通过具有超定对流边界条件的糊状区模式同时确定两个未知热系数
Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition
摘要：
考虑了Solomon-Wilson-Alexiades模型下含糊状区相变过程的半无限材料的两个未知热系数的同时确定问题。假设材料在其熔化温度下最初是液体，并且认为固化过程由于施加在固定面处的热通量而开始。相关的自由边界值问题是overspecified与对流边界条件的目的是同时确定的温度的固体区域，两个自由边界的糊状区和两个热系数之间的单位质量的潜热，导热系数，质量密度，比热和两个系数，其特征糊状区。假定糊状区的另一个自由边界、本体温度、固定面处的热流密度和传热系数是已知的。根据未知热系数的选择，出现了十五个相变问题。所有的研究，他们提出和明确的公式的未知数，除了充要条件的数据，以获得它们。表中总结了未知热系数的公式及其相应的数据限制。
英文摘要：
The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the Solomon-Wilson-Alexiades model is considered. The material is assumed to be initially liquid at its melting temperature and it is considered that the solidification process begins due to a heat flux imposed at the fixed face. The associated free boundary value problem is overspecified with a convective boundary condition with the aim of the simultaneous determination of the temperature of the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. The another free boundary of the mushy zone, the bulk temperature and the heat flux and heat transfer coefficients at the fixed face are assumed to be known. According to the choice of the unknown thermal coefficients, fifteen phase-change problems arise. The study of all of them is presented and explicit formulae for the unknowns are given, beside necessary and sufficient conditions on data in order to obtain them. Formulae for the unknown thermal coefficients, with their corresponding restrictions on data, are summarized in a table.
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