MHD Effect on the Thermocapillary Silicon Melt Flow in Various Annular Enclosures

To simulate thermocapillary magnetohydrodynamic (MHD) convection in different shallow annular enclosures filled with silicon melt, a 3D numerical approach using an implicit finite volume formulation is used. Radiation is emitted upward from the annular enclosure's free top surface, the bottom one heated vertically and is subjected to an external magnetic field. The steady and unsteady thermocapillary MHD flow in four annular enclosures (R = 0.5, 0.6, 0.7, and 0.8) field is studied. The effects of varying the annular gaps, R, on the hydrothermal wave number and azimuthal pattern are obtained. The effects of the magnetic field on azimuthal velocity, temperature disturbances, and the transition from oscillatory to steady flow are also depicted. The results reveal that: hydrothermal waves m = 4, m = 6 and m = 8 are observed in steady flow for R = 0.7, R = 0.6 and R = 0.5, respectively. Oscillatory flows dominated by a hydrothermal wave m = 3 are found also when R = 0.8. The azimuthal velocity and temperature fluctuations at the free surface decrease as the magnitude of the magnetic field (Ha) increases, and the oscillatory flow would turn steady when Ha exceeds a critical value.