Thermal runaway — warm a cell until it has nowhere to settle

Drag upward to warm the cell's surroundings; drag down to cool them. The arrow keys do the same, a step at a time. End goes straight to a hot day; Home returns to a cool one. Time is compressed — what you watch in a second takes about twenty minutes in a real cell. Sound is off until you turn it on.

What you are looking at

Every lithium cell makes a little heat all the time, from slow chemistry it cannot switch off. How much depends on temperature, and not gently: the rate follows an exponential, so a cell ten degrees warmer makes appreciably more heat than it did.

The case removes heat in proportion to how much hotter the cell is than its surroundings. Proportion against exponential is an unequal contest, but for a long way it does not matter, because the two still cross. Where they cross, the cell settles: it warms until the heat leaving equals the heat arriving, and then it stops. That crossing is the whole of a cell's thermal safety.

Raise the surroundings and the removal line slides right. The lower crossing — the one the cell actually sits at — climbs to meet the upper one. At some ambient they touch, and past it they do not meet at all. Nothing about the cell has changed. What has gone is the existence of a temperature it could settle at.

The two things worth taking away

The warning margin is about nine degrees, and it looks like nothing. Right at the edge, the cell sits roughly nine degrees above its surroundings — which is what a healthy cell under load looks like. There is no temperature you can read off the outside that distinguishes the last safe state from the first unsafe one.

It is set by the surroundings, not by the cell. The cell is the same object at every setting here. What decides its fate is the ambient it sits in and how well its case is coupled to that ambient — which are pack design decisions, made long before any cell is charged.

What is not verified

Stated plainly, because a piece whose value is trustworthiness should not overclaim. The first list is the part that would change how you read the result. The second is scope — true, worth saying, and not load-bearing.

• No engineer has reviewed this. If you are one and would check it, REVIEW.md says what would actually help and is meant to cost about fifteen minutes. The model is standard Semenov thermal-explosion theory and the built-in checks confirm it reproduces the closed-form criticality condition to within a fraction of a percent — but that check is the author's own, not a battery or process-safety engineer's.
• The kinetics are one lumped Arrhenius term, with an activation energy in the reported band for electrolyte and SEI decomposition, and a pre-exponential chosen so that criticality falls near eighty degrees ambient. A real cell has several reactions that start at different temperatures and feed each other, so the real curve is a stack of these, not one.
• The cell is one lump at one temperature. Real cells have internal gradients, and a hot spot runs away while the average looks calm — which makes the real case worse than the one drawn, not better.

Scope, for completeness. True of the model, and none of it changes the answer above.

• Nothing here models the vent itself. The run stops at the vent temperature because that is where this model stops being about heat balance and starts being about gas, pressure and combustion.
• Time is compressed about twelve hundredfold, and the real induction period near the critical ambient is hours. The slowness near the edge is real, and is itself a hazard: a pack can be past the point of no return long before anything shows.

Commissions

The subject changes; the method does not. If you have a failure mode, a mechanism, or a process that people keep getting wrong because the diagram cannot move, that is the shape of problem this suits. You get one file, the checks that hold it honest, and the notes explaining every decision including the ones that were reversed. Commissions start at £4,000 and take three to four weeks from an agreed brief. yinxueshi1017@gmail.com

Not commissioning anything? Still worth an email. If your version of this failed differently — other geometry, other numbers, a mechanism this piece leaves out — tell me in one line. Corrections are the main thing that decides what gets built next.