一类变导热系数下三维温度场解析模型

An Analytical Solution for the Temperature Field With Variable Thermal Conductivity

热传导过程中将材料考虑为无穷大时,其导热系数、容积和比热均为相同的温度函数,先通过Kirchhoff变换得到关于导热系数的偏微分方程,再通过傅里叶积分得到这类变导热系数下热传导方程的解,在外部为双椭球和半椭球热源下得到关于变导热系数的三维温度场解析模型。最后应用于熔化极气体保护电弧焊接(GMAW)和钨极惰性气体焊接(TIG),通过对比分析实验与计算结果说明这类温度场模型的可行性,从而推广了材料物理性能变化下这类热传导方程温度场解析模型。

Assuming that the material objects of heat conduction be infinite, the coefficient of thermal conductivity, the volume and specific heat be a same flmetion of temperature. By means of Kirchhoff transformation on the thermal conductivity, a partial differential equation of heat conduction coefficient is obtained,and analyzing sohltion is obtained by Fourier integral.Based on ellipsoid heat source and half ellipsoid heat source,an analyzing model of temperature field is obtained.Finally, Let heat conduction apply into GMAW and TIG,the feasibility of this kind of temperature field inodel is validated through the experiment, thus promoting the material physical properties changes under the model of the temperature field.