Heat Generation in Lithium-Ion Cells and Packs — Where the Energy Goes and Why It Matters

The heat your battery generates is not wasted energy — it is thermodynamic information. How much heat, from which sources, at which rates, tells you exactly whether your thermal management system will keep cells in their operating window or allow them to drift toward runaway.

Every lithium-ion battery pack converts some of its stored electrical energy to heat — not because of poor design, but because thermodynamics demands it. The question is not whether heat is generated but how much, from which physical mechanisms, at which locations in the pack, and at what rate relative to your thermal management system's dissipation capacity. Understanding heat generation physics correctly is what separates a thermal management system sized with real margins from one that fails on its first Indian summer.

The Bernardi Equation: Where All Heat Comes From

The foundational model for heat generation in battery cells is the Bernardi equation (1985):

# Bernardi heat generation equation
def heat_generation(I_A: float, R_cell_ohm: float,
                    T_K: float, dU_dT_V_per_K: float) -> float:
    """
    Bernardi (1985) heat generation model:
    Q = I^2 * R + I * T * (dU/dT)
    Q:      heat generated [W]
    I:      current [A] (positive = discharge)
    R:      total cell resistance [ohm]
    T:      cell temperature [K]
    dU/dT:  entropic heat coefficient [V/K]
    Negative dU/dT (common for NMC discharge) -> endothermic entropic term
    """
    Q_joule   = I_A**2 * R_cell_ohm         # irreversible Joule heating (always +ve)
    Q_entropy = I_A * T_K * dU_dT_V_per_K  # reversible entropic heat (can be -ve)
    return Q_joule + Q_entropy

# NMC 21700 at 25 deg C, 3C discharge
I    = 15.0    # A (3C for 5 Ah cell)
R    = 0.025   # ohm (DC internal resistance)
T    = 298.15  # K
dUdT = -0.0003 # V/K (typical NMC at 50% SOC)

Q_total   = heat_generation(I, R, T, dUdT)
Q_joule   = I**2 * R
Q_entropy = I * T * dUdT

print(f"Joule heating:    {Q_joule:.3f} W")
print(f"Entropic heat:    {Q_entropy:.3f} W  (endothermic)")
print(f"Total heat gen:   {Q_total:.3f} W")
print(f"Heat flux:        {Q_total / (0.021 * 0.070):.0f} W/m2  (per cell surface area)")

Q_total = I²·R  +  I·T·(dU/dT)  +  I·(U_OCV - U_terminal)

Breaking this down:

Term 1: I²·R (Joule heating / resistive heating) This is the irreversible ohmic dissipation in the cell's internal resistance. It scales with current squared — the dominant term at high rates. The internal resistance R includes: electrolyte ionic resistance, separator resistance, electrode electronic resistance, current collector resistance, and SEI film resistance.

Term 2: I·T·(dU/dT) (Entropic heat) This is the thermodynamically reversible heat exchange during lithium intercalation. The sign depends on the electrode chemistry and SOC: negative dU/dT means the cell absorbs heat on discharge (endothermic); positive dU/dT means it generates additional heat (exothermic). For graphite/LFP cells, the entropic contribution is significant and SOC-dependent — some SOC regions are endothermic during discharge, reducing net heat generation.

Term 3: I·(U_OCV - U_terminal) (Overpotential losses) This captures the additional losses from electrochemical kinetics (Butler-Volmer activation overpotential), mass transport (concentration overpotential), and contact-layer resistances not captured in the static DCIR. At high rates and low temperatures, this term becomes large as mass transport limitations grow.

Joule Heating: The Quadratic Relationship That Matters

The quadratic scaling of Joule heating with current is the most important relationship in battery thermal design. For a 100 Ah NMC prismatic cell with 2 mΩ DCIR:

The transition from 1C to 3C does not triple heat generation — it multiplies it by 9 (3²). This is why fast charging requires fundamentally different thermal management than standard charging. A system designed for 1C has 1/9th the thermal capacity needed for 3C charging.

Entropic Heat: Why LFP Runs Cooler

The temperature coefficient of OCV (dU/dT) varies with electrode chemistry and SOC. This has a direct effect on net heat generation:

LFP cathode: Has a significantly negative dU/dT region around 50–70% SOC. During discharge in this SOC window, the entropic term absorbs heat from the cell (the reaction is endothermic). This partially offsets Joule heating. During charging in the same SOC window, the cell releases this entropic heat — but since charging typically runs at lower rates than peak discharge, the total heat is still lower than NMC.

NMC cathode: The dU/dT is smaller and less SOC-dependent. Joule heating dominates at most practical rates.

Practical consequence: At identical C-rates, LFP cells generate measurably less total heat than NMC cells, particularly at moderate SOC levels. This is one reason LFP packs can be run without liquid cooling at lower discharge rates — the combination of thermally stable chemistry and lower net heat generation allows air cooling to be viable for 2W and 3W Indian applications at 1C continuous.

Contact Resistance Losses: The Hidden Heat Source

Cell-level heat generation is only part of the pack thermal story. Current must flow through: cell terminals → compression washers → busbars → intercell connections → HV cables → contactors → main fuses.

