A Theoretical Model of a Gaseous Combustion Wave Governed by a First-Order Reaction

Abstract

Numerical solutions are obtained for differential equations describing a hypothetical model of a laminar flame. A first-order irreversible reaction with approximately exponential dependence of rate upon temperature is assumed, with interdiffusion of reactant and product molecules. The temperature dependence of thermal conductivity, diffusion coefficient, and gas density is taken into account. When the equations are in suitable form, the dimensionless burning velocity is an eigenvalue whose magnitude depends on two dimensionless parameters; ε (the ratio of activation energy to burned gas temperature) and α (the ratio of heat flow to diffusional flow). An I.B.M. Card-Programmed Electronic Calculator was used to obtain solutions accurate to two percent, for a wide range of values of ε and α. Interdiffusion is found to reduce the burning velocity, the effect being more pronounced when ε is large. The results for α equal to unity are compared with the approximate burning-velocity equation of Zeldovich and Frank-Kamenetsky, and the latter is shown to be valid only when ε is large.