Title | Analysis of heat distribution in a niobium nitride membrane based on a three-dimensional model under pulsed electric current |
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Authors | E. V. Danilova^{1}, N. D. Kuzmichev^{1}, M. A. Vasyutin^{1}^{1}National Research Mordovian State University |

Annotation | The paper considers the process of heat propagation in an $NbN$ membrane when a current pulse passes through it based on an inhomogeneous three-dimensional thermal conductivity equation. A 3D model of the "contacts–membrane–substrate-environment" system is constructed. The maximum heating of the membrane is estimated. It is shown that the contact material (beryllium bronze BeCu) provides an effective heat sink from a superconducting membrane in a resistive state when a high-density current flows through it. |

Keywords | heat transfer, inhomogeneous heat equation, boundary value problem, beryllium bronze, $NbN$ membrane |

Citation | Danilova E. V., Kuzmichev N. D., Vasyutin M. A. ''Analysis of heat distribution in a niobium nitride membrane based on a three-dimensional model under pulsed electric current'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 61-65. Available at: https://conf.svmo.ru/files/2023/papers/paper08.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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