# COMSOL Blog

## Lithium-Ion Battery Model

##### Fanny Littmarck | January 21, 2013

On Friday I wrote about designing safer lithium-ion batteries, and showed you a few resources for helping people do just that. Now I’d like to show you a lithium-ion battery model and briefly run through how it can be created in COMSOL Multiphysics in three sequential studies.

Geometry of a lithium-ion battery. Three unit cells, one inlet connector channel, and one outlet
connector channel in the cooling fins.

### Liquid Cooled Lithium-Ion Battery Model

The lithium-ion battery model in question simulates the temperature profile in several battery cells and aluminum cooling fins in a liquid-cooled li-ion battery pack. It’s based on two assumptions. Namely, that the battery material and cooling fluid material properties can be calculated using an average temperature for the battery pack, and that the fluctuations in heat generation during the load cycle are notably slower than the heat transport within the battery pack. What does this mean for the model? Well, the first assumption works if the temperature variations in the battery pack are small. The second assumption just means that the thermal equilibrium is quasi-static for the given battery heat source and at a given operational point during the load cycle. (Quasi-stationary processes simplify theoretical thermal studies).

Supporting the second assumption: the velocity magnitude in the first
cooling fin infers that the residence time for the fluid time in the plates
is in a range of mere seconds.

The model is solved sequentially using COMSOL Multiphysics and the Batteries & Fuel Cells Module and the Heat Transfer Module, with one study per physics interface (three in total). First, the fluid flow of the liquid-cooled battery pack is modeled. The fluid is modeled using the same material properties as water, calculated using the input temperature. This is consistent with the first assumption, stated above. Next, a time-dependent study is conducted, solving solely for the 1D battery model. Here, the battery model is assumed to be of the same temperature as the cooling fluid’s inlet temperature. Finally, a stationary study is carried out, solving the quasi-stationary temperature of the battery pack. This step combines steps one and two (using the flow velocity from the first, and the average heat source taken from the last time step of the time-dependent simulation from the second study).

 Temperature in the lithium-ion batteries: the temperature variation is greater within a single cell (xz-plane) than through the depth of the pack (the y-axis). Temperature of the cooling fluid.