NATURAL-CONVECTION HEAT-TRANSFER IN A RECTANGULAR ENCLOSURE WITH A TRANSVERSE MAGNETIC-FIELD

In this paper the effect of a transverse magnetic field on buoyancy-dr iven convection in a shallow rectangular cavity is numerically investi gated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and coole d from the other. Both cases of a cavity with all rigid boundaries and a cavity with a free upper surface are considered. The study covers t he range of the Rayleigh number, Ra, from 10(2) to 10(5), the Hartmann number, Ha, from 0 to 10(2), the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made wit h an existing analytical solution (Garandet et al., 1992), based on a parallel flow approximation, and its range of validity is delineated. Results are presented for the velocity and temperature profiles and he al transfer in terms of Ha number. At high Hartmann numbers, both anal ytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two, Hartman lavers at the vicinity of t he walls normal to the magnetic field.