Heat Release Rate from Fuel Area

Heat release rate is the single most important number describing a fire — more than temperature, more than flame height, more than anything else, because everything else follows from it. This equation is where it comes from when the fire is fuel-controlled: mass leaving the fuel surface per unit area per second, multiplied by the energy that mass carries, multiplied by the area alight, multiplied by the fraction that actually burns.

Unlike almost everything else in this shard, there is no fitted constant here. It is a mass and energy balance and it is dimensionally honest in any unit system. All the difficulty is in the inputs.

The mass burning flux is not a property of the fuel. It is the rate at which the flame's own heat drives volatiles off the surface, so it depends on how much heat is coming back. For a liquid pool, the flux rises with diameter until the pool is roughly two metres across, at which point the flame becomes optically thick and radiation to the surface saturates; only above that does the flux settle at the free-burning value that handbooks tabulate. A 0.3 m pan of heptane burns at a fraction of the tabulated rate. For a solid, the flux depends on the flame, on anything else already burning nearby, and on the hot layer overhead — which is why the same material burns faster in a corner than in the open, and faster still once the room has filled with hot gas. That last feedback is what turns a growing fire into flashover.

The heat of combustion needs care about which one you have. Fire engineering uses the NET, or lower, value: the water formed leaves as vapour and its latent heat is never recovered. The GROSS value from a bomb calorimeter counts that heat and runs a few per cent high for hydrocarbons, more for wet or oxygenated fuels. Separately, some sources quote an EFFECTIVE heat of combustion with the combustion efficiency already folded in — use one of those and set $\chi = 1$, or the loss is counted twice.

The combustion efficiency itself is the fraction of the fuel's chemical energy that appears as heat. Clean fuels — methanol, methane — sit near 0.9 or above. Heavily sooting ones sit at 0.6 to 0.8. The missing energy has not disappeared. It walks out of the compartment as soot and carbon monoxide, and in an under-ventilated fire it can find air somewhere else and burn there — in a corridor, up a shaft, out of a window. Unburned fuel leaving a compartment is not a rounding error; it is a mechanism by which fires kill people who are nowhere near them.

And the area is the area actually alight, which for a growing fire is a moving target and for a rack of stored goods is emphatically not the footprint. This equation gives a steady-state ceiling for a stated area. It does not give a fire history, and it should be read as the answer to "how big can this get?" rather than "how big is it?".