Numerical solution of uni-directional solidification problem using the boundary-fitted coordinate system

Using the boundary-fitted coordinate system, we calculate the uni-directional solidification problem of semiconductor materials. The purpose of this study is to make clear the solid-liquid interface behavior of the materials. We investigate two cases of whether the motion of the melt is taken into consideration or not. Through the calculations that ignore the motion of the melt, some results are obtained: (1) when the temperature profile does not move, the solid-liquid interface shape is determined by the product of the temperature gradient and the thermal conductivity of the materials; (2) when the temperature profile moves at a constant velocity, the growth rate of the solid phase is described by the moving velocity of the temperature profile and a delay time which is related to the growth conditions. When the motion of the melt is considered in the governing equations, the transient Grashof number proposed in this study is found to be a good parameter describing the uni-directional solidification process. Moreover it is found that the motion of the melt has a little effect on the growth rate.