论文标题
非线性热系数的普通热方程的两阶段Stefan问题
Two-phase Stefan problem for generalized heat equation with nonlinear thermal coefficients
论文作者
论文摘要
在本文中，我们研究了一个具有可变横截面的半无限材料中传热的数学模型，当考虑到温度梯度的径向分量与轴向分量相比，当温度梯度的径向分量被忽略时。特别是，可以通过Stefan问题对广义热方程进行液体和固体阶段的温度分布。解决方案的方法基于相似性原理，这使我们能够将广义热方程式减少到非线性普通微分方程。此外，我们确定了两个阶段和自由边界的温度解决方案，这些阶段描述了沸腾和熔化界面的位置。通过使用固定点Banach定理提供解决方案的存在和独特性。
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is considered. In particular, the temperature distribution in liquid and solid phases of such kind of body can be modelled by Stefan problem for the generalized heat equation. The method of solution is based on similarity principle, which enables us to reduce generalized heat equation to nonlinear ordinary differential equation. Moreover, we determine temperature solution for two phases and free boundaries which describe the position of boiling and melting interfaces. Existence and uniqueness of the solution is provided by using the fixed point Banach theorem.
