Molten metals are heated and stirred by alternating currents and magnetic fields in a wide range of industrial devices. In this paper, the problem of identifying efficient and accurate methods of calculating the mean magnetic force field and its curl (the stirring-force density) from given magnetic-field data, in order to allow analysis of the resulting fluid motions in cases where there is axisymmetry, is considered. In one case the currents are azimuthal, in the other case the magnetic fields are azimuthal. Some surprisingly convenient and illuminating expressions can be found for the stirring force, or its dominant part in the high-frequency case of small skin depth.
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