Thermal Conductivity of the Active Layers

Before looking at how to thermally manage a battery pack we need to look at the thermal conductivity of the active layers.

If we look at the active layers of a cell the thermal conductivity in the plane of the layers is approximately 10x to 100x that through the planes.

This should not be unexpected as the electrodes are made from sheets of aluminium and copper. Two of the best materials for thermal conductivity.

These values though have a large range [Ref 1]:

• 15 to 160 W/mK In-Plane
• 0.2 to 8 W/mK Through-Plane

Measuring these values directly is difficult. If you measure components then they will be dry as the electrolyte evaporates quickly. If you instrument the cell then you are very likely to disturb some of the interfaces that determine the thermal conductivity. NREL [Ref 2] have shown a test and modelling approach to estimating these values more accurately.

This also means that the thermal performance of the active layers will be very dependent on the cell format and electrical configuration.

Thermal Conductivity versus SoC

The through plane thermal conductivity of a pouch cell was measured [Ref 3] and showed a negative parabolic dependence for fresh cells, where the highest thermal conductivity values were shown for the highest state of charge. This increase in conductivity at high SoC was shown for new and aged cells.

Thermal Conductivity versus SoH

For cells where a pressure was applied to the cell the thermal conductivity in plane decreased with age by around 4%.

Importance of Pressure

The through-plane thermal conductivity degraded by 4% when a pressure was applied to the cells [Ref 3]. When the cells were not under pressure the thermal conductivity degraded by 23% when they were aged.

References

1. Anisotropy Thermal Conductivity Tests of Batteries, Hot Disk
2. Chuanbo Yang and Lei Cao, “The Role of Interfacial Thermal Resistance in Li-Ion Battery Thermal Management“, NREL
3. Georgi Kovachev et al, “Thermal Conductivity in Aged Li-Ion Cells under Various Compression Conditions and State-of-Charge“, batteries
4. Guilherme Matheus Todys, S M Shadhin Mahmud, “Thermal Characterization of a Cylindrical Li-ion Battery Cell“, Masters Thesis, Chalmers University of Technology

Specific Heat Capacity of Lithium Ion Cells

The specific heat capacity of lithium ion cells is a key parameter to understanding the thermal behaviour. From literature we see the specific heat capacity ranges between 800 and 1100 J/kg.K

Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. Specific heat is the amount of heat per unit mass required to raise the temperature by kelvin (one degree Celsius).

Heat Generation in a Cell

The heat generation equation has two terms: Joule heating which is the irreversible term and Entropy change that is the reversible term.

At high currents Joule heating dominates as it is I²R_int. However, charging from low states of charge at lower currents and the entropy change is very significant.

This means that each battery needs to be fully characterised so that it can be modelled and optimised.

Thermal Interface Materials

The purpose of thermal interface materials (TIM) is to transfer heat between two solid surfaces. In the case of a battery this is normally between the outer surface of the cell case and a cooling plate.

Production tolerances of the cell, cooling plate and the assembly will mean there are gaps between the two surfaces. If a cell runs hotter than another cell then it will age faster or even become unstable if it gets very hot. Therefore it is important to run all of the cells at the same temperature and one element of that is a consistent thermal connection to the cooling system.