Strong-field electromagnetic stirring in the vertical gradient freeze process with a submerged heater

This paper treats a steady, axisymmetric melt motion due to electromagnetic (EM) stirring during vertical gradient freeze crystal growth with a submerged heater. There is a radial electric current through the melt from a graphite electrode around the crystal and melt to another graphite electrode at the center of the heater. There is a strong axial magnetic field produced by an external solenoid. Solutions are presented for the azimuthal and meridional velocities in the subregions of the melt. The melt motion depends on the electric currents through the crystal, even though the electrical conductivity of the crystal is much less than that of the melt.