Numerical Study of Mhd Natural Convection in an Inclined Rectangular Cavity with Internal Heat Generation Filled with a Porous Medium under the Influence of Joule Heating

Using an implicit finite difference method, the effect of Joule heating on the magnetohydrodynamic natural convection in an inclined rectangular enclosure with internal heat generation has been performed. The left and right walls of the enclosure are maintained at a constant temperature while the bottom and top walls are kept insulated. The values of the governing parameters are the Hartmann number, Ha=0, 5, 10 and 50, Joule heating parameter J=0, 0.005, 0.01 and 0.02, the aspect ratio a=0.01, 0.2, 0.5 and 1, the inclination angle =0, /6 and /3 and Rayleigh number Ra=10 and 10. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the streamlines and isotherms as well as the local Nusselt number is illustrated graphically to show interesting features of the solutions. It is found that, the local Nusselt number increases on the bottom wall as the enclosure aspect ratio increases.