Self-heating of combustible vapour in porous material when the fibres are entirely covered by fluid

A mathematical model of the self-heating of (porous) lagging material soaked in combustible fluid is presented which considers the fibres to be completely covered by the fluid and with the ignition taking place due to oxidation of the vapour. Because the fibres are completely covered, the evaporation term in this model is not dependent on the amount of liquid present. This leads to a simpler equation set in the temperature and amount of vapour only (the liquid equation is decoupled). It is found that if the heat transfer between solid and gas is large (such that a lumped energy approach is valid), there can be situations where ignition takes place after an initial temperature decrease. The model ignores diffusive effects and considers both the heat transfer and mass transfer in a lumped approach extending the classical Semenov theory to include extra heat losses due to the evaporative term but with important watershed behaviour due to the fresh supply of reactant. The mass transfer equation describing the conservation of combustible vapour is now added in parallel to the energy equation. Even though the dependence on combustible liquid is decoupled, the model serves to indicate how in principle spillage or leakage of fuel on porous material can lead to ignition when it is essentially the vapour which is undergoing self-heating.