Abstract The major goal of this article is to develop mathematical and numerical analysis of one phase moving boundary problem with conduction and convection effect when variable thermal conductivity depends on time and temperature and also latent heat is presented as the power function of position. In model-1 the temperature at the surface is described while in model-2 the heat flux condition is expressed in terms of power function of time. The numerical algorithms of these two models are obtained by using Legendre Wavelet Galerkin (LWG) and Legendre Wavelet Collocation (LWC) methods. LWG technique is used to obtain the numerical solution in case of constant properties while LWC technique is used for variable thermal conductivity. The effect of both convection term and variability of thermal conductivity with time and temperature on the moving interface is analyzed. Further variability of Stefan numbers, Peclet numbers and other parameters on the location of the moving interface is discussed in detail and is shown graphically.

中文翻译：

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基于Legendre小波的变潜热移动边界问题的数值解

摘要 本文的主要目标是对具有传导和对流效应的相移动边界问题进行数学和数值分析，当可变热导率取决于时间和温度并且潜热表示为位置的幂函数时。在模型 1 中描述了表面温度，而在模型 2 中，热通量条件用时间的幂函数表示。这两种模型的数值算法是利用勒让德小波伽辽金(LWG)和勒让德小波搭配(LWC)方法得到的。LWG 技术用于在恒定属性的情况下获得数值解，而 LWC 技术用于可变热导率。分析了对流项和热导率随时间和温度变化对移动界面的影响。详细讨论了移动界面位置上 Stefan 数、Peclet 数和其他参数的进一步变化，并以图形方式显示。