EXACT SOLUTION TO A STEFAN-TYPE PROBLEM FOR A GENERALIZED HEAT EQUATION WITH THE THOMSON EFFECT
Nauryz T.A. Kharin S.N. Briozzo A.C. Bollati J.
January 2025L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2025#16Issue 368 - 89 pp.
We study a one-dimensional Stefan type problem which models the behavior of electromagnetic fields and heat transfer in closed electrical contacts that arises, when an instantaneous explosion of the micro-asperity occurs. This model involves vaporization, liquid and solid zones, in which the temperature satisfies a generalized heat equation with the Thomson effect. Accounting for the nonlinear thermal coeffcient, the model also incorporates temperature-dependent electrical conductivity. By employing a similarity transformation, the Stefan-type problem is reduced to a system of coupled nonlinear integral equations. The existence of a solution is established using the fixed point theory in Banach spaces.
fixed point theorem , generalized heat equation , nonlinear integral equations , nonlinear thermal coeffcient , similarity solution , Stefan problem , Thomson effect
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International School of Economics Kazakh-British Technical University, 59 Tole Bi St, Almaty, 050005, Kazakhstan
Department of Mathematical Physics and Modelling, Institute of Mathematics and Mathematical Modelling, 125 Pushkin St, Almaty, 050010, Kazakhstan
Department of Matematics Universidad Austral CONICET, 1950 Paraguay St, S2000FZF, Rosario, Argentina
International School of Economics Kazakh-British Technical University
Department of Mathematical Physics and Modelling
Department of Matematics Universidad Austral CONICET
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