Natural Convection in a Cavity Filled with a Porous Medium with Variable Porosity and Darcy Number

This work presents a numerical analysis of the natural convection in a squared cavity with isothermal vertical walls. The cavity is filled with a saturated porous medium, and the classical equations for natural convection, mass, momentum, and energy balance, together with Brinkman's and Forchheimeir's models, are used to study the phenomenon. The system of equations is numerically solved through the finite volume method. For porous media with constant porosity, the results are compared to those found in the literature, with very good agreement. The influence of the variation of Darcy number in media with variable porosity is investigated. The results indicate that the inclusion of the variation of Darcy number affects significantly the velocity and temperature fields as well as the values of heat transfer rates.