A Unified Formulation for Diffusive and Nondiffusive Thermal Explosion Theory

A mathematical model is developed for the induction period of a parcel of slightly warm reactive gas mixture embedded in a cooler gaseous environment. High activation energy asymptotic methods are used to formulate the problem. The important parameters in the nondimensional equations are ratios of characteristic reaction, acoustic and conduction times in the thermally disturbed parcel of dimension V. The results of the formulation imply that a specified physicochemical system, with a known characteristic chemical time, will experience a traditional diffusively dominated thermal explosion if the dimension /’ is sufficiently small. In larger systems transport effects are negligible and the induction period process is described by reactive gasdynamic equations. The study provides a unified formulation for the induction period of all thermal reaction problems and specifies the relationship between classical thermal explosion theory for rigid materials and compressible gases and more contemporary efforts to study nondiffusive thermal reactions.