Inputs
Example data table
These examples illustrate typical outputs for different applications.
| Scenario | Pack | Current (A) | Cooling | Heat (W) | Peak (°C) | Status |
|---|---|---|---|---|---|---|
| E-bike commuter pack | 52s4p | 45 | Natural | 154 | 51.3 | Warning |
| EV burst acceleration | 96s6p | 420 | Liquid | 6,246 | 31.1 | Safe |
| Stationary storage, forced air | 120s3p | 110 | Forced | 1,749 | 56.2 | Critical |
Example values are illustrative. Your geometry, interfaces, and airflow can change results significantly.
Formula used
Entropic term (optional): Q̇E = Icell · T · (dU/dT)
Pack total: Q̇ = (Q̇J + Q̇E) · Ncells
Convection: Q̇conv = h·A·(T − Tamb)
Radiation: Q̇rad = ε·σ·A·(TK4 − Tamb,K4)
Coolant capacity: Q̇cap = ṁ·Cp·ΔTallow
Used in simulation: Q̇liq = min(Q̇tr, Q̇cap)
The temperature evolution is solved by time-stepping (Euler integration) over the selected duration.
How to use this calculator
- Enter series and parallel counts, then set the expected pack current.
- Provide cell resistance and duration at that current level.
- Fill thermal mass, surface area, ambient, and initial temperature.
- Choose a cooling method and set an appropriate heat transfer coefficient.
- If using a liquid plate, add U, contact area, and coolant limits.
- Press calculate, then export CSV or PDF for review.
Heat Sources in High-Power Packs
Joule heating dominates most operating points because it scales with current squared and cell resistance. Use Icell = Ipack / P, so adding parallel strings reduces I²R fast. Typical resistance ranges from 2 to 25 mΩ per cell, and it usually falls as temperature rises. The entropic term uses I·T·dU/dT; values between -1 and +1 mV/K are common and can flip sign with state of charge. Measure resistance at intended operating temperature.
Selecting Thermal Mass and Surface Area
Thermal mass sets how quickly temperature climbs for a given heat load. The model uses m·cp, so doubling mass or specific heat roughly halves the rate of rise. Battery assemblies often sit around 700 to 1200 J/kg·K depending on metals, plastics, and coolant plates. External area controls heat rejection to air and radiation; include enclosure surfaces that see airflow, and reduce area if insulation or tight packaging blocks exchange. Keep units consistent.
Convection and Radiation Benchmarks
Convection is captured with Q = h·A·ΔT, so choosing h is critical. Still air often behaves near 2–5 W/m²·K, natural convection near 5–12, and ducted fans commonly 20–80 depending on velocity and fins. Radiation grows with absolute temperature to the fourth power. For a 1 m² matte surface (ε≈0.9) at 60°C in 25°C ambient, radiative loss is about 225 W, which can rival weak airflow. Use emissivity near 0.2 for polished metals.
Liquid Plate Capacity and Flow Limits
Liquid plates remove heat by transfer and by coolant capacity. The transfer side is U·Acontact·(T − Tcool,in); practical U values are often 200–800 W/m²·K when interfaces are well coupled. Capacity is ṁ·Cp·ΔTallow. For 5 L/min water‑glycol (ρ≈1 kg/L, Cp≈3.6 kJ/kg·K) and ΔTallow=4°C, capacity is roughly 1.2 kW, so higher flow or allowed rise directly increases the cap. If inlet temperature rises during a cycle, recalculate with the higher value to maintain margin.
Interpreting Results for Engineering Decisions
Use peak temperature to judge risk, and use time‑to‑limit to understand short bursts. A common engineering target is to keep peaks at least 10°C below conservative limits to cover sensor error and aging. Because Joule heating is proportional to current squared, cutting current 10% reduces that component about 19%. If results are high, prioritize lowering resistance, increasing contact area, and improving h or U before adding mass, which increases weight. After calibration.
FAQs
What does the entropic coefficient change?
It adds reversible heat I·T·dU/dT on top of I²R. The sign can be heating or cooling, and it varies with chemistry and state of charge. If you do not have reliable dU/dT data, set it to zero.
How should I choose the air heat transfer coefficient h?
Use typical ranges as a starting point: 2–5 still air, 5–12 natural convection, and 20–80 forced air. Pick a conservative value, then refine it using airflow measurements and temperature tests on the real enclosure.
Why do more parallel cells usually lower Joule heating?
Pack current splits across parallel strings, so each cell sees I/P. Total Joule heat becomes proportional to I²/P for the same series count and resistance. Increasing P is often the fastest way to reduce heating at a fixed load.
When does liquid cooling become flow‑limited in this model?
If the coolant capacity ṁ·Cp·ΔTallow is smaller than U·A·ΔT, the cap dominates and extra transfer area will not help. Increase flow, raise allowable coolant rise, or lower inlet temperature to lift the cap.
What are the main limitations of this calculator?
It assumes a single uniform pack temperature and simple heat loss terms. It does not capture cell‑to‑cell gradients, contact resistances inside modules, or thermal runaway dynamics. Use multi‑node models and testing for critical designs.
How do I validate and calibrate the inputs?
Run a controlled load profile, log temperatures at multiple locations, and compare peak and time‑to‑limit. Adjust resistance, area, and h or U within measured ranges until predictions track data. Then apply conservative margins for aging and uncertainty.