Flame Zeldovich, Frank-Kamenetskii-Semenov

Considering that the temperature difference 9 must be equivalent to (T - T9 in the Zeldovich-Frank-Kamenetskii-Semenov thermal flame theory, the reaction time corresponding to the reaction zone 6 in the flame can also be approximated by... 

In the next section, the flame speed development of Zeldovich, Frank-Kamenetskii, and Semenov will be discussed. They essentially evaluate this term to eliminate the unknown ignition temperature 7] by following what is now the standard procedure of narrow reaction zone asymptotics, which assumes that the reaction rate decreases very rapidly with a decrease in temperature. Thus, in the course of the integration of the rate term lv in the reaction zone, they extend the limits over the entire flame temperature range T0 to T. This approach is, of course, especially valid for large activation energy chemical processes, which are usually the norm in flame studies. Anticipating this development, one sees that the temperature term essentially becomes... 

As implied in the previous section, the Russian investigators Zeldovich, Frank-Kamenetskii, and Semenov derived an expression for the laminar flame speed by an important extension of the very simplified Mallard-Le Chatelier approach. Their basic equation included diffusion of species as well as heat. Since their initial insight was that flame propagation was fundamentally a thermal mechanism, they were not concerned with the diffusion of radicals and its effect on the reaction rate. They were concerned with the energy transported by the diffusion of species. 

Later, there were improvements in the thermal theories. Probably the most significant of these is the theory proposed by Zeldovich and Frank-Kamenetskii. Because their derivation was presented in detail by Semenov [4], it is commonly called the Semenov theory. These authors included the diffusion of molecules as well as heat, but did not include the diffusion of free radicals or atoms. As a result, their approach emphasized a thermal mechanism and was widely used in correlations of experimental flame velocities. As in the... 

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