KEVOS® MAKEOS · Engineering
Battery Pack Heat Check (Irreversible and Reversible Heat, Temperature Rise, Cooling)
How much heat does this battery pack make while charging or discharging at this current, how much of it is reversible, and how hot will it get with the cooling it has?
Heat generation of a battery pack by Bernardi’s energy balance: the irreversible (resistive) heat I²R in each cell, the reversible (entropic) heat from the cell’s open-circuit voltage temperature coefficient, which the reversible-cell equation of Helmholtz relates to the heat the cell exchanges with its surroundings, the pack total, the heat left after cooling, and the temperature rise over the duty with the cells’ heat capacity, against the largest rise you allow, with the cooling needed to stay within it.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Operation | choice | Whether the pack is being discharged or charged (sets the sign of the reversible heat). |
| Current through each cell | A | Current through each cell: pack current divided by the number of cells in parallel. |
| Cell internal resistance | mΩ | Internal (DC) resistance of one cell at this temperature and state of charge, from the cell data sheet or a pulse test. |
| Entropic coefficient (dU/dT of open-circuit voltage) | mV/K | Change of the cell’s open-circuit voltage with temperature, from the cell maker or published measurements; it varies with state of charge and can be negative. |
| Cell temperature | °C | Cell temperature during the duty. |
| Pack and duty | ||
| Cells in the pack | cells | Number of cells in the pack. |
| Mass of each cell | kg | Mass of one cell. |
| Specific heat of the cells | J/(kg·K) | Average specific heat of the cells, from the cell maker or a calorimeter test. |
| Duration of the duty | min | Length of the charge or discharge. |
| Heat removed by cooling | W | Heat the cooling system removes from the pack at this temperature. |
| Largest temperature rise allowed | K | Largest temperature rise you allow over the duty (from the cell maker’s limits). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Operation
- What it is
- Whether the cells are being discharged or charged, which reverses the direction of the reversible (entropic) heat.
- Units and format
- Choose one of 2 options from the list: Discharging; Charging.
- Example
- The form opens with “Discharging” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Switching mode reverses the sign of the reversible heat per cell.
- Get it right
- The resistive heat is the same either way; only the entropic part changes sign.
What this means: Current through each cell
- What it is
- The current flowing through each individual cell, the pack current shared between the cells connected in parallel.
- Units and format
- Enter a number in A: amperes. The form accepts 0 A to 10000 A. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 A as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Resistive heat rises with the square of the current, reversible heat in proportion to it.
- Get it right
- Divide the pack current by the number of parallel cells; do not use the whole pack current per cell.
What this means: Cell internal resistance
- What it is
- The internal resistance of one cell, which turns part of the current into heat whichever way it flows.
- Units and format
- Enter a number in mΩ: mΩ. The form accepts 0 mΩ to 1000 mΩ. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mΩ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Resistive heat rises in proportion.
- Get it right
- Use the DC resistance at the working temperature and state of charge; cold cells have much higher resistance.
What this means: Entropic coefficient (dU/dT of open-circuit vol…
- What it is
- How much the cell’s open-circuit voltage changes per kelvin of temperature, which measures the reversible heat the cell absorbs or releases as it reacts.
- Units and format
- Enter a number in mV/K: mV/K. The form accepts -5 mV/K to 5 mV/K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 mV/K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- On discharge a positive value absorbs heat and cools the cell; on charge it adds heat.
- Get it right
- It changes with state of charge and can be negative; enter it in millivolts per kelvin from cell data.
What this means: Cell temperature
- What it is
- The temperature of the cells, used as the absolute temperature in the reversible heat term.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -40 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The reversible heat rises in proportion to the absolute temperature.
- Get it right
- Use the cell temperature, not the room temperature, if the pack is already warm.
Pack and duty
What this means: Cells in the pack
- What it is
- The number of cells in the pack, which multiplies the heat per cell and the heat capacity.
