Delayed thermal explosion in porous media: Method of invariant manifolds

The phenomenon of gaseous thermal explosion in porous media filled with a combustible evaporating fuel is modelled using the spatially uniform approach. The proposed mathematical model including four highly nonlinear ordinary differential equations is studied analytically by the geometrical asymptotic method of integral manifolds. The main parametric classification of the dynamical system behaviour is obtained: conventional ('fast') explosion and delayed explosion. The paper focuses on the delay effects, which are due to competition between the exothermic chemical reaction and heat sink to the liquid phase. The delay time estimations are derived analytically. The theoretical results are justified by the numerical simulations.