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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

12:03:33 - INFO - LOGGING (log: True)
12:03:33 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
12:03:33 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.141ms)
12:03:33 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:33 - INFO - --------------------   1% | 0.2s<16.9s | 10.9 it/s
12:03:34 - INFO - ####----------------  20% | 0.8s<1.8s | 11.6 it/s
12:03:34 - INFO - ###########---------  56% | 1.0s<0.3s | 11.4 it/s
12:03:34 - INFO - #################---  88% | 1.0s<0.1s | 11.4 it/s
12:03:34 - INFO - #################### 100% | 1.1s<--:-- | 11.2 it/s
12:03:34 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1138.76 ms)

Python

Effect of Cooling Conditions

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

Python

12:03:35 - INFO - LOGGING (log: True)
12:03:35 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
12:03:35 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.130ms)
12:03:35 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:35 - INFO - --------------------   1% | 0.1s<9.7s | 18.9 it/s
12:03:35 - INFO - ####----------------  20% | 0.5s<1.5s | 15.4 it/s
12:03:35 - INFO - ###########---------  56% | 0.7s<0.3s | 14.1 it/s
12:03:36 - INFO - #################---  88% | 0.8s<0.1s | 13.7 it/s
12:03:36 - INFO - #################### 100% | 0.8s<--:-- | 13.8 it/s
12:03:36 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 834.76 ms)
12:03:36 - INFO - LOGGING (log: True)
12:03:36 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
12:03:36 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.116ms)
12:03:36 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:36 - INFO - --------------------   1% | 0.1s<9.6s | 19.1 it/s
12:03:37 - INFO - ####----------------  20% | 0.4s<1.0s | 20.1 it/s
12:03:37 - INFO - ###########---------  56% | 0.6s<0.2s | 19.5 it/s
12:03:37 - INFO - #################---  88% | 0.6s<0.0s | 19.5 it/s
12:03:37 - INFO - #################### 100% | 0.7s<--:-- | 19.0 it/s
12:03:37 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 662.63 ms)
12:03:37 - INFO - LOGGING (log: True)
12:03:37 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
12:03:37 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.093ms)
12:03:37 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
12:03:37 - INFO - --------------------   1% | 0.1s<9.8s | 18.8 it/s
12:03:38 - INFO - ####----------------  20% | 0.5s<1.1s | 18.1 it/s
12:03:38 - INFO - ###########---------  56% | 0.6s<0.2s | 17.7 it/s
12:03:38 - INFO - #################---  88% | 0.7s<0.0s | 17.6 it/s
12:03:38 - INFO - #################### 100% | 0.7s<--:-- | 17.8 it/s
12:03:38 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 716.46 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.