General Considerations for Extinction Based on Kinetics

Alternatively, in Equation (9.108), the convective heat flux could be approximated as 

Let us reconsider the critical flame temperature criterion for extinction. Williams [25], in a review of flame extinction, reports the theoretical adiabatic flame temperatures for different fuels in counter-flow diffusion flame experiments. These temperatures decreased with the strain rate (ua0/x), and ranged from 1700 to 2300 K. However, experimental measured temperatures in the literature tended to be much lower (e.g. Williams [25] reports 1650 K for methane, 1880 K for iso-octane and 1500 K for methylmethracrylate and heptane). He concludes that 1500 50 K can represent an approximate extinction temperature for many carbon-hydrogen-oxygen fuels burning in oxygen-nitrogen mixtures without chemical inhibitors . 

Macek [27] examined the flammability limits for premixed fuel-air systems and small diffusion flames under natural convection conditions, and computed the equilibrium flame temperature for these flame systems. Data were considered for the alkanes and alcohols at their measured premixed lower flammability limits, and at their measured 

1 A demonstration of the similarity of extinction in premixed and diffusion flames 

The control volume analysis of the premixed flame of Section 4.5.4 can be used together with the analysis here in Section 9.9 for the diffusion flame to relate the two processes. We assume the kinetics is the same for each and given as in Equation (9.102). Since we are interested in extinction, it is reasonable to assume the heat loss from the flame to be by radiation from an optically thin flame of absorption coefficient, k  

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