A model for the propagation of a flame up a vertical combustible wall is presented. The model is based on the assumption of a uniform heat flux from the flame into the wall. The size of the flame and the heat flux are determined by the rate of release of flammable gases through pyrolysis within the wall. Some analytical and numerical solutions are obtained, with just one simple class of models giving rise to a great range of flame behaviours; from extinction to accelerating waves, and from pulsating travelling waves to irregularly varying flames. Also some possible modifications of the model are discussed.
- fire spread
- integro-differential equations
- linear stability