A mathematical model for determining and analyzing temperature regimes in a battery pack of electric trucks

A mathematical model for the determination of the temperature field and the analysis of temperature regimes in lithium-ion batteries have been developed. Using the theory of generalized functions, the thermophysical parameters of the structural components of a battery are represented by a single mathematical relation. A function in the form of the product of the generalized thermal conductivity coefficient for temperature was introduced, which avoided the differentiation of the product of two generalized functions as a result of constructing the initial differential equation of thermal conductivity, which was obtained with discontinuous coefficients. An analytical solution of this equation is determined, which is expressed by the temperature value at the conjugation surfaces of the layers of the structure. A relation was obtained to determine these values ​​and expressions for constant integration. To determine the numerical values ​​of the temperature in the design of the battery nodes, as well as to analyze the temperature gradients in its environment caused by the heterogeneity of the components due to heating, an algorithm and computational programs have been developed that allow to analyze lithium-ion batteries for their normal functioning. Using numerical programs, numerical values ​​of the temperature were obtained for given values ​​of the power of the internal heat sources, which made it possible to construct curves that reflect the behavior of the temperature field depending on the spatial coordinate. The angular points on the curve are revealed, which indicate the presence of a phase transition in the design of lithium-ion battery assemblies. As a consequence, it becomes possible to determine the permissible temperature values ​​for the fire safety of these batteries.