MHD convection over non isothermal ellipse embedded in fluid saturated porous medium

Analysis has been carried out to determine the effects of uniform magnetic field on the combined forced and free convection flow of an electrically conducting fluid over a non-isothermal body with elliptic shape in a saturated porous medium. The continuity, Darcy law and energy equations are transformed into non-dimensional form then solved numerically using keller--box method. It is found that four dimensionless groups are required to describe the problem under consideration; the first one is the Hartmann number (Ha), which reflects the magnetic field strength, the second one is the mixed convection parameter (Ra/Pe), the third one is the adjusting factor of the geometry (I), and the fourth one is the modified Eckert number (Ec* ). Dimensionless velocity profiles, temperature profiles and Nusselt Number are shown in tables and figures. It is found that the increase of (Ha) decreases the Nusselt numbers and the increase of (Ra/Pe) increases velocity inside boundary layer and consequently increases heat transfer values. The effect of the geometry parameter is found to decrease the temperature and hence increases the heat transfer rates. The effect of (Ec*) is found to decrease the heat transfer rates while increasing temperature inside the boundary layer.