Three-dimensional oscillatory mixed convection in a Czochralski silicon melt under the axial magnetic field

Abstract

A three-dimensional time dependent computational model is developed to simulate the oscillatory mixed convection of the melt during the crystal growth in Czochralski crucible. To study the magnetic damping effects on the growth process, an axial steady magnetic field is considered. The governing equations of continuity, momentum, energy, and electric potential subject to Boussinesq approximation applied to gravity term, have been solved numerically by a computer program developed in FORTRAN language based on finite volume method in conjunction with SIMPLER and TDMA Algorithms. The obtained results show a good agreement with experimental data available in the literature. Without magnetic field, the flow structure shows an irregularity, and the critical Reynolds number decreased in function of Richardson number owing to the destabilizing contribution of the convection. The applied of the magnetic field involves an important regulation of the flow structure and the instability delayed for higher values of the Reynolds number. The magnetic stability diagram which is established shows the dependence of the critical Reynolds number with the increase of the Hartmann number, for various values of the Richardson number. This work confirms the possibility of stabilization of a liquid metal flow in mixed convection by application of a magnetic field.