Computation of MHD buoyant flows at low Pr in a cubic enclosure with a full resolution of the Hartmann layers

Computational results are presented for buoyant MHD flow in a cubic enclosure with differential or internal heating. The magnetic induction B was horizontal and perpendicular to the main temperature gradient. The Prandtl number was 0.0321, the Rayleigh number was 105 and the wall/fluid conductance ratio was 10−2. The Hartmann number ranged from 0 to 1000. Simulations were performed by a general purpose CFD code with extra terms modelling MHD forces and electrical quantities. The method allows the treatment of general configurations of engineering interest, although only the simple above geometry was considered here. In previous work an approximate “ad hoc ” treatment (HLA approach) was used for the Hartmann layers which line the walls perpendicular to B, while in the present work the Hartmann layers were explicitly resolved by the computational grid (HLD approach) and no simplifying assumption was used. Results compared well with those based on the HLA approach and showed otherwise unresolved details of the solution in the near-wall regions. 1