Purpose

The main purpose of this paper is given below: To present a mathematical model of a two-phase Stefan problem including a moving phase change material and variable thermophysical properties. To find a numerical solution of the problem to discuss the dependence of considered phase change problem on variable thermal conductivity, variable specific heat and Peclet number.

Design/methodology/approach

In this paper, a numerical solution of the problem is obtained using the front-fixing method in tandem with the explicit finite difference scheme. The authors have also discussed the consistency and stability of proposed numerical scheme.

Findings

In this study, it is observed that the considered scheme is an efficient tool that provides sufficiently accurate results for exploring the behaviors of moving interface (free boundary) and temperature profile for a nonclassical two-phase free boundary problem. In this study, the authors have observed that the parameters α1 and α2 influence the temperature profiles of the liquid region and the solid region. It is also found that the free boundary propagates faster when the authors increase the parameter α1 or decrease the parameter α2.

Originality/value

From the literature, it is seen that most of the two-phase problems with free boundary in an infinite domain are considered by the authors with constant thermophysical properties. Because it is possible to establish an analytical solution of two-phase problems with free boundary in case of an infinite domain. Moreover, a two-phase problem in a finite domain involving moving phase change material with the unidirectional speed is not considered. Therefore, the authors have considered a two-phase free boundary problem with variable thermal coefficients.

中文翻译：

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在有限域中使用 MPC 材料解决两相自由边界问题的数值方法

 目的

本文的主要目的如下：提出一个两相 Stefan 问题的数学模型，包括移动相变材料和可变的热物理性质。为了找到问题的数值解，讨论所考虑的相变问题对可变热导率、可变比热和 Peclet 数的依赖性。

设计/方法/方法

在本文中，使用前固定方法与显式有限差分方案结合使用，获得了该问题的数值解。作者还讨论了所提出的数值方案的一致性和稳定性。

 发现

在本研究中，观察到所考虑的方案是一种有效的工具，它为探索非经典两相自由边界问题的移动界面（自由边界）和温度曲线的行为提供了足够准确的结果。在这项研究中，作者观察到参数 α1 和 α2 会影响液体区域和固体区域的温度分布。研究还发现，当作者增加参数 α1 或减小参数 α2 时，自由边界传播得更快。

 原创性/价值

从文献中可以看出，作者认为大多数在无限域中具有自由边界的两相问题都是用恒定的热物理性质来考虑的。因为在无限域的情况下，可以建立具有自由边界的两相问题的解析解。此外，没有考虑有限域中涉及以单向速度移动相变材料的两相问题。因此，作者考虑了一个具有可变热系数的两相自由边界问题。