Prandtl Number Effect on Be´nard Convection in Porous Media

A numerical study of buoyancy-driven two-dimensional convection in a fluid-saturated horizontal porous layer is reported emphasizing the nonlinear inertial effect on heat transport. The Forchheimer–Brinkman–Darcy–Boussinesq formulation and a single energy equation for the volume-average temperature are used. Closure to the wavenumber selection problem is sought through a criterion based on the Glansdorff and Prigogine theory of nonequilibrium thermodynamics. Good agreement with laboratory data and the analogy with the Rayleigh–Be´nard problem are corroborative facts which justify similar non-Darcian formulations and demonstrate the role of the quadratic inertial terms in decreasing the mean convective heat transfer across the layer.