Battery knowledge · Thermal management and heat transfer
Thermal mass
A body’s total heat capacity seen as a buffer against temperature change. A 500 kg pack at about 1 kJ/(kg·K) stores roughly 500 kJ per kelvin, so 10 kW of uncooled heat warms it only about 1.2 K a minute. Together with the thermal resistance to the coolant it sets the pack’s thermal time constant. [1]
- Also called
- thermal inertia, thermal time constant
- Relationship
- τ = m·cₚ·R_th
Example
Calculate a thermal time constant
With mass 0.5 kg, cₚ = 900 J/(kg·K) and R_th = 2 K/W, the lumped thermal time constant is 900 s, or 15 min. The calculation assumes a nearly uniform internal temperature.
Explore the graph
Thermal resistance sets the steady temperature rise; thermal mass sets the response time.
Steady rise: 10 K. Time constant: 8.333 min.
ΔT = P R_th [1 − exp(−t / (C_th R_th))]
Illustrative model. C_th = 500 J/K, fixed ambient and heat input, uniform temperature.
Use in Lemonergy
Design protocol or analysis tool
Inspect pack temperature
The separate Charge session can include a lumped thermal node.
Equation or tool to use
- Charge session thermal node
Balances heat and exchange
Inputs & settings
- Ambient temperature
- Thermal mass (J/K)
- Conductance (W/K)
- Heater availability
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Provide thermal mass and conductance.
- Compare two ambient temperatures.
Example. 100 kJ/K thermal mass and 100 W/K conductance give a 1000 s no-source temperature-difference time constant.
Observe. Temperature limits can pause charge; heater and mass are separate.
One node does not resolve gradients, coolant geometry or runaway. Studio’s native charger instead uses external temperature.
Open Design → Charge session →Lemonergy Studio blocks
Thermal state-space model worked example
Linear thermal rise model with a positive diagonal heat-capacity descriptor. User supplies validated matrices.
Blocks to use
- Thermal state-space model
Solves a linear temperature-rise model with positive diagonal heat capacities. Heat inputs drive the state; output temperatures add the configured ambient temperature to the linear result.
Inputs & settings
- Use the parameter values in the block reference.
- Bundled example verified on the production release of 28 October 2026.
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Review the block inputs, units and model limits.
- Open the Studio example and run its bundled model.
- Compare the output channels with the numerical checks; change one input and run again.
Example. Use the defaults below with Heat inputs = [10, 0] W. At 0 s, Temperature outputs is [298.15, 298.15] K. Additional checks are listed below.
Observe. Inspect the outputs and numerical checks on the block reference page.
Supports a positive diagonal descriptor, not an arbitrary descriptor matrix. No finite-element import or conserving thermal adapter; supplied matrices determine heat conservation and stability. The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.
Open Studio example →Studio interfaces connected to this concept
These components declare this quantity or operation. Their individual pages distinguish authoring metadata from numerical verification.
References & further reading
Technical references
- A General Energy Balance for Battery Systems
Dawn Bernardi, Ellen Pawlikowski, John Newman · Journal of The Electrochemical Society · 1985
Technical reference · Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- University Physics Volume 2, §1.6: Mechanisms of Heat Transfer
OpenStax, Rice University
Topic background · Conduction, convection, radiation and thermal resistance.