EXISTENCE AND UNIQUENESS FOR ONE-PHASE SPHERICAL STEFAN PROBLEM WITH NONLINEAR THERMAL COEFFICIENTS AND HEAT FLUX CONDITION

Nauryz T. Kharin S.
2022 Academic Publications Ltd.

International Journal of Applied Mathematics
2022 #35 Issue 5 645 - 659 pp.

We study a non-classical one-phase Stefan problem for heat transfer in spherical domain of electrical contact materials when heating process on electrical contact surface arises. Mathematical model involves non-linear thermal coefficients and heat flux condition at a known free boundary. Solution of the problem based on similarity principle. Moreover, we determine the temperature distribution in melted zone and the free boundary on melting interface whether direct Stefan problem is considered. The existence and uniqueness of similarity solution to the problem is established. Solutions for constant and linear thermal coefficients and existence of uniqueness for particular cases are provided.

Fixed point , Nonlinear/linear thermal coefficients , Similarity solution , Stefan problem

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Kazakh British Technical University, Almaty, A05H1T2, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, A26G7T4, Kazakhstan
Al-Farabi Kazakh National University, Almaty, A15E3B4, Kazakhstan

Kazakh British Technical University
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

10 лет помогаем публиковать статьи Международный издатель

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