Geodesic
Mathematical modeling of heat transfer in the film-substrate-thermostat system during heating of an electrically conductive film by a high-density pulse current
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 1, pp. 82-90.

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Mathematical modeling of heat transfer in the film-substrate-thermostat system with a pulsed flow of high-density current through an electrically conductive film has been carried out. On the basis of the simulation, the analysis of the heating of a niobium nitride film with a high resistivity near the critical temperature of the transition to the superconducting state is made. The inhomogeneous heat conduction equation which is solved numerically, simulates heat transfer in the film-substrate-thermostat system for the third on the left and the first on the right initial boundary value problem. Using the symmetry of the problem, the parameter $H$ is determined, which is equal to the ratio of the heat transfer of the film surface to its thermal conductivity; this parameter is necessary for effective heat removal. It is shown that effective heat removal from films can be provided by current-carrying and potential clamping contacts made, for example, of beryllium bronze. This makes possible to study the current-voltage characteristics of superconductors near the critical transition temperature to the superconducting state with high-density currents $(10^4 - 10^5 A/cm^2)$ without significant heating of the samples.
Keywords: inhomogeneous heat conduction equation, 1st initial-boundary value problem, 3rd initial-boundary value problem, pulsed heating by current.
Mots-clés : niobium nitride membrane 
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N. D. Kuzmichev; M. A. Vasyutin; E. V. Danilova; E. A. Lapshina. Mathematical modeling of heat transfer in the film-substrate-thermostat system during heating of an electrically conductive film by a high-density pulse current. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 1, pp. 82-90. http://geodesic.mathdoc.fr/item/SVMO_2021_23_1_a5/

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