HYDROMAGNETIC NATURAL CONVECTION IN A TILTED RECTANGULAR POROUS ENCLOSURE

Abstract

A study is made of natural convection within an inclined porous layer saturated by an electrically conducting fluid in the presence of a magnetic field. The long side walls of the cavity are maintained at a uniform heat flux condition, while the short side walls are thermally insulated. On the basis of a parallel flow model, the problem is solved analytically to obtain a set of closed-form solutions. Scale analysis is applied to the case of a boundary layer flow regime in a vertical enclosure. Comparison between the fully numerical and analytical solutions is presented for 0 ≤, Ra ≤, 10³ ≤, Ha ≤, 10, and -180 ° ≤, Φ ≤, 180°, where Ra, Ha, and Φ denote the Rayleigh number, Hartmann number, and inclination of the enclosure, respectively. It is found that the analytical solutions can faithfully predict the influence of a magnetic field on the flow structure and heat transfer for a wide range of the governing parameters. For a boundary layer flow regime in a vertical cavity the results of the scale analysis agree well with approximations of the analytical solution. For this situation it is found that the Nusselt number is Nu = O.5Ra^2/5 / ( 1 + Ha²) ^2/5. For a horizontal cavity heated from below the critical Rayleigh number for the onset of motion, determined from a stability analysis, corresponds to that for the existence of unicellular convection using the parallel flow approximation. In general, it is demonstrated that, with the application of an external magnetic field, the temperature and velocity fields are significantly modified and the Nusselt number is decreased with increasing Ha.