Modeling and Simulation of MHD Melt Convection and Heat Transfer in CZ Crystal Growth

Abstract

This paper presents an axisymmetric swirl incompressible thermal lattice Boltzmann model to study the magnetohydrodynamics (MHD) melt flow and heat transfer at high Grashof number and high Reynolds number under external magnetic field in Czochralski (CZ) crystal growth process. The model is built based on the double distribution function lattice Boltzmann equation (DDF-LBE) and is verified by benchmark problem. By using the proposed model, the evolution relationship of melt flow, temperature is constructed under the combined effects of Lorenz force, rotating inertia force and thermal buoyancy force. Furthermore, the flow patterns and the temperature distribution of silicon melt under different magnetic field strengths are simulated. The simulation results show that with the increase of magnetic field strength, the melt velocity is reduced, which suppresses the melt convection and is beneficial for suppressing the fluctuation of melt. And the temperature gradient below the crystal growth interface increases in the case of crystal rotation, which is helpful to increase the crystallization rate. The combination of Cusp magnetic field, crucible rotation and crystal rotation can be used as an effective method in the production of high-quality crystal.