EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES
Kassabek S.A. Kharin S.N. Suragan D.
2022L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2022#13Issue 351 - 66 pp.
In this paper, we present exact and approximate solutions of the Stefan problems in ellipsoidal coordinates. We consider two models of electrical contact heating for melting process. The first problem describes the contact heating for liquid and solid zones based on the two-phase Stefan problem, where time t is present as a parameter. Contact heating including softening processes are described by a mathematical model based on the three-phase Stefan problem for the ellipsoidal heat equation. Numerical results are presented and discussed
Electrical contact heating , Heat balance integral method , Joule heating , Softening stage , Stefan problems
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Department of Mathematics, Nazarbayev University, 53 Kabanbay batyr St, Astana, Kazakhstan
International School of Economics, Kazakh British Technical University, 59 Tole bi St, Almaty, Kazakhstan
Department of Mathematics
International School of Economics
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