A three-dimensional battery module in the shape of a block is taken to generate heat uniformly throughout. The temperature rise as a function of time is worked out based on equations for heat conduction in solids. After appropriate nondimensionalization, the maximum temperature rise depends on the thermal aspect ratios (defined herein). By a superposition integral, the method can be extended to a time-dependent heat-generation rate, as appropriate for a driving profile
Temperature Rise in A Battery Module with Constant Heat-Generation
Newman, J., & Tiedemann, W. (1995). Temperature Rise in A Battery Module with Constant Heat-Generation. Journal of the Electrochemical Society, 142(4), 1054-1057.