Theory of Flames Produced by Unimolecular Reactions. I. Accurate Numerical Solutions

The time dependent flame equations are presented in complete generality, including the effects of thermal diffusion, radiation, external forces, and pressure variations. The one-dimensional steady-state laminar flame supported by the unimolecular reaction A → B is studied carefully with special emphasis on the effects of heat transfer to the flame-holder. It is found that in agreement with Spalding's work on a somewhat different model there is a maximum amount of heat transfer which permits a steady state. For heat transfers less than this maximum there are two possible solutions of the flame velocity. The smaller of these flame velocities corresponds to an unstable mode. At exceedingly low pressures the flame velocity becomes comparable to the velocity of sound.