Thermal explosion in a combustible gas mixture with general Arrhenius reaction-rate laws: criticality and its disappearance

Previous analyses of thermal explosion in combustible gas mixtures containing fuel droplets are extended to permit a more general temperature dependence of reaction rate for most typical practical reactions under physically realistic assumptions. The mathematical formulation representing the physical model involves a system of three highly non-linear ordinary differential equations. The present study focuses on analytical investigation of thermal stability of highly combustible gas mixture when the consumption of reactant and evaporation of fuel droplets are relatively small compared with their initial conditions inside the combustion chamber before ignition commences, which reduce the system of equations to one in terms of the explosive behaviour. Consequently, generalised analytical expressions for critical ignition and extinction gas temperatures, transitional values of gas temperature θ g , activation energy β and intensity of combustion and evaporation ε 1 parameters are obtained when the impact of thermal radiation is negligible. Also, effects of thermal radiation are evaluated numerically in the following cases: (a) sensitized (b) Arrhenius and (c) bimolecular temperature dependence of reaction rates.