A solution is developed for a nondiffusive thermal explosion in a reactive gas confined to a bounded container Ω with a characteristic length l'. The process evolves with a spatially homogeneous time-dependent pressure field because the characteristic reaction time t'R is large compared to the acoustic time l'/C'0 where C'0 is the initial sound speed. Exact solutions, in terms of a numerical quadrature are obtained for the induction period temperature, density and pressure perturbations as well as for the induced velocity field. Traditional single-point thermal runaway singularities are found for temperature and density when the initial temperature disturbance has a single point maximum. In contrast, if the initial maximum is spread over a finite subdomain of Ω, then the thermal runaway occurs everywhere. Asymptotic expansions of the exact solutions are used to provide a complete understanding of the singularities. The perturbation temperature and density singularities have the familiar logarithmic form — ln (t'e — t') as the explosion time le is approached. The spatially homogeneous pressure is bounded for single-point explosions but is logarithmically singular when global runaway occurs. Compression heating associated with the unbounded perturbation pressure rise is the physical source of the global thermal runaway.
All Science Journal Classification (ASJC) codes
- Chemical Engineering(all)
- Energy Engineering and Power Technology
- Fuel Technology
- Physics and Astronomy(all)