In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number. The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.
We analyze analytically the effects of anisotropy in permeability and that of a transverse magnetic field on thermal convection in a porous medium saturated with a binary fluid and confined in a horizontal cavity. The porous medium, of great extension, is subjected to various conditions at the thermal and solutal boundaries. The axes of the permeability tensor are oriented obliquely with respect to the gravitational field. Based on a scale analysis, the velocity, temperature, and heat and mass transfer rate fields were determined. These results were validated by the study of borderline cases which are: pure porous media and pure fluid media discussed in the literature. It emerges from this study that the anisotropy parameters influence the convective flow. The application of a transverse magnetic field significantly reduces the speed of the flow and thereby affects the temperature field and the rate of heat and mass transfer.
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