MHD buoyant flow in a cubical enclosure at low to high Hartmann number

The numerical calculations are performed for Hartmann numbers of 100−5000, Rayleigh numbers of 104−106 and wall conductance ratios of 0−∞ at Pr=0.01. It is observed that an increase in the applied magnetic field decreases the flow velocity and Nusselt number. At Ra=104, Hartmann numbers beyond 200 cause the complete suppression of the core velocity. For higher Ra, complete suppression is found only at increased values of Ha (Ha=500 and Ha=1000 for Ra=105 and Ra=106 respectively). At higher Ha, the heat transfer is mostly purely due to conduction and the Nusselt number is close to unity. For a fixed Ha and Ra, it is seen that an increase in wall conductivity decreases convective motion and the average Nusselt number, as the walls become more conducting. The effect of the magnetic field applied parallel to the temperature gradient is more pronounced over the other orthogonal directions because it directly acts against the buoyancy force.