On the Matrix Method for Solving Heat Conduction Problems in a Multilayer Medium in the Presence of Phase Transitions

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 267; no. 6; pp. 698 - 705
• Main Authors: Gladyshev, Yu. A., Kalmanovich, V. V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 04.11.2022; Springer; Springer Nature B.V
• Subjects: Conduction heating; Conductive heat transfer; Heat sources; Mathematics; Mathematics and Statistics; Matrix methods; Multilayers; Phase transitions; Stationary processes; Symmetry; Temperature distribution; Thermodynamics; Transition points; 34B05; heat equation; mathematical model; matrix method; multilayer medium; phase transition; 34B60; 80A20
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-022-06163-6

This paper is devoted to the applicability of the matrix method for solving the heat equation for multilayer media in the case where a phase transition is possible in some layer. We consider only stationary processes in the absence of internal heat sources. We propose a general method for layer systems with translation, axial, or central symmetry based on the technique of generalized Bers powers. Using this method, we perform calculations for one substance, when after a phase transition, the system becomes a two-layer system. We consider the dependence of the coordinate of the phase-transition point on the external temperature and compare results obtained for media with types of symmetry indicated above. A temperature field is constructed for multilayer media with various types of symmetry when a phase transition has occurred in a certain layer.