Base vs side cooling of cylindrical cells is often brought up in online discussions and in many OEMs designing battery packs. We looked at this before within Thermal Conduction in a Cell, however, I think it is worth expanding this topic.

The Tesla design cools the side of the cell and the Lucid Motors cools the base of the cell.

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It is best to start with the basics of thermal conduction.

We have a material of length, d and cross-sectional area, A that is hot, T_{2} at one end and cold, T_{1} at the other end. Knowing the thermal conductivity, k of the material we can calculate the heat, Q.

As a very rough first order calculation let’s take the cylindrical cell and assume it is the thermally conducting rod.

End cooling of the cell as per the Lucid Air.

21700 cell:

- axial thermal conductivity = 11.55 W/m.K
- distance d = 0.07m
- cross-sectional area, A = 0.000346 m
^{2}

The maximum working temperature difference end to end is normally specified by the cell manufacturer as 2°C.

A 2°C temperature gradient would be generated with a heat flux of 0.11W. If the cell has an internal resistance of 0.025Ω then a current of 2.14A would generate a joule heating value of 0.11W, this is a discharge rate of less than 0.5C, this cell is not being pushed hard.

This temperature difference might be allowed to increase to 5°C or even 10°C for short transient events.

We could increase the area of contact between the coolant and the cell, this would give a greater heat flux for a given temperature delta.

21700 cell:

- radial thermal conductivity = 0.83 W/m.K
- distance d = 0.021m
- cross-sectional area, A = 0.00108 m
^{2}

Note: I’ve tried to align the assumptions on this calculation with the bottom cooled cell and used the same equations. This means I have assumed a contact area of 18mm x 60mm and assumed this is a rectangular block of active material. Perhaps some big assumptions, but this is a rough estimate. A 2°C temperature gradient would be generated with a heat flux of 0.09W and shows that these two methods are roughly comparable.

This is very approximate as the joule heating is distributed throughout the cell, however, this gives a feel as to the steady state conditions under which a temperature gradient can be generated.

If you have run full 3D thermal calculations on cell cooling systems that you can share online then do please drop us a line.

### Cell Diameter vs Height

Taking this calculation further, maybe too much of an over-simplification, we can look at cell diameter versus cell height. I think this might be a good first indicator.

For the side cooling we have fixed the angle at 80° and the cooling plate covers 90% of the height of the cell. The distance for the side cooling is assumed to be the diameter of the cell.

For the base cooling we have assumed that just the base area is cooled. The distance is the height of the cell.

The axial and radial thermal conductivity numbers are from Guilherme Matheus Todys and S M Shadhin Mahmud [2] who measured these values on a 21700 cell. Using these numbers and scaling to larger and smaller cells is extrapolating this data too far, hence this is just a first order approximation.

The delta Temperature has been fixed at 2K for both options and then the heat flux in W calculated.

The plot is then calculated as the Base heat flux – Side heat flux.

A negative value when the side cooling is better and a positive vale when the base cooling is better.

### Conclusions

- For the dimensions of the 21700 cell base cooling gives ~12% greater heat flux, for the same temperature gradient, than side cooling.
- If we listen to Peter Rawlinson’s description of the Lucid Motors battery design he points out that the base cooling design gives a more consistent thermal connection to the cell.
- In the end though this probably comes down to the package dimensions and whether you can fit a slightly taller base cooled design or a wider/longer side cooled design.
- One point not explored here is that with a side cooled cell design the busbars that join the cells together will have to be slightly longer to accommodate thickness of the cooling plates.
- Base cooling is better in this simplified calculation for all normal size cylindrical cells.

##### Benefits of Aluminium Cell Housings for Cylindrical Lithium-ion Batteries

Thermal simulations reveal significant improvements in cooling performance at 3C fast-charging of the aluminium housing version compared to nickel-plated steel reference cell. The impact of the cell housing material is particularly pronounced in case of a sidewall cooling. In this case, simulation reveals differences in maximum temperature (hot spot) of 11°C after 10 minutes.

### References

- Yannic Troxler, Billy Wu, Monica Marinescu, Vladimir Yufit, Yatish Patel, Andrew J. Marquis, Nigel P. Brandon, Gregory J.Offer, “The effect of thermal gradients on the performance of lithium-ion batteries“, Journal of Power Sources, Volume 247, 1 February 2014, Pages 1018-1025
- Guilherme Matheus Todys, S M Shadhin Mahmud, “Thermal Characterization of a Cylindrical Li-ion Battery Cell“, Masters Thesis, Chalmers University of Technology