  We study two thermo-electrochemical models for lithium-ion batteries. The
first is based on volume averaging the electrode microstructure whereas the
second is based on the pseudo-two-dimensional (P2D) approach which treats the
electrode as a collection of spherical particles. A scaling analysis is used to
reduce the volume-averaged model and show that the electrochemical reactions
are the dominant source of heat. Matched asymptotic expansions are used to
compute solutions of the volume-averaged model for the cases of constant
applied current, oscillating applied current, and constant cell potential. The
asymptotic and numerical solutions of the volume-averaged model are in
remarkable agreement with numerical solutions of the thermal P2D model for
(dis)charge rates up to 2C, and reasonable agreement is found at 4C.
Homogenisation is then used to derive a thermal model for a battery consisting
of several connected lithium-ion cells. Despite accounting for the Arrhenius
dependence of the reaction coefficients, we show that thermal runaway does not
occur in the model. Instead, the cell potential is simply pushed closer to the
open-circuit potential. We also show that in many cases, the homogenised
battery model can be solved analytically, making it ideal for use in on-board
thermal management systems.
