Temperature and Current Distribution in Thin‐Film Batteries

For electric‐vehicle and hybrid‐vehicle applications, it is expedient to determine what factors are likely to limit battery performance and determine cell designs that optimize operation for a particular application. This paper provides a derivation of the governing equations and an analytic solution useful for thin‐film battery design. Specifically, differential equations consistent with a two‐dimensional representation of a thin‐film battery are developed based on the underlying physical chemistry. A perturbation approach is used to derive a simpler set of governing equations, and associated analytic solutions for cell energy, power, and thermal characteristics are constructed. The analytic solution of this work assumes a secondary current distribution and linear kinetics for the porous electrodes; the associated system of model equations is thus linear. These assumptions should be valid for short times after the start of charging or discharging from a quiescent state.