Ignition by radiant heat is a threshold phenomenon described not by temperature but by heat flux, the power arriving on each square metre of surface, in kilowatts per square metre. Below a material's critical heat flux the surface loses heat to the air and by re-radiation as fast as it gains it, settles at a steady warm temperature, and never ignites no matter how long it is exposed; for common woods that threshold is around \( 10 \) to \( 13 \ \mathrm{kW/m^2} \) with a pilot present. Above the threshold the surface heats until pyrolysis is vigorous enough to ignite, and the delay before that happens shortens sharply as flux rises, so a fuel that takes minutes at \( 15 \ \mathrm{kW/m^2} \) takes seconds at \( 50 \). Thin fuels reach the point sooner than thick ones because there is less mass to heat. The confusion this resolves is the belief that any exposure eventually ignites, which is why a fixed separation distance from a flame front can genuinely protect a structure. After this Concept you can judge whether a given radiant exposure will ignite a fuel at all, and roughly how quickly.
A lumped-capacitance energy balance models a thin, thermally-thin solid sample exposed to a uniform, constant radiative (and convective) heat flux: the rate of change of the sample's heat content equ…