Each junction has a contact resistance. For bolted connections on aluminium busbars:

• Clean, properly torqued bolted connection: 0.1–0.5 mΩ
• Slightly oxidised aluminium surface: 1–5 mΩ
• Corroded or under-torqued connection: 5–50+ mΩ

At 200A (2C on a 100 Ah pack), a 5 mΩ contact resistance generates 200A² × 5 mΩ = 200 W of heat at a single connection point. This is a highly localised heat source — a thermal hotspot — that can exceed the maximum temperature of adjacent cells or cause connection material degradation.

Pack-Level Heat Accumulation

For a 60 kWh NMC pack discharging at 2C (120 kW) with 97% round-trip efficiency:

# Pack thermal resistance network -- temperature rise estimation
def pack_temperature_rise(P_heat_W: float, R_thermal_K_per_W: float,
                           T_coolant_degC: float = 25.0) -> float:
    """
    Lumped thermal model: delta_T = P * R_th
    Returns maximum cell temperature in pack.
    """
    delta_T = P_heat_W * R_thermal_K_per_W
    return T_coolant_degC + delta_T

# Thermal resistance breakdown for a 20-cell module
R_cell_to_cooling = {
    "Cell core to surface":         0.15,    # K/W (NMC 21700)
    "Cell surface to TIM":          0.08,    # K/W (thermal interface material)
    "TIM to cold plate":            0.05,    # K/W (2 W/m*K TIM, 1mm thick)
    "Cold plate to coolant":        0.03,    # K/W (liquid cooled)
}

R_total = sum(R_cell_to_cooling.values())
P_per_cell = heat_generation(15.0, 0.025, 298.15, -0.0003)

T_max = pack_temperature_rise(P_per_cell, R_total)
print(f"
Thermal resistance breakdown:")
for layer, R in R_cell_to_cooling.items():
    print(f"  {layer:<35} {R:.2f} K/W")
print(f"
Total R_th:  {R_total:.2f} K/W")
print(f"Heat/cell:   {P_per_cell:.2f} W at 3C")
print(f"T_max cell:  {T_max:.1f} deg C  (coolant at 25 deg C)")

• Total heat generated during discharge: 60 kWh × 3% = 1.8 kWh = 6,480 kJ
• If discharged in 30 minutes: average heat generation rate = 6.48 MJ / 1800 s = 3,600 W = 3.6 kW
• If pack mass is 400 kg with average specific heat ~900 J/(kg·°C): adiabatic temperature rise = 6,480,000 / (400 × 900) = 18°C

This 18°C adiabatic temperature rise is the minimum cooling system must remove to maintain the same temperature as it started. With 45°C Indian ambient, a pack that starts at 35°C (already 10°C above ambient) would reach 53°C in this scenario without cooling — above the NMC maximum operating temperature.

Thermal Runaway Heat Generation: Orders of Magnitude Above Normal

Normal heat generation during operation is 2–5% of the energy throughput. Thermal runaway heat generation is fundamentally different:

• SEI decomposition: ~75–200 J/g of cell
• Electrolyte oxidation by delithiated NMC cathode: ~500–1,500 J/g of cell
• Aluminium current collector oxidation by electrolyte: ~50–100 J/g
• Lithium reaction with electrolyte (at full delithiation): ~2,000+ J/g

A single 100 Ah NMC 811 cell weighing ~0.8 kg can release 50,000–100,000 J during thermal runaway — equivalent to 14–28 Wh in a few seconds to minutes. For a 200-cell pack, this is 2.8–5.6 MWh of thermal energy if all cells propagate — the equivalent of a small petrol fire.

Thermal management systems are not designed to manage thermal runaway heat — the heat release rate far exceeds any practical cooling system's capacity. Thermal management's role is to prevent cells from reaching thermal runaway onset temperature. Once runaway begins, the engineering objective shifts to containment and propagation delay.

Chemistry Comparison for Thermal Management Design

# Chemistry comparison: heat generation at 1C and 3C
import numpy as np

chemistries = {
    #           R_dc(ohm)  dU/dT(V/K)  capacity(Ah)  name
    "NMC 811":  (0.022,   -0.00030,    5.0),
    "NMC 622":  (0.028,   -0.00020,    4.5),
    "LFP":      (0.035,    0.00010,    3.0),   # LFP: endothermic entropic at discharge -> positive
    "LCO":      (0.030,   -0.00025,    2.8),
}

T_K = 298.15

print(f"{'Chemistry':<12} {'Q @ 1C (W)':>12} {'Q @ 3C (W)':>12} {'Entropic direction':>20}")
print("-" * 58)
for chem, (R, dUdT, cap_Ah) in chemistries.items():
    I_1C = cap_Ah * 1.0
    I_3C = cap_Ah * 3.0
    Q_1C = heat_generation(I_1C, R, T_K, dUdT)
    Q_3C = heat_generation(I_3C, R, T_K, dUdT)
    direction = "endothermic" if dUdT < 0 else "exothermic"
    print(f"{chem:<12} {Q_1C:>12.2f} {Q_3C:>12.2f} {direction:>20}")

Key Takeaways