Natural convection in porous media with anisotropic dispersive thermal conductivity

Abstract

A numerical simulation is undertaken in order to study the effect of anisotropy of the effective thermal conductivity tensor on heat transport in the porous medium Rayleigh-Bénard problem. The momentum equation includes an inertial drag (Forchheimer) term. The effective thermal conductivity tensor, in the energy equation, contains an isotropic stagnant component and a hydrodynamic dispersive component with principal axes aligned with the local velocity vector and with magnitude proportional to the local velocity amplitude. A parametric study of two-dimensional steady cellular convection reveals the following. (1) Dispersion increases the net heat transfer after a Rayleigh number ~ 100–200. As the degree of anisotropy of the effective thermal conductivity is increased, the wall averaged Nusselt number is decreased. (2) Using the available Rayleigh number-wavenumber variation data does not affect the divergence between simulation and experiment.