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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

22:12:54 - INFO - LOGGING (log: True)
22:12:54 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
22:12:54 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.168ms)
22:12:54 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
22:12:55 - INFO - --------------------   1% | 0.2s<23.3s | 7.9 it/s
22:12:56 - INFO - ####----------------  20% | 1.1s<2.5s | 8.2 it/s
22:12:56 - INFO - ###########---------  56% | 1.3s<0.4s | 8.3 it/s
22:12:56 - INFO - #################---  88% | 1.4s<0.1s | 8.6 it/s
22:12:56 - INFO - #################### 100% | 1.6s<--:-- | 8.3 it/s
22:12:56 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1576.70 ms)

Python

Effect of Cooling Conditions

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

Python

22:12:57 - INFO - LOGGING (log: True)
22:12:57 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
22:12:57 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.161ms)
22:12:57 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
22:12:58 - INFO - --------------------   1% | 0.2s<23.0s | 8.0 it/s
22:12:58 - INFO - ####----------------  20% | 1.0s<2.2s | 9.0 it/s
22:12:59 - INFO - ###########---------  56% | 1.3s<0.4s | 8.6 it/s
22:12:59 - INFO - #################---  88% | 1.4s<0.1s | 8.4 it/s
22:12:59 - INFO - #################### 100% | 1.5s<--:-- | 8.6 it/s
22:12:59 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1524.99 ms)
22:13:00 - INFO - LOGGING (log: True)
22:13:00 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
22:13:00 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.200ms)
22:13:00 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
22:13:00 - INFO - --------------------   1% | 0.2s<23.0s | 8.0 it/s
22:13:01 - INFO - ####----------------  20% | 1.1s<2.5s | 8.2 it/s
22:13:01 - INFO - ###########---------  56% | 1.4s<0.5s | 8.0 it/s
22:13:01 - INFO - #################---  88% | 1.5s<0.1s | 8.0 it/s
22:13:01 - INFO - #################### 100% | 1.6s<--:-- | 7.9 it/s
22:13:01 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1625.34 ms)
22:13:02 - INFO - LOGGING (log: True)
22:13:02 - INFO - BLOCKS (total: 5, dynamic: 2, static: 3, eventful: 0)
22:13:02 - INFO - GRAPH (nodes: 5, edges: 7, alg. depth: 2, loop depth: 0, runtime: 0.160ms)
22:13:02 - INFO - STARTING -> TRANSIENT (Duration: 1800.00s)
22:13:02 - INFO - --------------------   1% | 0.2s<23.1s | 8.0 it/s
22:13:03 - INFO - ####----------------  20% | 1.2s<2.7s | 7.7 it/s
22:13:03 - INFO - ###########---------  56% | 1.4s<0.5s | 7.4 it/s
22:13:04 - INFO - #################---  88% | 1.6s<0.1s | 7.5 it/s
22:13:04 - INFO - #################### 100% | 1.7s<--:-- | 8.0 it/s
22:13:04 - INFO - FINISHED -> TRANSIENT (total steps: 13, successful: 13, runtime: 1675.89 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.