Magnetohydrodynamic liquid-metal flows and power losses in a rectangular channel with a moving conducting wall

Abstract

Fully developed, viscous liquid-metal flows and power losses in a rectangular channel in a uniform, external magnetic field were studied for moderate Hartmann numbers and different channel aspect ratios. The channel was assumed to have insulating side walls parallel to the field, a perfectly conducting moving top wall, and a stationary bottom wall perpendicular to the field. Exact series solutions and numerical calculations are presented for velocity profiles, induced magnetic field distributions, current densities, voltage profiles, and viscous and joulean power losses. The joulean and viscous dissipation are computed from squared quantities involving infinite series with double summations for finite M. The diverging series derived for the viscous power losses is made convergent by slightly modifying the velocity profile of the conducting fluid at the moving interface. The effect of the applied field is to produce an eddy current that accelerates the bulk fluid to velocities greater than those without the field, but because of the presence of the side walls, the velocities are less than in one-dimensional couette flow. Except at small aspect ratios and Hartmann number, almost the entire power loss resulted from the component of the induced current parallel to the applied field.