HYDROMAGNETIC NATURAL-CONVECTION IN A TILTED RECTANGULAR POROUS ENCLOSURE

A study is made of natural convection within an inclined porous layer saturated by an electrically conducting fluid in the presence of a mag netic field. The long side walls of the cavity are maintained at a uni form heat flux condition, while the short side walls are thermally ins ulated. On the basis of a parallel flow model, the problem is solved a nalytically to obtain a set of closed-form solutions. Scale analysis i s applied to the case of a boundary layer flow regime in a vertical en closure. Comparison between the fully numerical and analytical solutio ns is presented for 0 less-than-or-equal-to Ra less-than-or-equal-to 1 0(3), 0 less-than-or-equal-to Ha less-than-or-equal-to 10, and -180-de grees less-than-or-equal-to PHI less-than-or-equal-to 180-degrees, whe re Ra, Ha, and PHI denote the Rayleigh number, Hartmann number, and in clination of the enclosure, respectively. It is found that the analyti cal solutions can faithfully predict the influence of a magnetic field on the flow structure and heat transfer for a wide range of the gover ning parameters. For a boundary layer flow regime in a vertical cavity the results of the scale analysis agree well with approximations of t he analytical solution. For this situation it is found that the Nussel t number is Nu = 0.5Ra2/5 / (1 + Ha2)2/5. For a horizontal cavity heat ed from below the critical Rayleigh number for the onset of motion, de termined from a stability analysis, corresponds to that for the existe nce of unicellular convection using the parallel flow approximation. I n general, it is demonstrated that, with the application of an externa l magnetic field, the temperature and velocity fields are significantl y modified and the Nusselt number is decreased with increasing Ha.