Implications Concerning General Ignition Processes from the Analysis of Homogeneous, Thermal Explosions

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Abstract
Two recent approximate analyses of ignition in homogeneous, adiabatic systems with fuel consumption specifically included are discussed and compared with the derived exact solution of the problem. The singularity present in both approximate solutions is shown to be the same as that found in the exact solution, and is characteristic of the time required to establish nearly complete chemical reaction. A similar situation is shown to exist for ignition in non-adiabatic, homogeneous systems—the classical Semenov problem—causing the proposal and discussion of a thesis that a correct description of any ignition event must always include the transient behavior as quasi-steady combustion is approached. Intuitively satisfying, the theoretical and experimental implications of this thesis are discussed.