Two-phase Stefan problem for generalized heat equation with nonlinear thermal coefficients
Nauryz T. Briozzo A.C.
December 2023Elsevier Ltd
Nonlinear Analysis: Real World Applications
2023#74
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component. In particular, the temperature distribution in liquid and solid phases of such kind of body can be modeled by Stefan problem for the generalized heat equation. The method of solution is based on similarity principle, which enables us to reduce generalized heat equation to nonlinear ordinary differential equation. Moreover, we determine temperature solution for two phases and free boundaries which describe the position of boiling and melting interfaces. Existence and uniqueness of the similarity type solution is provided by using the fixed point Banach theorem.
Fixed point theorem , Incomplete gamma function , Nonlinear integral equations , Nonlinear thermal coefficient , Similarity solution , Stefan problem
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Department of International School of Economics, Kazakh-British Technical University, Tole Bi 59, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Pushkina 125, Almaty, Kazakhstan
CONICET, Argentina
Depto de Matemática, F.C.E.,Universidad Austral, Paraguay 1950, Rosario, S2000FZF, Argentina
Department of International School of Economics
Institute of Mathematics and Mathematical Modeling
CONICET
Depto de Matemática
10 лет помогаем публиковать статьи Международный издатель
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