In 1974 Liñán published the first complete analysis of the asymptotic structure of nonpremixed flames based on the one-step second-order reaction. Although the analysis was conducted for the steady counterflow flame with unity Lewis number, it was subsequently recognized that the analysis is of such a canonical nature that the results are applicable to many laminar flame situations. Specifically, since one of the flame regimes identified has the characteristics of a premixed flame, the analysis is actually applicable to both nonpremixed and premixed flames. Furthermore, since the flame response is ultimately determined by that of the reaction zone, many subsequent analyses of other flame configurations invariably end up with the structure equations and, hence, solutions first derived by Liñán. We shall study these structures in this chapter.

We shall first present a separate analysis of the reaction zone structure of premixed flames, with the solution expressed in terms of some general boundary conditions that are to be supplied by the outer solutions for individual situations. From our study of the ignition of a combustible by a hot surface in Section 8.2, we anticipate that such a generalized formulation is possible for situations involving thin reaction zones embedded within flames. The concept of delta-function closure will also be introduced.

For nonpremixed flames, we have studied their combustion characteristics in the reaction-sheet limit in Chapter 6. It was demonstrated that much can be learned about the bulk combustion and flame behavior without any specification of the nature of the chemical reaction, except for the implicit assumption that they occur infinitely fast relative to diffusion.