Three-dimensional flow in a thin annular layer of silicon melt with bidirectional temperature gradients

Bidirectional temperature gradients coexist virtually in surface tension driven flows. However, the simulations have been performed to the flow with only one temperature gradient. A series of 3D numerical simulations are conducted to investigate the Marangoni-thermocapillary flow of silicon melt in a thin annular layer with bidirectional temperature gradients. The temperature gradients are produced by the temperature difference T between walls and the constant heat flux q on the bottom, respectively. When changing q, the melt presents different state evolutions at different T. Furthermore, two critical q are found, one makes the minimum melt temperature higher than the crystallization temperature and the other makes the flow unsteady. Both of the critical heat fluxes decrease with increasing T. q contributes more to the elevation of the melt temperature, while T contributes more to the enhancement of the melt instability. In addition, the melt on the free surface flows mainly along the radial direction.