The specific heat capacity is a measure of how much energy is necessary to raise the temperature of a system a given amount. A system with a higher specific heat capacity is said to have a higher thermal mass, meaning that with the same amount of heat, it will have a lower temperature rise.
Determining the specific heat capacity of the battery pack is important to be able to determine non steady-state thermal characteristics of the pack - how long can we produce X power through the cells before a temperature rise of X degrees occurs?
Because the battery pack is made up of many parts and many different materials with different thermal conductivities, specific heat capacities, etc., we will focus only on the materials that are physically located close to the cells, and have a good thermal coupling to the cells.
We will also assume that all the other components that are in the high current path (and thus produce heat) have a small enough power loss compared to their thermal mass that they can be neglected (relays, connectors, etc.)
Here is a table that outlines some of the materials we are using the in battery pack, and their associated thermal characteristics. The values in the table are not to be used for mathematical calculations (ans so were significantly rounded), and were only used to determine relative thermal capacities between the parts of the pack.
| Material | Thermal Conductivity (W/m k) | Specific Heat Capacity (J/kg K) | Link |
|---|---|---|---|
| LG MJ1 18650 | We will assume temperature within the 18650s is uniform | ~830 | |
| Nickel | ~90 | ~440 | http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html |
| EMS Sigma 60 | ~200 Rough weighted average of nickel, steel, and copper | ~400 Copper, Nickel, and Steel are all around this same value | |
| Acetal | 0.3 - 0.37 | 1400 - 1500 | https://www.dupont.com/content/dam/dupont/products-and-services/plastics-polymers-and-resins/thermoplastics/documents/Delrin/Delrin%20Design%20Guide%20Mod%203.pdf |
| Fish Paper | 0.29 | 1687 | https://dielectricmfg.com/knowledge-base/fish-paper/ |
| PETG | 0.29 | 1200 | https://www.sd3d.com/wp-content/uploads/2017/06/MaterialTDS-PETG_01.pdf |
| Air | 0.025 | 1005 | https://www.engineeringtoolbox.com/air-properties-d_156.html |
Unit converter used here: https://converter.eu/heat_capacity/#0.403_BTU/Pound_°F_in_Joule/Kilogram_°C
Given that the 18650s, the Nickel, and the EMS Sigma 60 have thermal conductivities a few orders of magnitude higher than the rest of the materials, only the metals will be used for the rest of the calculations (this is expected since metals and plastics are very far apart when it comes to thermal properties).
Mass of the relevant materials used in the battery pack:
| Material | Mass (kg) | Note |
|---|---|---|
| 18650s | 41.5 | 24P 36S, 864 cells, 48g/cell |
| Nickel | 0.8 | Nickel Strips |
| EMS Sigma 60 | 1.54 | ((8500mm2 x 2 x 0.3 x 18) + (16350mm2 x 0.3 x 18)) x 8.55g/cm3 / 1000mm3/cm3 |
To raise the temperature of the battery pack by 1 degree celcius (assuming a uniform temperature distribution), we must heat up all of the materials in the table above by 1 degree celsius.
1 Joule = 1 Watt x 1 Second
| Material | Calculation | Joules per Degree Celsius |
|---|---|---|
| 18650s | 41.5kg * 830J/kg K | 34 445 |
| Nickel | 0.8kg * 440J/kg K | 352 |
| EMS Sigma 60 | 1.54kg * 400J/kg K | 616 |
| TOTAL | ~35.5 kJ |
Looking at our temperature rise for a 75A discharge, we find that it takes roughly 1000 seconds to heat up the pack from 33 to 43 degrees Celsius. *This is only for 1 module, but the result can be scaled to the pack.
At around 75A, according to the battery heat production page, we are producing just under 330W of heat for the pack.
330W * 1000s = 330 000J
With our estimate of the specific heat capacity of 35.5kJ/deg C, 330kJ of energy should result in: 330kJ / 35.5kJ/deg C = 9.3 deg C.
So, the thermal mass of the pack being 35.5kJ/deg C is a very reasonable estimate.