Battery knowledge · Thermal management and heat transfer
Thermal gradient
A change of temperature with position — within a cell from core to surface, or across a pack from coolant inlet to outlet. Packs are commonly designed to keep cells within about 5 °C of each other, because warmer cells age faster and, in parallel, carry more current, so a gradient grows into an imbalance.
- Also called
- temperature gradient, temperature spread, temperature uniformity
Example
Thermal management and heat transfer: an example situation
Equal total heat in different layouts can produce different gradients. Average temperature can miss a hot spot.
Read Thermal gradient alongside Biot number in this context. The ratio of the resistance to heat conduction inside a body to the resistance to convection at its surface. Below about 0.1 the body heats almost uniformly and a lumped thermal model is adequate; large, strongly cooled cells with poor through-plane conductivity exceed it and need a model that resolves the internal gradient.
Use in Lemonergy
Lemonergy Studio blocks
Edge-cooled plate worked example
A plate with four thermal contacts and a defined coolant path. Explore which body connects to each contact and how pressure drives coolant through the plate.
Blocks to use
- Edge-cooled plate
Four metal temperature nodes form a fixed 2 × 2 conduction mesh with four thermal contact ports. Coolant follows one two-segment edge path. Metal and coolant have finite heat storage. Pressure difference drives reversible mass and enthalpy transport; hydraulic dissipation enters the coolant energy balance. Each liquid boundary requires an explicit pressure/temperature reservoir.
Inputs & settings
- Use the parameter values in the block reference.
- Bundled example verified on the production release of 28 October 2026.
- Coolant inlet boundary
Sets 200 kPa and 300 K at plate a; supplies coolant for the positive pressure difference.
- Coolant outlet boundary
Sets 100 kPa at plate b; receives coolant. Its 300 K supply temperature is used if flow reverses.
- Warm bodies 1–4
Four passive bodies initially at 320 K, connected through h to plate h1–h4. Stored heat falls as the bodies cool; no continuous heater is attached.
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. The bundled model connects four thermal masses initially at 320 K to a 310 K plate, with 300 K coolant reservoirs at 200 kPa and 100 kPa. With channel resistance 10^6 Pa s/kg, the total flow is 0.1 kg/s and hydraulic dissipation is 10 W. After 0.2 s all four loads cool below their initial temperature. The loads cool from stored sensible heat; no continuous heater is attached.
Observe. Inspect the outputs and numerical checks on the block reference page.
Fixed 2 × 2 metal mesh and the stated coolant path. Constant properties and single-phase incompressible coolant. No arbitrary liquid junction solver, configurable grid, resolved channel geometry or phase change.
Open Studio example →Lemonergy Studio blocks
Parallel-channel plate worked example
A plate with four thermal contacts and a defined coolant path. Explore which body connects to each contact and how pressure drives coolant through the plate.
Blocks to use
- Parallel-channel plate
Four metal temperature nodes form a fixed 2 × 2 conduction mesh with four thermal contact ports. Coolant follows two parallel two-segment paths. Metal and coolant have finite heat storage. Pressure difference drives reversible mass and enthalpy transport; hydraulic dissipation enters the coolant energy balance. Each liquid boundary requires an explicit pressure/temperature reservoir.
Inputs & settings
- Use the parameter values in the block reference.
- Bundled example verified on the production release of 28 October 2026.
- Coolant inlet boundary
Sets 200 kPa and 300 K at plate a; supplies coolant for the positive pressure difference.
- Coolant outlet boundary
Sets 100 kPa at plate b; receives coolant. Its 300 K supply temperature is used if flow reverses.
- Warm bodies 1–4
Four passive bodies initially at 320 K, connected through h to plate h1–h4. Stored heat falls as the bodies cool; no continuous heater is attached.
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. The bundled model connects four thermal masses initially at 320 K to a 310 K plate, with 300 K coolant reservoirs at 200 kPa and 100 kPa. With channel resistance 10^6 Pa s/kg, the total flow is 0.2 kg/s and hydraulic dissipation is 20 W. After 0.2 s all four loads cool below their initial temperature. The loads cool from stored sensible heat; no continuous heater is attached.
Observe. Inspect the outputs and numerical checks on the block reference page.
Fixed 2 × 2 metal mesh and the stated coolant path. Constant properties and single-phase incompressible coolant. No arbitrary liquid junction solver, configurable grid, resolved channel geometry or phase change.
Open Studio example →Lemonergy Studio blocks
U-channel plate worked example
A plate with four thermal contacts and a defined coolant path. Explore which body connects to each contact and how pressure drives coolant through the plate.
Blocks to use
- U-channel plate
Four metal temperature nodes form a fixed 2 × 2 conduction mesh with four thermal contact ports. Coolant follows one four-segment U path. Metal and coolant have finite heat storage. Pressure difference drives reversible mass and enthalpy transport; hydraulic dissipation enters the coolant energy balance. Each liquid boundary requires an explicit pressure/temperature reservoir.
Inputs & settings
- Use the parameter values in the block reference.
- Bundled example verified on the production release of 28 October 2026.
- Coolant inlet boundary
Sets 200 kPa and 300 K at plate a; supplies coolant for the positive pressure difference.
- Coolant outlet boundary
Sets 100 kPa at plate b; receives coolant. Its 300 K supply temperature is used if flow reverses.
- Warm bodies 1–4
Four passive bodies initially at 320 K, connected through h to plate h1–h4. Stored heat falls as the bodies cool; no continuous heater is attached.
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. The bundled model connects four thermal masses initially at 320 K to a 310 K plate, with 300 K coolant reservoirs at 200 kPa and 100 kPa. With channel resistance 10^6 Pa s/kg, the total flow is 0.1 kg/s and hydraulic dissipation is 10 W. After 0.2 s all four loads cool below their initial temperature. The loads cool from stored sensible heat; no continuous heater is attached.
Observe. Inspect the outputs and numerical checks on the block reference page.
Fixed 2 × 2 metal mesh and the stated coolant path. Constant properties and single-phase incompressible coolant. No arbitrary liquid junction solver, configurable grid, resolved channel geometry or phase change.
Open Studio example →References & further reading
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- A General Energy Balance for Battery Systems
Dawn Bernardi, Ellen Pawlikowski, John Newman · Journal of The Electrochemical Society · 1985
Topic background · Battery energy balance and irreversible and reversible heat contributions. Reduced thermal models require explicit assumptions and current-sign conventions.
- University Physics Volume 2, §1.6: Mechanisms of Heat Transfer
OpenStax, Rice University
Topic background · Conduction, convection, radiation and thermal resistance.