the distribution of temperature is not always linearized in both solid phase and liquid phase. The linearization only expresses when the interface velocity approaches zero.
The thermal conditions must be adjusted as crystal grows, otherwise, the crystal growth rate would be not equal to the design rate, therefore, the temperature adapted the energy conservation in the liquid phase should decreases with the interface moving ahead at a constant velocity. That is to say, the heat power should be similarly reduced along a route calculated through a formula introduced in this paper.
When the design rate exceeds a critical value, the liquid must be initially undercooled.