In general, spanwise per
iodic vortices are favoured with no change in the critical wavenumber.
However, when the flow is restricted to being two-dimensional, the cr
itical wavenumber is also modified. The result of this analysis provid
es a straightforward qualitative and quantitative means whereby experi
mental tests can be used to validate or otherwise the Forchheimer mode
l of the effect of fluid inertia. (C) 1997 Elsevier Science Ltd.