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Electrothermal Coupling with an External Thermal Model

CellElectrical uses PyBaMM's isothermal electrochemistry and exposes heat generation as an output. Wiring it to LumpedThermal creates a closed electrothermal feedback loop directly in PathSim — useful for pack-level thermal networks or custom cooling models.

Model

LumpedThermal implements a single-node energy balance:

MATHDISPLAY0ENDMATH

CellElectrical outputs total heat generation [W], which LumpedThermal accepts directly — no unit bridging needed.

Python

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  from .autonotebook import tqdm as notebook_tqdm

Simulation: 1 C Discharge with Electrothermal Feedback

Python

13:58:48 - INFO - LOGGING (log: True)
13:58:48 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
13:58:48 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.236ms)
13:58:48 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
13:58:48 - INFO - --------------------   1% | 0.2s<19.8s | 9.3 it/s
13:58:49 - INFO - ####----------------  20% | 0.9s<2.0s | 10.2 it/s
13:58:49 - INFO - ###########---------  56% | 1.1s<0.4s | 9.8 it/s
13:58:49 - INFO - #################---  88% | 1.2s<0.1s | 9.9 it/s
13:58:49 - INFO - #################### 100% | 1.3s<--:-- | 9.9 it/s
13:58:49 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1311.84 ms)

Python

Effect of Cooling Conditions

Sweep of MATHINLINE0ENDMATH from adiabatic to liquid-cooled to show the impact on voltage and temperature.

Python

13:58:50 - INFO - LOGGING (log: True)
13:58:50 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
13:58:50 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.203ms)
13:58:50 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
13:58:51 - INFO - --------------------   1% | 0.2s<19.0s | 9.7 it/s
13:58:51 - INFO - ####----------------  20% | 0.9s<1.9s | 10.6 it/s
13:58:51 - INFO - ###########---------  56% | 1.1s<0.3s | 10.6 it/s
13:58:52 - INFO - #################---  88% | 1.1s<0.1s | 10.5 it/s
13:58:52 - INFO - #################### 100% | 1.2s<--:-- | 10.7 it/s
13:58:52 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1237.85 ms)
13:58:52 - INFO - LOGGING (log: True)
13:58:52 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
13:58:52 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.226ms)
13:58:52 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
13:58:52 - INFO - --------------------   1% | 0.2s<19.5s | 9.4 it/s
13:58:53 - INFO - ####----------------  20% | 0.9s<1.8s | 10.9 it/s
13:58:53 - INFO - ###########---------  56% | 1.1s<0.4s | 10.3 it/s
13:58:53 - INFO - #################---  88% | 1.2s<0.1s | 10.7 it/s
13:58:54 - INFO - #################### 100% | 1.3s<--:-- | 10.2 it/s
13:58:54 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1276.54 ms)
13:58:54 - INFO - LOGGING (log: True)
13:58:54 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
13:58:54 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.195ms)
13:58:54 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
13:58:54 - INFO - --------------------   1% | 0.2s<17.6s | 10.5 it/s
13:58:55 - INFO - ####----------------  20% | 0.7s<1.4s | 13.8 it/s
13:58:55 - INFO - ###########---------  56% | 0.9s<0.3s | 14.1 it/s
13:58:55 - INFO - #################---  88% | 0.9s<0.0s | 14.1 it/s
13:58:55 - INFO - #################### 100% | 1.0s<--:-- | 14.3 it/s
13:58:55 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 993.49 ms)

Python

Summary

CellElectrical + LumpedThermal form a closed electrothermal feedback loop; PathSim resolves the coupling at each step.
CellElectrical outputs total heat [W], which connects directly to LumpedThermal's input — no unit conversion needed.
Stronger cooling keeps the cell cooler and slightly raises the discharge voltage.
For DAE models (e.g. DFN), see notebook 03.