Magnetohydrodynamic liquid-metal flows in a rectangular channel with an axial magnetic field, a moving conducting wall, and free surfaces

Fully developed, viscous liquid-metal velocity profiles and induced magnetic field contours were studied for Hartmann number of M=2 and 10 and for different load currents for a particular rectangular channel configuration (two-dimensional Couette flow). The rectangular channel was assumed to have a homogeneous external (axial) magnetic field parallel to the moving, perfectly conducting top wall and the stationary, perfectly conducting bottom wall. The two stationary side walls were also perfect conductors. The small gap between the moving wall and each side wall was an insulating, free surface. The method of weighted residuals was used to obtain truncated series solutions for the variables of interest. The heavy load currents across the channel were obtained by simulating an external potential to the conducting moving wall. The load currents in each case were opposed by the induced electric field. Since there is no pressure gradient, the flow along the channel is driven by the viscous effects of the moving wall and the Lorentz body force and is retarded by the stationary walls. The circulation is driven by the generator that is due to the axial variation of velocity in an axial magnetic field. The numerical data presented show that the radial gap and the free surface region represent electrical resistances in parallel between the perfectly conducting stationary wall and the perfectly conducting moving wall.