Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative–convective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion–convection equation is assumed to depend on temperature and time. In each case, an equivalent ordinary differential problem is obtained giving rise to a system of an integral equation coupled with a condition for the parameter that characterizes the free boundary, which is solved through a double-fixed point analysis. Some solutions for particular thermal coefficients are provided.

考虑了一个半无限平板的不同单相Stefan问题，其中包括运动相变材料以及与温度有关的热系数。证明至少有一个相似解的存在是在固定面上强加Dirichlet，Neumann，Robin或辐射对流边界条件。假设扩散对流方程的对流项中出现的速度取决于温度和时间。在每种情况下，都获得了一个等效的常微分问题，从而产生了一个积分方程系统，该方程组加上一个表征自由边界的参数的条件，这可以通过双不动点分析来解决。提供了针对特定热系数的一些解决方案。