Nonaxisymmetric flow in a finite-length cylinder with a rotating magnetic field

This paper treats the flow of an electrically conducting liquid in an insul ating cylinder with a spatially uniform, transverse, relating magnetic fiel d. The frequency of the externally applied magnetic field is sufficiently l ow that this field penetrates throughout the liquid. Previous researchers h ave treated the steady, axisymmetric flow driven by the azimuthal average o f the electromagnetic body force. This paper presents an analytical solutio n for the nonaxisymmetric flow perturbation driven by the deviation of the body force from its azimuthal average. For the magnetic held strengths and frequencies currently used in crystal-growth processes, the values of the i nteraction parameter N and the Reynolds number Re, both based on the freque ncy of the magnetic field, are small and large, respectively. The results o f the appropriate asymptotic analysis show that the ratio of the nonaxisymm etric flow to the axisymmetric one is extremely small, thus validating the common neglect of the nonaxisymmetric flow. Therefore a rotating magnetic f ield may provide beneficial stirring without disturbing the desirable axisy mmetric distribution of additives in the liquid. (C) 1999 American Institut e of Physics. [S1070-6631(99)01407-5].