N. D. Kuzmichev, E. V. Danilova, M. A. Vasyutin

National Research Ogarev Mordovia State University (Saransk, Russian Federation)

Abstract. A numerical calculation of the evolution of the temperature distribution in the longitudinal section of a niobium nitride membrane when it is heated by an electric current pulse is performed. Mathematical modeling was carried out on the basis of a two-dimensional initial-boundary value problem for an inhomogeneous heat equation. In the initial boundary value problem, it was taken into account that current and potential contacts to the membrane serve simultaneously as contacts for heat removal. The case was considered for the third from the left and the first from the right initial-boundary value problem. Analysis of the numerical solution showed that effective heat removal from the membrane can be provided by current-carrying and potential clamping contacts made, for example, of beryllium bronze. This makes it possible to study the current-voltage characteristics of superconducting membranes near the critical temperature of the transition to the superconducting state by currents close to the critical density without significant heating.

Key Words: inhomogeneous two-dimensional heat conduction equation, numerical analysis, evolution of temperature distribution, 1st and 3rd initial-boundary value problems, cross section, niobium nitride membrane, current contact, potential contact, pulsed heating by current

For citation: N. D. Kuzmichev, E. V. Danilova, M. A. Vasyutin. Numerical analysis of heating by a current pulse of a niobium nitride membrane in its longitudinal section. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 23:4(2021), 424–432. DOI: https://doi.org/10.15507/2079-6900.23.202104.424–432

Information about the authors:

Nikolay D. Kuzmichev, Professor, Department of Computer Science and CAD-technology, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), D. Sci. (Mathematics and Physics), ORCID: http://orcid.org/0000-0001-6707-4950, kuzmichevnd@yandex.ru

Ekaterina V. Danilova, Post-Graduate Student, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), ORCID: https://orcid.org/0000-0003-0554-3795, danilova29-94@mail.ru

Mikhael A. Vasyutin, Associate Professor, Department of Computer Science and CAD-technology, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Mathematics and Physics), ORCID: http://orcid.org/0000-0002-4856-7407, vasyutinm@mail.ru