Математичні моделі визначення температурних режимів у елементах літій-іонних акумуляторних батарей
| Autor: | I. Ye. Ovchar, V. B. Loik, V. I. Havrysh, I. G. Kozak, O. V. Kuspish, O. S. Korol, R. R. Shkrab |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematical model
Differential equation Mathematical analysis 020206 networking & telecommunications 020101 civil engineering 02 engineering and technology Geometric shape 0201 civil engineering Thermal conductivity Heat transfer 0202 electrical engineering electronic engineering information engineering lcsh:SD1-669.5 General Earth and Planetary Sciences Cylinder Boundary value problem lcsh:Forestry Internal heating літій-іонні акумуляторні батареї теплопровідність конвективний теплообмін температурне поле термочутливе середовище тепловіддача General Environmental Science Mathematics |
| Zdroj: | Науковий вісник НЛТУ України, Vol 30, Iss 5, Pp 128-134 (2020) |
| ISSN: | 2519-2477 1994-7836 |
| DOI: | 10.36930/40300521 |
| Popis: | New mathematical models for determining and analyzing temperature regimes in individual elements of lithium-ion batteries, which are geometrically described by isotropic half-space and space with an internal heat source of cylindrical shape, have been improved and presented. Cases are also considered for half-space, when the fuel-releasing cylinder is thin, and for space, when it is heat-sensitive. For this purpose, using the theory of generalized functions, the initial differential equations of thermal conductivity with boundary conditions are written in a convenient form. In the course of research, to solve the obtained boundary value problems of thermal conductivity, the integral Hankel transformation was used, and as a result, analytical solutions in the images were obtained. The inverse Hankel integral transformation was applied to these solutions, which made enabled obtaining the final analytical solutions of the initial problems. The obtained analytical solutions are presented in the form of improper convergent integrals. Computational programs have been developed to determine the numerical values of temperature in these structures, as well as to analyze the heat transfer in the elements of lithium-ion batteries due to different temperature regimes due to heating by internal heat sources concentrated in the cylinder volume. Using these programs, graphs are given that show the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial radial and axial coordinates. The obtained numerical values of temperature indicate the correspondence of the given mathematical models for determining the temperature distribution to the real physical process. The software also allows analyzing media with internal heating concentrated in spatial figures of regular geometric shape in terms of their heat resistance. As a result, it becomes possible to increase it, to determine the allowable temperatures of normal operation of lithium-ion batteries, to protect them from overheating, which can cause the destruction of not only individual elements but also the entire structure. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|