标题： 融化过程的相似性解与对流边界条件 显示英文标题

标题： Similarity solutions for thawing processes with a convective boundary condition

摘要： 对于饱和无限大多孔介质中一维数学模型的融化问题，当相变引起密度跳跃，并在固定面 $x=0$上施加对流边界条件时，考虑相似性解。根据物理参数的不同情况进行了分析，只有当数据满足一个不等式时，才能得到一种显式相似性解。此外，得到了涉及自由边界定义系数的单调性性质，该性质相对于描述固定面 $x=0$处传热的系数获得。本文考虑的在固定面 $x=0$上具有对流条件的Stefan问题与在相同面上具有温度条件的Stefan问题（Fasano-Primicerio-Tarzia, Math. Models Meth. Appl. Sci., 9 (1999), 1-10）之间的关系进行了分析，并获得了使两个问题等价的物理参数条件。此外，还获得了关于在固定面 $x=0$上具有温度或对流边界条件的问题的自由边界特征系数应满足的不等式。 显示英文摘要

摘要： Similarity solutions for a one-dimensional mathematical model for thawing in a saturated semi-infinite porous media is considered when change of phase induces a density jump and a convective boundary condition is imposed at the fixed face $x=0$. Different cases depending on physical parameters are analysed and an explicit solution of a similarity type is obtained if and only if an inequality for data is verified. Moreover, a monotony property respect to the coefficient which characterizes the heat transfer at the fixed face $x=0$ is obtained for the coefficient involved in the definition of the free boundary. Relationship between the Stefan problem with convective condition at $x=0$ considered in this paper and the Stefan problem with temperature condition at the same face studied in (Fasano-Primicerio-Tarzia, Math. Models Meth. Appl. Sci., 9 (1999), 1-10) is analized and conditions for physical parameters under which both problems became equivalents are obtained. Furthermore, an inequality to be satisfied for the coefficient which characterizes the free boundary of the problem with a temperature or a convective boundary condition at the fixed face $x=0$ is also obtained.