ISSN 2079-6900 (Print)
ISSN 2587-7496 (Online)

#### Middle Volga Mathematical Society Journal

DOI 10.15507/2079-6900.25.202303.150-158

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 35J60

#### Mathematical Models of Joint Calculation of Electric and Thermal Fields in Electrochemical Systems (in Electrolytes)

F. V. Lubyshev, A. M. Bolotnov, M. E. Fairuzov

Ufa University of Science and Technology (Ufa, Russian Federation)

Abstract. This paper studies mathematical models for a joint calculation of electric and thermal fields in electrochemical systems (in electrolytes). As is known, passing of electric current through an electrolyte is accompanied by release of Joule heat. The consequence of temperature redistribution in an electrochemical system is a change in the main physical and chemical parameters: viscosity and density of the conductive medium, specific electrical and thermal conductivity, heat transfer coefficient, etc. Taking into account in mathematical models the mutual influence of thermal and electric fields is of particular importance in the technologies of electrolysis of non-ferrous metals (primarily in the industrial production of aluminum) that is accompanied by high-temperature conditions and intensive electrical heat and mass transfer. The processes of electrolytic-plasma removal of coatings, polishing of parts and plasma-electrolytic oxidation attract special attention from the machine-building industry due to the possibility of qualitative improvement of surface properties. In the article correctness of statements of nonlinear models are investigated. The question of unique solvability of the system is explored and a priori estimates of the generalized solution in the Sobolev norms are established. Also, the system of nonlinear partial derivative equations considered in the paper can describe a mathematical model for the joint calculation of electric and thermal fields in solid conductors of electricity and heat.

Key Words: mathematical modeling, nonlinear system of elliptic equations, mixed boundary value problem, generalized solution, operator equation, Sobolev spaces, a priori estimate

For citation: F. V. Lubyshev, A. M. Bolotnov, M. E. Fairuzov. Mathematical Models of Joint Calculation of Electric and Thermal Fields in Electrochemical Systems (in Electrolytes). Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 25:3(2023), 150–158. DOI: https://doi.org/10.15507/2079-6900.25.202303.150-158

Submitted: 03.06.2023; Revised: 11.07.2023; Accepted: 25.08.2023