- Units and format
- Enter a number in cells: cells. The form accepts 1 cells to 100000 cells. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 cells as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pack heat and heat capacity both rise with it, so the rise depends on the cooling share per cell.
- Get it right
- Count every cell, series and parallel; for a pack of modules multiply cells per module by modules.
What this means: Mass of each cell
- What it is
- The mass of one cell, which with its specific heat sets how much heat it absorbs per degree of temperature rise.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 1000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A heavier cell warms more slowly for the same heat.
- Get it right
- Use the cell’s own mass; the pack casing and busbars add heat capacity this model leaves out.
What this means: Specific heat of the cells
- What it is
- The average heat needed to warm one kilogram of the cell by one kelvin, combining its electrodes, electrolyte and case.
- Units and format
- Enter a number in J/(kg·K): J/(kg·K). The form accepts 0.000001 J/(kg·K) to 10000 J/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 J/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher specific heat lowers the temperature rise for the same heat.
- Get it right
- Take it from the cell maker or a calorimeter test; it differs between cell chemistries and formats.
What this means: Duration of the duty
- What it is
- The length of the charge or discharge at this current, over which the net heat accumulates in the cells.
- Units and format
- Enter a number in min: minutes. The form accepts 0.000001 min to 100000 min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The temperature rise grows in proportion to the duration.
- Get it right
- For a full charge or discharge use the time at this current, not the total time on charge.
What this means: Heat removed by cooling
- What it is
- The rate at which the cooling system removes heat from the pack at its working temperature.
- Units and format
- Enter a number in W: watts. The form accepts 0 W to 10000000 W. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 W as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Subtracts directly from the pack heat, lowering the temperature rise.
- Get it right
- Use the cooling achieved at the pack’s temperature difference to the coolant or air, not the fan or chiller rating.
What this means: Largest temperature rise allowed
- What it is
- The largest temperature rise of the pack you allow over the duty, the pass or fail limit for the check.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0.000001 K to 200 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the cooling needed; the heat does not change.
- Get it right
- Set it from the cell maker’s maximum temperature less the starting temperature.
Method and formulas
- Per cell (Bernardi energy balance): heat = I² R − I_d T (dU/dT), with I_d positive on discharge and negative on charge, T in kelvin.
- The reversible term is the heat the cell exchanges at its terminal energy change: by Helmholtz’s reversible-cell equation v − T dv/dT = u (Fermi eq 134), T dv/dT per unit charge is heat absorbed from the surroundings.
- Pack heat = cells × heat per cell; temperature rise = (pack heat − cooling) × time ÷ (cells × mass × specific heat); cooling needed = pack heat − allowed rise × heat capacity ÷ time.
- Example: 5.4 W resistive and -1.7889 W reversible heat per cell; the pack warms 2.9 K in 30 min.
Limitations
- Lumped model: the pack is one uniform temperature; real cells have hot spots at the centre and the tabs, so the maximum cell temperature is higher than this average.
- Screening aid only: battery thermal limits and safety are governed by the cell maker’s data, the applicable standards and qualified review.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size cooling for a forklift, AGV or storage battery pack
- See whether a fast charge will overheat a pack
- Compare resistive and entropic heat at different currents
Who it is for
- Electrical and mechanical design engineers
- Maintenance engineers
- Battery system integrators
What you get
- Irreversible and reversible heat per cell
- Pack heat and heat left after cooling
- Temperature rise over the duty and cooling needed
Interpreting the result
- Resistive heat grows with the square of the current while reversible heat grows in proportion, so the entropic term matters most at low currents and can even cool the cell.
References
- Fermi E., Thermodynamics (Dover Publications, 1956; first published by Prentice-Hall, 1937), pp. 94–97. Method reference; no text, examples or tables are reproduced.
- Bernardi D., Pawlikowski E. and Newman J., A General Energy Balance for Battery Systems, Journal of the Electrochemical Society 132 (1), 5–12 (1985).
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