【摘要】 工程里出现许多问题中,传热是和传导介质中的相变一起发生的,或由于通过介质传播的某些化学反应产生组份的变化。这些现象一般地伴随在活性区域中的放热或者吸热。这些现象的例子如熔解和凝固过程,象燃烧那样的化学反应,食物的冷冻,烧铸过程中金属的凝固,霜冻的渗入土地和烧蚀的空气动力学方面。直角座标系Stefan反问题的分析解出现时间较长。这问题讨论移动界面中带有边界条件物质的相变。举例来说,已经解决了移动界面方程S(τ)=ατ~β中含有时间变量导热的相变问题,在这问题中获得了一个用无穷级数表示的严格解。作为它的特例,能够得到Lanford导出的两个严格解。本文获得一维球Stefan反问题的近似解。它适用于向内和向外相变。这近似解与奇异摄劝解比较,结果很接近。更多还原

【Abstract】 Many problems arise in engineering in which heat transfer is accompanied by a change of phase in the conducting medium or the composition changes because of some chemical reaction which is propagated through the medium. Such phenomena as these are generally aceompaxied by either the release or absorption of thermal energy in the active zone. Examples of such phenomena are the melting or solidification processes, chemical reactions such as combustion, the freezing of food, the solidification of metals in the casting, the penetration of frost into the earth, and the aerodynamic phenomenon of ablation. Long ago analytic solutions to the inverse Stefan problem were presented in Cartersian and sperical coordinates. This problem deals with the phase change of a substance with the boundary conditions specified at the moving boundary. As an example, a conduction phase change problem with a time variation of the moving front S(τ)=ατ~βis solved and an exact solution expressed by an infinite series is found, from which two special exact solutions obtained by Langford can be derived. An approximate solution is obtained for outward and inward spherical inverse Stefan problem. Compared the approximate solution with perturbation solution, the resuet is near the same.更多还原