Mathematical modeling of heat transfer in the system «pipeline

Title	Mathematical modeling of heat transfer in the system «pipeline – pressure sensor»
Authors	P. A. Velmisov¹, P. M. Abrashkin¹, A. V. Likanin¹ ¹Ulyanovsk state technical university
Annotation	The one-dimensional nonstationary problem of temperature distribution in the mechanical system «pipeline – pressure sensor» is considered. A numerical and analytical method of solution based on the Galerkin method is proposed. The solution of the problem is reduced to integration of a system of linear ordinary differential equations of the first order with constant coefficients. In the case when the temperature at the pipeline inlet is constant, the analytical solution of the problem is constructed using the method of separation of variables.
Keywords	heat exchange, pipeline, pressure sensor, differential equations, Galerkin method, method of separation of variables.
Citation	Velmisov P. A., Abrashkin P. M., Likanin A. V. ''Mathematical modeling of heat transfer in the system «pipeline – pressure sensor»'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 28-31. Available at: https://conf.svmo.ru/files/2024/papers/paper04.pdf. - Date of access: 16.10.2024.