An exact solution to a Stefan problem with variable thermal conductivity\n and a Robin boundary condition

2017/06/21 by Andrea N. Ceretani, Ceretani, Andrea N., Natalia N. Salva +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1706.06984

openalex publication_date 2017/06/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this article it is proved the existence of similarity solutions for a\none-phase Stefan problem with temperature-dependent thermal conductivity and a\nRobin condition at the fixed face. The temperature distribution is obtained\nthrough a generalized modified error function which is defined as the solution\nto a nonlinear ordinary differential problem of second order. It is proved that\nthe latter has a unique non-negative bounded analytic solution when the\nparameter on which it depends assumes small positive values. Moreover, it is\nshown that the generalized modified error function is concave and increasing,\nand explicit approximations are proposed for it. Relation between the Stefan\nproblem considered in this article with those with either constant thermal\nconductivity or a temperature boundary condition is also analysed.\n

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