Mathematical model of thermal phenomena of closure electrical contact with Joule heat source and nonlinear thermal coefficients
Bollati J. Briozzo A.C. Kharin S.N. Nauryz T.A.
January 2024Elsevier Ltd
International Journal of Non-Linear Mechanics
2024#158
The mathematical model describing the dynamics of closed contact heating which involves vaporization of the metal when instantaneous explosion of micro-asperity occurs is presented through a Stefan type problem. The temperature field for metallic vaporization zone is introduced as heat resistance that decreases linearity. Temperature fields for liquid and solid phases of the metal described by spherical heat equations with nonlinear thermal coefficients and Joule heat source have to be determined as well as the free boundaries. Joule heating component depends on space and time variable when alternating current is considered. Solution method of the problem based on similarity variable transformation is applied which enables us to reduce the problem to an ordinary differential equations and nonlinear integral equations. Existence and uniqueness of the integral equations are proved by using fixed point theorem in Banach space.
Joule heat source , Nonlinear thermal coefficients , Stefan problem
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Depto. Matemática, FCE, Univ. Austral, Paraguay 1950, Rosario, Argentina
CONICET, Buenos Aires, Argentina
Kazakh-British Technical University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Narxoz University, Almaty, Kazakhstan
Depto. Matemática
CONICET
Kazakh-British Technical University
Institute of Mathematics and Mathematical Modeling
Narxoz University
10 лет помогаем публиковать статьи Международный издатель
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