  Thermal electrochemical models for porous electrode batteries (such as
lithium ion batteries) are widely used. Due to the multiple scales involved,
solving the model accounting for the porous microstructure is computationally
expensive, therefore effective models at the macroscale are preferable.
However, these effective models are usually postulated ad hoc rather than
systematically upscaled from the microscale equations. We present an effective
thermal electrochemical model obtained using asymptotic homogenisation, which
includes the electrochemical model at the cell level coupled with a thermal
model that can be defined either at the cell or the battery level. The main
aspects of the model are the consideration of thermal effects, the diffusion
effects in the electrode particles, and the anisotropy of the material based on
the microstructure, all of them incorporated in a systematic manner. We also
compare the homogenised model with the standard electrochemical Doyle, Fuller &
Newman model.
