Darcy-Bénard Convection using a Non-Fourier Thermal Model

Abstract

In the paper the effect of replacing the classical Fourier thermal model by the non-classical non-Fourier thermal model on Darcy-Benard convection in a fluid-saturated densely-packed porous medium is studied and, in particular, how the Nusselt numbers of the solid and fluid phases are affected by the adoption of such a model is considered. A weighted average Nusselt number is also defined and analyzed to study the overall heat transfer in the case of steady finite-amplitude convection which is amenable to analytical treatment. Sub-critical instability is ruled out in mono-diffusive convection but the inclusion of a second diffusing component or rotation is shown to facilitate its manifestation.