Fire Safety Science Digital Archive

Merzhanov and Averson have recently reviewed thermal ignition theory and, in particular, the various approximate theories for calculating the time at which thermal instability leads to large rises in temperature when the surface of a self-heating material is subjected to a constant thermal flux. Subsequently, Bradley showed that his computer calculations corresponded in effect to a mean between two simple conventional results, and Linan and Williams have derived the same relation. This was of a form different from previous ones, viz: ???0^1/4 where ? is a dimensionless flux and ?0 is a dimensionless temperature rise dependent on ? and the time, which is thereby found as a function of ?. This paper shows how a simple approximation to the conduction loss term in the basic differential equation can lead analytically to this result, agreeing within 1 per cent with Linan and William's result obtained by a different theoretical development.