A solidification process for a semi-infinite material is presented through a non-linear two-phase unidimensional Stefan problem, where a convective boundary condition is imposed at the fixed face $x=0$. The volumetric heat capacity and the thermal conductivity are non-linear functions of the temperature in both solid and liquid phases and they verify a Storm-type relation. A certain inequality on the heat transfer coefficient $h$ is established in order to get an instantaneous phase change process. We determine sufficient conditions on the parameters of the problem in order to prove the existence and uniqueness of a parametric explicit solution for the Stefan problem.

中文翻译：

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具有非线性热系数和对流边界条件的两相Stefan问题

通过非线性两相一维Stefan问题提出了半无限材料的凝固过程，其中在固定面上施加了对流边界条件 $X=0$。固相和液相温度的体积热容和导热率都是温度的非线性函数，它们证明了Storm型关系。传热系数存在一定的不等式$H$为了得到一个瞬时的相变过程，需要建立一个常数。我们确定问题的参数的充分条件，以证明Stefan问题的参数显式解决方案的存在和唯一性。