Abstract We study the dynamics of supercooled solidification of a pure material in a finite domain subject to isothermal boundary conditions. At early stages when the liquid can effectively be treated as semi-infinite, we derive asymptotic solutions in the limits of both strong and weak latent-heat release, corresponding to large and small effective Stefan numbers, respectively. In particular, the solutions describing a rapid recalescence followed by a gradual change in the interfacial temperature are derived. Once the finite extent becomes effective, the system relaxes to an intermediate stage. For large Stefan numbers, the intermediate stage is quasi-steady, with the linear temperature profiles in the two phases and the interface temperature close to an equilibrium melting temperature. For Stefan numbers less than unity, the intermediate stage has a traveling-wave temperature profile in the liquid, similar to that in the one-sided problem, and a self-similar profile in the solid, where the temperature is close to the interface temperature through the whole solid except for a thermal boundary layer far from the interface. The model is applied to water, copper and salol, providing estimates for the freezing rates, interface position, and the recalescence and complete-freezing times in these pure systems.

中文翻译：

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有限域中过冷熔体的再辉动力学和凝固

摘要 我们研究了受等温边界条件影响的有限域中纯材料的过冷凝固动力学。在液体可以有效地被视为半无限的早期阶段，我们在强潜热释放和弱潜热释放的极限下推导出渐近解，分别对应于大和小有效 Stefan 数。特别是，导出了描述快速再辉光随后界面温度逐渐变化的解决方案。一旦有限范围变得有效，系统就会放松到中间阶段。对于大的 Stefan 数，中间阶段是准稳态的，两相中的温度曲线呈线性，界面温度接近平衡熔化温度。对于小于 1 的 Stefan 数，中间阶段在液体中具有行波温度分布，类似于单边问题中的行波温度分布，在固体中具有自相似分布，其中温度接近整个固体的界面温度，除了一个远离界面的热边界层。该模型适用于水、铜和 Salol，提供对这些纯系统中冻结速率、界面位置以及再辉和完全冻结时间的估计。