Frequency effects of a rotating magnetic field on fluid flow in vertical cylinders

The body force generated by a rotating magnetic field applied to a cylindrical column of liquid metal of finite height is investigated theoretically. Although an exact analytical formula has not been found, the proposed approach leads to a good approximate solution. It is demonstrated that the force field is significantly affected by the angular frequency of the rotating magnetic field. In the low-frequency limit, only the azimuthal component is present, while in the high frequency regime, a complex force field is induced which is composed of both azimuthal and meridional components. The resulting azimuthal flow in the Stokesian regime has been numerically obtained and a counter-rotating profile has been demonstrated. The calculated results can be used to determine the fluid flow behavior during crystal growth in a weak rotating magnetic field.