A comparative study of two-dimensional natural convection in an isotropic porous medium

Abstract

One of the most commonly used models describing flow through porous media is the Brinkman-extended Darcy model, often called the Brinkman model. This model has been modified in the literature by including the usual inertia terms of the Navier-Stokes equations. In some other works, the basic Brinkman model has been modified by introducing
the Forchheimer model. This latter model enables one to account for certain other nonlinear features of the flow. It is thus desirable to investigate the relative merits of employing the Brinkman model with inertia terms and the Forchheimer model, in porous media flows. In the present work, we have considered steady, two-dimensional natural convection taking place entirely in a rectangular porous cavity using both models. Assuming that the upper and lower walls of the cavity are adiabatic while the side walls are isothermal, we have solved the governing partial differential equations numerically. The effects of these models have been analyzed and compared based on the results obtained for the physical quantities of interest. A number of plots illustrating the effects of Darcy number and Rayleigh number on the streamlines and isotherms, have been shown. We have also computed the maximum absolute value of stream function and the average Nusselt number. It is seen from these results that the two models are more sensitive to Darcy number.