Soret Convection in a Shallow Porous Cavity under a Magnetic Field and Submitted to Uniform Fluxes of Heat and Mass

Combined effects of magnetic field and thermodiffusion (Soret effect) on natural convection within an electrically conducting binary mixture, confined in a horizontal sparsely packed porous enclosure subjected to uniform fluxes of heat and mass, is studied analytically and numerically. In the limit of a shallow enclosure, an analytical solution is derived using the parallel flow approximation. The approximate analytical solution is validated against the numerical solution of the full governing equations using a finite difference method. Interesting flow bifurcation phenomena are obtained herein and discussed. The linear stability theory and the parallel flow concept are used to determine explicitly the thresholds for the onset of stationary,subcritical and oscillatory convections as functions of the governing parameters. The obtained results showed the existence of different regions in the (N, Le) plane that correspond to different parallel flow behaviors. The number and the locations of these regions depend on the Soret parameter. The existence of a codimension-۲ point is demonstrated. The effects of the Hartmann number on the fluid flow intensity and heat and mass transfer characteristics are also discussed.