On the validity of a numerical model predicting heat and mass transfer in porous square cavities with a bottom thermal and solute source: case of pollutants spreading and fuel leaks

Abstract

The present work refers to the study of natural convection into a confined porous medium, driven by cooperating thermal and solutal buoyancy forces. The side walls are maintained at a uniform temperature and concentration, lower than that of a heat and solute source, which located at the center of the bottom wall, the rest of the horizontal walls are kept insulated. The physical model for the momentum conservation equation makes use of the Brinkman extension of the classical Darcy equation, the set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. To account for the effects of the main parameters such the buoyancy ratio, the Lewis and porous thermal Rayleigh numbers, as well as the source length, heat and mass transfer characteristics are widely inspected and then, new powerful correlations are proposed, which predict within ±1% the numerical results. Note that the validity of the used code was ascertained by comparing our results with experimental data and numerical ones already available in the literature.