Effect of thermal dispersion on free convection in a fluid saturated porous medium

The present article considers a numerical study of the thermal dispersion effect on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. The Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and dispersion thermal diffusivity due to mechanical dispersion. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration. The finite element implementations are prepared by using the Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours and profiles as well as heat transfer rate in terms of the Nusselt number, which are shown on graphs, have been presented.