Numerical Simulation of 3-D free convection in porous media due to combined surface forced convection and internal heat generation

A three-dimensional fluid-saturated porous medium model for natural convective flow has been developed, taking into account inertial and viscous forces within the fluid. The model consists of a cube with a top surface partially exposed to a steady, uniform convective heat flux and the entire domain to uniform internal heat generation. The differential equations for the Brinkman-extended Darcy model were formulated and non-dimensionalized, with numerical solutions obtained using the Galerkin finite element method. The results have been validated by comparison with previously published reports. It has been observed that the applied boundary conditions result in a central toroidal vortex driven by buoyancy, which in turn influences the isothermal profile. The shape and intensity of these vortices is significantly affected by a combination of dimensionless parameters such as Rayleigh number, Darcy number, and porosity