Flow Transitions in Buoyancy-Induced Non-Darcy Convection in a Porous Medium Heated From Below

Thermoconvective instabilities in horizontal porous layers heated from below are studied numerically by employing the Brinkman-Forchheimer extended Darcy formulation. The onsets of stable and oscillatory convection are found to be strong functions of the governing parameters: fluid Rayleigh and Prandtl numbers, Darcy number, and conductivity ratio. The effects of porosity and specific heat ratio are pronounced only in the fluctuating convection regime. At the onset, the oscillatory convection is highly periodic, but with an increase in convective motions the disorder increases monotonically and the fluctuations become highly random. These results do not confirm the possibility of reverse transition from a more-disordered to a less-disordered state as predicted by the Darcy model (Kimura et al., 1986). The applicability of Darcy formulation is thus highly restricted in the case of a Be´nard convection problem. In a randomly oscillating convective state, the heat transfer rate varies substantially with time.