An earlier paper (MRC TSR no. 1803) indicated that rational analysis of the governing equations of combustion can be based on activation-energy asymptotics. As an example, the basic problem of combustion theory is treated, namely the premixed plane flame (i.e. the unlimited one-dimensional steady solution).

Perturbations of a plane premixed flame propagating steadily along a uniform duct are considered. These may be caused by heat loss through the sides of the duct, for which conditions are steady, or by slight variations in the cross section, when a slowly varying flame results. Such unsteadiness may also be self-induced. The results, which concern quenching, stability and velocity changes as well as the behavior of an elementary burner, are remarkably sensitive to whether the Lewis number is greater or less than one. (Author).

This report is Chapter VII of the twelve in a forthcoming research monograph on the mathematical theory of laminar combustion. Cylindrical and spherical premixed flames are discussed, the latter with a view to application to the burning monopropellant drop. Cylindrical flames have a planar character, while spherical flames exhibit ignition and extinction.

This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.

This report is Chapter XI of the twelve in a forthcoming research monograph on the mathematical theory of laminar combustion. The investigation is narrowed to the stability of freely propagating premixed flames, the only area that has yielded to mathematical analysis so far. Special emphasis is placed on the cellular flames that are found experimentally to be the result of instability. (Author).

Explores the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact.