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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] F. W. Carter, T. Khaire, C. Chang, V. Novosad, “Low-loss single-photon NbN microwave resonators on Si”, Appl. Phys. Lett., 115:9 (2019) | DOI

[2] Y. Suzuki, N. Iguchi, K. Adachi, A. Ichiki, T. Hioki, C.-W. Hsu, R. Sato, S. Kumagai, M. Sasaki, J.-H. Noh, Y. Sakurahara, K. Okabe, O. Takai, H. Honma, H. Watanabe, H. Sakoda, H. Sasagawa, H. Doy, S. Zhou, H. Hori, S. Nishikawa, T. Nozaki, N. Sugimoto, T. Motohiro, “Complete fabrication of a traversable 3 $\mu$ m thick NbN film superconducting coil with Cu plated layer of 42 m in length in a spiral three-storied trench engraved in a Si wafer of 76.2 mm in diameter formed by MEMS technology for a compact SMES with high energy storage volume density”, J. Phys.: Conf. Series, 897:1 (2017)

[3] L. I. Tyrchak, P. V. Plotnikov, Osnovy chislennyh metodov, Fizmatlit Publ., Moscow, 2005, 304 pp. (In Russ.)

[4] V. F. Formalev, D. L. Reviznikov, CHislennye metody, Fizmatlit Publ., Moscow, 2006, 406 pp. (In Russ.)

[5] ed. I. K. Kikoin, Tablicy fizicheskih velichin. Spravochnik, Atomizdat Publ., Moscow, 1976, 1008 pp. (In Russ.)

[6] V. A. Ohorzin, Komp'yuternoe modelirovanie v sisteme Mathcad: ucheb. posobie, Finansy i statistika Publ., Moscow, 2006, 144 pp. (In Russ.)