Follow a heat pulse into a neighboring cell
Heat conduction can activate an event in a neighboring thermal mass. In this example, cell 1 releases a finite heat pulse, cell 2 samples its temperature, and a latched trigger starts a second pulse. You will trace the event logic, reproduce the two temperature histories and verify the complete energy balance in Lemonergy.
The prepared model is tr-propagation, reference version 1. Its 48 blocks and 64 connections combine continuous thermal states with sampled logic in the Rust/WebAssembly engine. First try passive heat exchange and single-cell finite release if these building blocks are new to you.
Open and inspect the complete model
Open prepared examples and choose Two cells: triggered heat propagation. The complete supplied model loads automatically. Choose Run prepared model to calculate a fresh result with Rust/WebAssembly, then select blocks to inspect their read-only parameters and connections. You can download the original model data for reference.
The public viewer lets you inspect, run and explore this prepared example. To change parameters, connect blocks, import a file or save an edited model, choose Edit with Pro. The Design app opens the selected example in its authenticated Pro editor; the workflow guide explains both experiences.
Every required block is included. The extra energy-accounting branches measure the model's balance; they do not represent additional physical cells.
Define the balances and event rules
The cells begin at the same temperature. Each loses heat to the environment, and a conductive link transfers equal and opposite heat between them:
q12 = G (T1 − T2)
C dT1/dt = P1 − H (T1 − Ta) − q12
C dT2/dt = P2 − H (T2 − Ta) + q12
P1 = 200 W for 0 ≤ t < 10 s; otherwise 0 W
P2 = 200 W for t2 ≤ t < t2 + 10 s; otherwise 0 W
Cell 1 starts from a time-seeded command at 0 s. Cell 2 starts at the first 0.1 s sampling instant when T2 is strictly greater than 320 K. Each latch remembers its trigger permanently; a separate timer shuts off heat after ten seconds.
| Input | Value | Where to inspect it |
|---|---|---|
| Heat capacity C | 20 J/K per cell | Both Thermal balance blocks |
| Initial temperatures | 300 K, 300 K | Both temperature Integrators |
| Inter-cell conductance G | 2 W/K | inter-cell-heat Gain |
| Ambient conductance H | 1 W/K per cell | Thermal balance blocks and ambient-heat Gains |
| Ambient temperature Ta | 300 K | ambient-temperature Constant |
| Release power | 200 W per triggered cell | Both release-heat Gains |
| Release duration | 10 s | Both On-delay timers |
| Sample time | 0.1 s | Both latches and timers |
| Cell 1 seed | 0 to 1 at 0 s | Step block |
| Cell 2 threshold | Strictly greater than 320 K | Threshold Constant and Compare |
| Observation window | 0–40 s | Solver settings |
For an independent reference, let m = (T1 + T2)/2 − Ta and d = (T1 − T2)/2. Between event instants, dm/dt = (P1 + P2)/(2C) − Hm/C and dd/dt = (P1 − P2)/(2C) − (H + 2G)d/C. Their closed-form exponential solutions supply reference temperatures independently of the block solver.
Understand every block group
Select a block in the prepared diagram to inspect its read-only parameters and connections. In the table, cell-i means the listed group exists once for each of the two cells.
| Block or group | Parameters and units | Role |
|---|---|---|
ambient-temperature, zero, one · Constants | 300 K, 0, 1 | Supply the ambient state and logic levels |
negative-ambient · Gain | −1 | Form −Ta for ambient-loss accounting |
cell-1-seed · Step; seed-threshold · Constant | Before 0, after 1, at 0 s; threshold 0.5 | Seed cell 1 |
cell-1-trigger · Compare | Seed ≥ 0.5 | Create cell 1 set condition |
cell-2-threshold · Constant; cell-2-trigger · Compare | 320 K; T2 > threshold | Create the neighboring set condition |
cell-i-latched · Boolean latch | Sample 0.1 s; initial 0; reset connected to zero | Keep trigger memory |
cell-i-release-complete · On-delay timer | Sample 0.1 s; delay 10 s | Mark the end of each pulse |
cell-i-negative-timer · Gain; cell-i-release-remaining · Sum | −1; two inputs | Calculate 1 − timer output |
cell-i-release-gate · Product | Latch × release-remaining; scale 1 | Enable the finite pulse |
cell-i-release-heat · Gain | 200 W per unit logic level | Produce heat power |
cell-i-temperature-rate · Thermal balance | C = 20 J/K; H = 1 W/K | Calculate dTi/dt from net heat, Ti and Ta |
cell-i-temperature · Integrator | Initial 300 K; rate gain 1 | Accumulate temperature |
cell-i-release-energy · Integrator | Initial 0 J; rate gain 1 | Accumulate the heat released by that cell |
cell-i-above-ambient · Sum; cell-i-ambient-heat · Gain | Ti − Ta; gain 1 W/K | Measure heat transferred to ambient |
cell-i-negative-initial · Constant; cell-i-temperature-change · Sum | −300 K; two inputs | Form Ti − Ti(0) |
cell-i-stored-energy · Gain | 20 J/K | Calculate stored-energy change |
negative-cell-2-temperature · Gain; inter-cell-temperature-difference · Sum | −1; two inputs | Form T1 − T2 |
inter-cell-heat · Gain; negative-inter-cell-heat · Gain | 2 W/K; −1 | Compute equal and opposite link heat |
cell-1-net-heat, cell-2-net-heat · Sums | P1 − q12; P2 + q12 | Feed each Thermal balance |
total-ambient-heat · Sum; ambient-energy · Integrator | Two inputs; initial 0 J, gain 1 | Accumulate total environmental loss |
total-release-energy · Sum; negative-release-energy · Gain | Two inputs; −1 | Form the negative released-energy total |
energy-residual · Sum | Four inputs | Stored change + ambient energy − released energy |
In the Pro editor, changing a physical parameter can require an accounting change too: if you edit C, update the corresponding stored-energy gain; if you edit H, update the ambient-heat gain. This keeps the independent energy check consistent with the physical balances.
