Burning down the house: The time to ignition of an irradiated solid

The combustion of a wooden door irradiated with thermal energy is studied in this paper. The problem is relevant to the mechanism by which house fires propagate, for example. A novel method is presented for computing the time-dependent behaviour of the temperature, which is also a function of a spatial coordinate. A boundary-integral method is used to reduce the mathematical formulation of the problem to a coupled system of Volterra-type integral equations, combined with a nonlinear rate equation. An efficient numerical method is used to solve this system with great accuracy. The time to ignition is obtained from these numerical solutions, and we show that spatial effects can cause an ignition event to occur at lower values of the incident radiation than would be expected from the classical steady-state ignition diagram. This is expected to have important consequences in understanding fire spread in buildings.