Structure of One-Dimensional Laminar Flames

The general equations are simplified for a one-dimensional laminar flame in the steady state (Hi). 

Conservation of individual chemical species is given by the following equation  

The mass fraction Gi of the mass velocity M differs from the mass fraction of the local mixture when diffusion is taking place. Ki is the ordinary reaction rate of chemical kinetics, expressed as mole/unit volume/unit time, which is measured in a static experiment as a function of temperature and composition if the flame is in local thermal equilibrium. If not, this equation serves only as a measure of the nonequilibrium local reaction rate. 

These equations contain a number of assumptions. First of all, they are a result of a dilute gas approximation in which binary diffusion coefficients, which may be assumed independent of composition, are used. Secondly, thermal diffusion has been neglected although this assumption should be verified for the system under investigation. It appears that the flux due to thermal diffusion could be a substantial fraction of the ordinary diffusion flux for some systems (F6). 

The assumption has been made that the pressure drop across a flame is so small that the momentum equation may be ignored. The steady-state restriction in the ordinary continuity equation ensures that the mass flux M is constant throughout. The mass flux is converted to the interesting parameter, burning velocity, by use of the cold gas density. 

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