Analysis of some nonlinear premixed flame phenomena

A set of nonlinear, coupled, algebraic conservation relations have been used to describe the bulk response of nonadiabatic stretched premixed flames in terms of the flame temperature, the characteristic thicknesses of the preheat and mass diffusion zones ahead of the flame, and the mass fluxes at the upstream and downstream boundaries of these zones. Specific cases studied include adiabatic stretched flames, nonadiabatic unstretched flames with distributed conductive and radiative heat losses, and stretched flames with conductive heat loss; these cases encompass and extend practically all previous theoretical models on this class of nonlinear premixed flame phenomena. Solutions exhibit the characteristic extinction turning-point behavior, while the predicted extinction states also agree well with those asymptotic results that have been derived. The study also examines and distinguishes the various possible definitions of flame stretch and discusses the relation of the flammability limit with radiative heat loss.