Effect of Perpendicular Magnetic Field on Free Convection in a Rectangular Cavity

The steady free convective flow of a viscous incompressible and electrically conducting fluid in a two-dimensional cavity in the presence of a magnetic field applied normal to the plane of the cavity is investigated. The side vertical walls of the cavity are heated differentially while the horizontal walls are assumed to be insulated. The governing equations are re-formulated in terms of vorticity and stream function. The resulting boundary value problem is solved numerically using an alternating direction implicit (ADI) method. A number of plots illustrating the influence of Hartmann number and Rayleigh number on the streamlines and isotherms as well as the velocity and temperature profiles are shown. Furthermore, results for the average Nusselt number and the maximum absolute stream function have been obtained, and these are compared with the corresponding results in the literature when the magnetic field is applied along the cavity in the horizontal direction.