Transient three-dimensional thermal model for batteries with thin electrodes

Abstract

A three-dimensional analytical model is proposed to investigate the thermal response of batteries, with a plurality of thin electrodes, to heat generation during their operation. The model is based on integral-transform technique that gives a closed-form solution for the fundamental problem of unsteady heat conduction in batteries with orthotropic thermal conductivities, where the heat generation is a function of both temperature and depth-of-discharge. The full-field solutions take the form of a rapidly converging triple infinite sum whose leading terms provide a very simple yet accurate approximation of the battery thermal behavior with modest numerical effort. The accuracy of the proposed model is tested through comparison with numerical simulations. The method is used to describe spatial and temporal temperature evolution in a sample pouch type lithium-ion polymer battery during galvanostatic discharge processes while subjected to convective–radiative cooling at its surfaces (the most practical case is considered, when surrounding medium is at a constant ambient temperature). In the simulations, emphasis is placed on the maintenance of the battery operational temperature below a critical temperature. Through definition of a surface-averaged Biot number, certain conditions are highlighted, under which a two-dimensional thermal analysis is applicable.