Numerical Study of Laminar Natural Convection in Porous Media: Darcy -Brinkman-Forcheimer Model

Abstract

In this article, we present a two-dimensional study of laminar natural convection in porous enclosure. The horizontal walls of the enclosure are thermally insulated, where as the left and right vertical walls are maintained respectively at different temperatures TC (warm temperature) and Tf (cold temperature).we present the differential equations modeling the phenomenon studied according to Darcy- Brinkman – Forcheimer model. after the dimensionless form of the equation we have four dimensionless numbers: the Prandtl number Pr the thermal Grashof Gr, the aspect ratio A, the Darcy number Da. The results allowed us to conclude the following: Increasing of Grachof number with a constant Darcy number, so we areThe increase of convection and as a result the increase in flow velocity and heat transfer.at constant of Grachof number whith decreasing of the Darcy number, the medium is impermeable which slow motion of the convection phenomenon. so we are a degradation speed and heat transfer. Finaly We executed the program calculates with the real data of oil reservoir.