The most critical input in the thermal analysis of a battery pack is how much heat the cell generates — and that number is not constant. The energy balance of Bernardi, Pawlikowski and Newman splits cell heat generation into two parts [1]:
The irreversible (joule) part. It arises from internal resistance, rises with the square of the current, and always heats.
The reversible (entropic) part. It comes from the variation of the open-circuit voltage with temperature. It depends on state of charge and can change sign — meaning the cell cools over some parts of the charge range.
A model built on a single fixed W-per-cell figure gets the temperature history along the discharge curve wrong. Heat generation should at minimum be defined as a function of state of charge and current.
The acceptance criterion: spread, not peak
Two criteria have to hold together:
- Absolute temperature must stay within the manufacturer's operating range.
- Cell-to-cell spread must be small — a typical target is a few degrees.
The second is usually the governing one. Cells running at different temperatures age at different rates, and since the pack's capacity is set by its weakest cell, unevenness in the temperature distribution is written straight into service life. What battery analysis looks for is therefore the distribution, not the mean.
Time scales
A pack has large thermal inertia; the cooling circuit responds in seconds while the pack heats over minutes to hours. This is a classic conjugate, transient problem, and solving the fluid side fully at every step is needlessly expensive.
The quantity being sought is also transient by definition: the temperature history through a fast-charge cycle, the peak reached at the end of a drive cycle. See the note on steady versus transient.
Runaway is a different problem
Normal-operation analysis and thermal runaway analysis are not the same model. In runaway the heat comes not from electrochemistry but from decomposition reactions; it rises exponentially with temperature and is orders of magnitude above normal operation.
The engineering question here is usually not "will the cell heat up" but "will it propagate": when one cell goes into runaway, does it trigger its neighbour? That is an insulation and heat-path problem, and the answer lies in the thermal resistance between cells and the geometry of the venting paths. Where gas venting is involved the problem also becomes compressible.
References
- Bernardi, D., Pawlikowski, E. & Newman, J. (1985). A general energy balance for battery systems. Journal of the Electrochemical Society, 132(1), 5–12. DOI: 10.1149/1.2113792
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.