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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{SVMO_2021_23_1_a5,
     author = {N. D. Kuzmichev and M. A. Vasyutin and E. V. Danilova and E. A. Lapshina},
     title = {Mathematical modeling of heat transfer in the film-substrate-thermostat system during heating of an electrically conductive film by a high-density pulse current},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {82--90},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2021_23_1_a5/}
}
TY  - JOUR
AU  - N. D. Kuzmichev
AU  - M. A. Vasyutin
AU  - E. V. Danilova
AU  - E. A. Lapshina
TI  - Mathematical modeling of heat transfer in the film-substrate-thermostat system during heating of an electrically conductive film by a high-density pulse current
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2021
SP  - 82
EP  - 90
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2021_23_1_a5/
LA  - ru
ID  - SVMO_2021_23_1_a5
ER  - 
%0 Journal Article
%A N. D. Kuzmichev
%A M. A. Vasyutin
%A E. V. Danilova
%A E. A. Lapshina
%T Mathematical modeling of heat transfer in the film-substrate-thermostat system during heating of an electrically conductive film by a high-density pulse current
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2021
%P 82-90
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2021_23_1_a5/
%G ru
%F SVMO_2021_23_1_a5
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/