Enthalpy, flame propagation

Under the present conditions of negligible diffusion, flame propagation in the solid is associated with an excess enthalpy per unit area given by PsCps(T — Tq) dx just ahead of the reaction sheet. This excess provides a local reservoir of heated reactant in which a flame may propagate at an increased velocity. If = KI(Ps ps) denotes the thermal diffusivity of the solid, then for the steady-state solution, the thickness of the heated layer of reactant is on the order of where is the steady-state flame... 

It is found experimentally that limit mixtures, incapable of supporting combustion waves, nevertheless have theoretical thermodynamic flame temperatures of the order of 1000° C. or more. It is, therefore, not immediately clear why combustion waves, albeit slowly propagating, should not develop in mixtures possessing such substantial chemical enthalpy. The question arises whether the observed limits of flammability are true limits or whether such mixtures are actually capable of supporting combustion waves but are prevented from doing so by experimental limitations. Experimentalists believe that the limits are true. On the other hand, no theoretical criterion for the limit is obtained from the steady-state equations of the combustion wave. That is, the equations describe combustion waves without differentiating between mixtures that are known to be flammable and mixtures that are known to be nonflammable. Therefore, for nonflammable mixtures the combustion wave becomes unstable to perturbations and thus disappears (7). Conversely, for flammable mixtures the combustion wave can overcome perturbations—i.e., it returns to the steady state after being perturbed. 

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