Abstract
The buoyant convection in a long vertical rectangular enclosure under the presence of a horizontal uniform magnetic field is investigated. Two opposite vertical walls are kept at different temperatures and the other four walls are thermally insulating. The main parameters of this study are the Grashoff number Gr, and the Hartmann number Ha. The applied magnetic field is either perpendicular or parallel to the temperature gradient. In both configurations, if it is large enough, it damps out the buoyant flow and ensures a conductive heat flux, but with different scaling laws: Gr/Ha for the perpendicular case, Gr/Ha 2 for the parallel case. This first paper focuses on the fully-established flow, far from the top and the bottom of the enclosure, in the limit of high Ha. Analytical solutions are derived and serve as reference to validate the numerical results. An analytical model of the Hartmann layers describes directly their influence on the core flow, saves important computational resources and yields quite accurate results.
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