Using a Magnetic Field to Reduce Thermocapillary Convection in Thin Annular Pools

Abstract

This paper presents the investigation of thermocapillary convection in three-dimensional (3-D) thin pools with three cases of annular gaps containing silicon melt under a vertical magnetic field. The model was composed of two vertical walls: the inner is cold, and the outside is hot. Radiation is emitted upward from the free top surface, and the bottom is heated vertically. Both cases are considered in this study, electrically insulating all walls; and only the bottom wall is electrically conducting for three annular gaps. The governing equations were solved numerically through the finite volume method. The effects of different parameters such as the Hartmann number, annular gaps on the temperature distribution, the hydrothermal wave number, and azimuthal patterns, as well as the transition from 3-D steady to axisymmetric flows, were investigated. The results showed three hydrothermal waves are observed in a 3-D steady flow. It was also found that with the increasing Hartmann number, the azimuthal velocity, the temperature fluctuation, and the electric potential decreased. The results also revealed that a stronger magnetic field was needed for the transition from unsteady flow to a nonaxisymmetric steady flow and at the end to steady axisymmetric flow. The findings revealed that electromagnetic damping is more prominent when the bottom wall is electrically conducting than when all walls are insulating.