Abstract
The liquid-metal flow between a smooth moving wall and a two-dimensional, periodic, static wall with a uniform magnetic field that is perpendicular to both walls is treated. This problem models the flow in a liquid-metal sliding electrical contact with extremely large electric currents. The periodic static wall models the surface of a metal-fiber brush. The flow for a two-dimensional static wall is very different from that for a smooth static wall and involves large electrically driven spatial oscillations of the velocity, with swirling motion around the hills and valleys of the periodic surface. Solutions are presented (1) for large magnetic-field strength and arbitrary dimensionless periodic wall height, and (2) for arbitrary magnetic-field strength and small periodic wall height. Comparison of the two solutions indicates that viscous effects reduce the large velocity oscillations for typical electrical contacts.
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