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Thermal electrochemical models for porous electrode batteries (such aslithium ion batteries) are widely used. Due to the multiple scales involved,solving the model accounting for the porous microstructure is computationallyexpensive, therefore effective models at the macroscale are preferable.However, these effective models are usually postulated ad hoc rather thansystematically upscaled from the microscale equations. We present an effectivethermal electrochemical model obtained using asymptotic homogenisation, whichincludes the electrochemical model at the cell level coupled with a thermalmodel that can be defined either at the cell or the battery level. The mainaspects of the model are the consideration of thermal effects, the diffusioneffects in the electrode particles, and the anisotropy of the material based onthe microstructure, all of them incorporated in a systematic manner. We alsocompare the homogenised model with the standard electrochemical Doyle, Fuller &Newman model.

Derivation of an Effective Thermal Electrochemical Model for Porous Electrode Batteries using Asymptotic Homogenisation