Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium

A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle γ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle γ = 0, π/6, π/4 and π/2, Hartmann number Ha = 0, 1, 5, 10 and 50, Rayleigh number Ra = 10, 100, 103 and 105, and the aspect ratio a = 0.01, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number NuY decreases on the bottom wall as γ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.