Run the model and inspect the event
- Confirm the loaded model has 48 blocks, 64 connections and a 0–40 s window.
- Keep the fixed solver settings below and the 0.1 s latch/timer sample times.
- Choose Run prepared model. Check that the comparison and full-trace completeness pass.
- Use Scope signal to inspect Cell 2 temperature, then Cell 2 trigger memory and Cell 2 released heat. The neighboring pulse begins at 9.7 s.
- Inspect Cell 1 released heat. It ends at 10 s while cell 2 continues releasing heat until 19.7 s.
- Inspect each released-energy signal, Energy transferred to ambient and Energy balance residual. Use the comparison CSV export to inspect exact event rows.
- Choose Download run evidence to retain the fresh model/result comparison and Download results CSV for the sampled signals. The original model data is available under Model, method and references.
| Solver setting | Reference value |
|---|---|
| Method | Dormand–Prince 4(5) |
| Initial / minimum / maximum step | 0.001 / 1e−10 / 0.1 s |
| Relative / absolute tolerance | 1e−11 / 1e−12 |
| Maximum steps | 100,000 |
| Algebraic tolerance / iteration limit | 1e−10 / 30 |
| Implicit tolerance / iteration limit | 1e−10 / 20 |
After the run, move Display time to inspect numerical Display outputs at retained solver times. Choose a signal’s Scope button, or use Scope signal, to view its full trajectory and reference-error plot. Scrubbing changes the inspected time, not the prepared model or its result.
Read the temperature and energy results
The table contains rounded analytical checkpoints. Power outputs are right-continuous: the new power applies at an event instant, while temperature and energy remain continuous.
| Time (s) | T1 (K) | T2 (K) | P1 (W) | P2 (W) | Meaning |
|---|---|---|---|---|---|
| 0 | 300.000000 | 300.000000 | 200 | 0 | Seeded pulse starts |
| 5 | 336.389826 | 307.850018 | 200 | 0 | Conduction heats the neighbor |
| 9.6 | 356.307302 | 319.936020 | 200 | 0 | Neighbor remains below threshold |
| 9.7 | 356.660718 | 320.199843 | 200 | 200 | First sampled trigger for cell 2 |
| 10 | 357.748910 | 323.922570 | 0 | 200 | Cell 1 pulse ends |
| 19.7 | 346.838739 | 380.306723 | 0 | 0 | Cell 2 pulse ends |
| 40 | 322.934307 | 323.143518 | 0 | 0 | Both cells are cooling |
Do not round the 9.6 s temperature to 320 K when deciding the event. Its unrounded value is below the strict threshold. The 9.7 s event is a sampled-model result, not a continuous crossing-time estimate.
| Energy at 40 s | Expected value |
|---|---|
| Cell 1 release | 2,000 J |
| Cell 2 release | 2,000 J |
| Transfer to ambient | 3,078.443512 J |
| Combined stored-energy increase | 921.556488 J |
| Stored increase + ambient transfer − release | 0 J analytically |
The retained thermal report, generated 1 October 2026 at 18:52:33 UTC, passed with 410 output points and a maximum energy-balance residual of approximately 1.18e−11 J. This historical record is separate from the fresh run shown in the interface screenshots.
Fixed full-trace gates are 1e−6 K for temperatures, 1e−10 W for release power, 1e−3 J for energies and exactly zero latch error. Original settings, every accepted point, all 0.1 s instants and both trigger/end times must also match. See how to read validation results for the difference between final-value agreement and complete trace agreement.
Explore weaker coupling (Pro)
Choose Edit with Pro to open this example in the authenticated Design editor. The following changes require Pro editing. Use Run blocks & compare there to solve the edited graph; the public prepared model stays unchanged.
Save the reference model, then change Gain on inter-cell-heat from 2 to 0.1. Keep the other parameters unchanged and rerun. The neighbor should remain below the trigger threshold over 40 s, and total release should fall from 4,000 J to 2,000 J. The edited model will differ from this page's frozen propagation reference.
For a matching reference and a full interpretation of that experiment, load Two cells: reduced thermal coupling. Comparing these cases also shows the tradeoff: a weaker link reduces neighboring heating while letting the seeded cell become hotter during its own pulse.
Troubleshoot and assess the scope
| Observation | Check |
|---|---|
| Cell 2 never triggers in the original case | G = 2 W/K, threshold 320 K, strict greater-than comparison and both thermal connections |
| Cell 2 appears to trigger at 9.6 s | Read unrounded data and exact sample instants; do not infer an event from rounded chart labels |
| Heat continues after ten seconds | On-delay settings and the 1 − timer branch |
| Trigger memory drops when heat stops | The timer gates heat; the latch reset should stay connected to zero |
| Energy residual grows | Opposite signs of link heat, matched C/H accounting gains and release-energy integrators |
This authored lumped model verifies a numerical implementation. Its rectangular release, constant properties and sampled trigger do not represent measured battery reaction kinetics. Gas, flame, radiation, venting, ejecta, electrochemistry and spatial gradients are outside its scope. A pass is not physical validation or a safety claim.
References and related reading
The retained model and report bind this example to its historical inputs and numerical evidence. The cited external architecture documentation in this page's sources is background, not a measured reference dataset; MATLAB/Simscape was not executed for that retained check. Continue with thermal propagation verification, battery thermal management or the example library.