轴对称相变热传导变分原理及其应用

VARIATIONAL PRINCIPLE OF AXISYMMETRICAL PHASE CHANGE HEAT TRANSFER AND ITS APPLICATION

给出了轴对称相变热传导问题的偏微分方程及三类边界条件,构造了其相应的泛函,证明了一阶变分为零与原问题的等价性。采用等效热容法处理相变潜热。最后,对一个工程中典型的轴对称相变热传导问题-电渣重熔中的金属凝固过程-进行了相界面的模拟计算,计算结果与实验值吻合。

This paper constructs the functional corresponding with ASHT on the basis of being given the partial differential equations and their initial and boundary conditions. And then it is proved that the equivalence between the equations and the extreme of the functional, namely one order variational equals zero. After discussing the evaluating method of latent heat by the method of equivalent thermal capacitance, an example of engineering application with axisymmetrical heat transfer is simulated, which is of the phase interface in Electroslag Melting. The result shows the efficiency of the theory given here.