熔体热辐射对晶体中温度场和应力场的影响

Affect of Radiation on Temperature Distribution and Thermal Stress Distribution

熔体热辐射被晶体逐渐吸收的过程是光子将能量转移到晶格的过程。用导热微分方程描述晶体中温度场时，把吸收的辐射热当做晶体产生的内热，方程从Ｌａｐｌａｃｅ形式变为Ｐｏｓｓｏｎ形式。仅从顶表面耗散热量的情况下，不考虑对辐射的吸收，晶体中轴向温度梯度为恒值。考虑对辐射的吸收，固液界面处轴向温度梯度最小，向上逐渐增加，最后趋于恒值。但这个恒值比不考虑辐射吸收时大，晶体具有较高的温度。晶体对熔体热辐射平均吸收系数是决定影响大小的主要因素。当吸收系数接近于零时（晶体完全透明）或吸收系数很大时（晶体完全不透明）辐射对晶体温度场的影响可忽略不计。辐射的吸收使晶体下部热应力轴向分量变小，晶体上部热应力轴向分量变大。

The course that the radiation of the melt enter the crystal and is absorbed is a course of energy transference from photon to crystal matrix. If absorbed heat of radiation is regarded as internal generative heat,the temperature distribution is described by Posson differential equation. Using simple boundary condition, the temperature gradient along the z direction is a constant while the generative internal heat is not considered. Using same boundary condition, the temperature gradient along the z direction is gradually increasing to a constant from the solid liquid interface to the top of crystal while the internal heat generative is considered. The thermal stress is decreasing in part of the crystal near the interface. The absorbed coefficient of crystal for the radiation of the melt is an important factor affecting on the temperature distribution and the thermal stress distribution. If the absorbed coefficient is near zero(the crystal is quite transparence) or large (the crystal is quite opaque), the temperature distribution and the thermal stress distribution are not affected by the radiation.