In this paper the effect of a transverse magnetic field on buoyancy-driven convection in a shallow rectangular cavity is numerically investigated (horizontal Bridgman configuration). The enclosure is insulated on the top and bottom walls while it is heated from one side and cooled 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 the range of the Rayleigh number, Ra, from 102 to 105, the Hartmann number, Ha, from 0 to 102, the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A, from 1 to 6. Comparison is made with 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 heat transfer in terms of Ha number. At high Hartmann numbers, both analytical and numerical analyses reveal that the velocity gradient in the core is constant outside the two Hartmann layers at the vicinity of the walls normal to the magnetic field.
Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field
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Alchaar, S., Vasseur, P., and Bilgen, E. (August 1, 1995). "Natural Convection Heat Transfer in a Rectangular Enclosure With a Transverse Magnetic Field." ASME. J. Heat Transfer. August 1995; 117(3): 668–673. https://doi.org/10.1115/1.2822628
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