MHD natural convection in an inclined cavity filled with a fluid saturated porous medium with heat source in the solid phase

A numerical investigation of unsteady magnetohydrodynamic free convection in an inclined square cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field inclined with the same angle of the inclination of the cavity is applied. The governing equations are formulated and solved by a direct explicit finite-difference method subject to appropriate initial and boundary conditions. Two cases were considered, the first case when all the cavity walls are cooled and the second case when the cavity vertical walls are kept adiabatic. A parametric study illustrating the influence of the Hartmann number, Rayliegh number, the inclination angle of the cavity and the dimensionless time parameter on the flow and heat transfer characteristics such as the streamlines, isotherms and the average Nusselt number is performed. The velocity components at mid section of the cavity as well as the temperature profiles are reported graphically. The values of average Nusselt number for various parametric conditions are presented in tabular form.