Effect of an electromagnetic field on natural convection in an inclined porous layer

Abstract

An investigation is conducted to study the effect of an electromagnetic field on free convection of in inclined rectangular porous cavity saturated with an electrically conducting fluid. The enclosure has the long side walls heated isothermally, while the short ends are thermally insulated. A uniform magnetic field is applied normal to the heated walls. The porous medium, modeled according to Darcy's law, is assumed to be isotropic. The dimensionless governing equations are derived in terms of the characteristic dimensionless parameters; namely, the Rayleigh number R, the magnetic Hartmann number Ha, the cavity aspect ratio A, and the inclination angle 9. An approximate analytical solution is presented for the boundary-layer flow regime within a vertical cavity. A linear stability analysis is made to determine the effect of the magnetic field on the onset of convection in a horizontal layer heated from below. A numerical study is performed to assess and extend the results of the analytical solutions. It is found that with application of an external magnetic field, the temperature and velocity fields are significantly modified.