Battery Thermal Management
Theory: battery heat and cooling
Overview
What matters most in battery pack thermal design?
Li-ion cells degrade faster when hot and risk fire at high temperature, so keeping temperature in range comes first. Heat scales with current squared, rising sharply in fast charging and high power. And heat moves poorly inside the cell, so the core may be hot even when the surface is cooled. Let's calculate a 21700 cell's temperature for different discharge rates and cooling methods.
Heat generation
The first term is Joule heat from internal resistance; the second is reversible (entropic) reaction heat. Only Joule heat is considered here. Heat per discharge is current squared times time, so even though discharge time shrinks as 1/C, adiabatic rise grows in proportion to C-rate.
Temperature history and internal difference
A lumped equation treating the cell as one temperature, plus the steady core-to-surface difference from radial conduction. When the Biot number hr/(2k) exceeds 0.1, internal differences can't be ignored.
Bernardi's equation
Expressing battery heat as Joule plus reversible heat was set out by Bernardi and co-workers in the US in 1985 and remains the basis of battery thermal analysis. Since EVs spread in the 2010s, liquid cooling to keep cells around 15–35 °C and designs to stop cell-to-cell thermal propagation have become priorities. Thermal design bears directly on safety as well as performance and life.
Worked example: a 21700 cell
21 mm diameter, 70 mm long, 70 g, specific heat 1000 J/kgK, 5 Ah, internal resistance 20 mΩ, radial conductivity 0.5 W/mK (assumed). Discharge starts at 25 °C ambient.
| C-rate | Current | Heat | Adiabatic rise | Natural air 10 | Forced air 50 | Liquid-like 300 | Core−surface |
|---|---|---|---|---|---|---|---|
| 0.5C | 2.5 A | 0.12 W | 12.9 K | 27.3 °C | 25.5 °C | 25.1 °C | 0.3 K |
| 1C | 5 A | 0.50 W | 25.7 K | 33.8 °C | 26.9 °C | 25.3 °C | 1.1 K |
| 2C | 10 A | 2.00 W | 51.4 K | 53.0 °C | 32.5 °C | 26.3 °C | 4.6 K |
| 3C | 15 A | 4.50 W | 77.1 K | 75.6 °C | 41.8 °C | 27.8 °C | 10.2 K |
Cooling columns give the end-of-discharge temperature (lumped) for each heat transfer coefficient (W/m²K). Core-to-surface is a steady estimate during discharge. Biot numbers are 0.11, 0.53 and 3.2 for h = 10, 50 and 300.
With liquid cooling the surface stays at 28 °C even at 3C, yet the core is 10 K hotter.
Dozens of layers of wound electrodes and thin separators conduct poorly in the radial direction. Raising h cools the surface, but the core's heat exit is set by this low conductivity. So with liquid cooling the design focus shifts to core temperature and cell-to-cell spread in the pack rather than surface temperature. Equally important, internal resistance rises with ageing and cold: at 40 mΩ, double, a 2C discharge's adiabatic rise reaches 103 K. Margin with new cells may vanish with aged ones.
Thermal design tips
- Estimate heat for the worst duty (fast charge, high power, hot ambient).
- Allow for internal resistance growth with ageing and cold.
- Include cell anisotropy (radial versus axial conductivity).
- A common target keeps cell-to-cell differences within about 5 K across the pack.
- Assess whether runaway in one cell can propagate to neighbours.
“Fast charging stopped in winter”
In one electric car, fast charging on winter mornings saw the current heavily throttled mid-charge. At low temperature internal resistance rises, and charge current must be limited to prevent lithium plating. Pre-conditioning that warms the battery before charging was added. Battery thermal management means warming as well as cooling; keeping the optimal range serves performance, life and safety alike.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Designing with new-cell resistance | Overheats when aged | Check aged values |
| Judging by surface only | Core overheating missed | Evaluate core temperature |
| Isotropic conductivity | Wrong internal ΔT | Use anisotropy |
| Always ignoring reversible heat | Errors at low rates | Include when significant |
| Ignoring cell spread | Some cells age faster | Analyse the whole pack |
I'd like to learn related topics.
Try the EV battery cold-plate tool, battery model tool and battery calendar-aging tool. Related pages include transient conduction with heat generation and lumped capacitance.