A new way of ascertaining whether or not a reacting mixture will explode uses just three timescales: that for chemical reaction to heat up the fluid containing the reactants and products, the timescale for heat conduction out of the reactor, and the timescale for natural convection in the fluid. This approach is developed for an n-th order chemical reaction, A → B occurring exothermically in a spherical, batch reactor. The three timescales are expressed in terms of the physical and chemical parameters of the system. Numerical simulations are performed for laminar natural convection occurring; also, a theoretical relation is developed for turbulent flow. These theoretical and numerical results agree well with previous experimental measurements for the decomposition of azomethane in the gas phase. The new theory developed here is compared with Frank-Kamenetskii's classical criterion for explosion. This new treatment has the advantage of separating the two effects inhibiting explosion, viz. heat removal by thermal conduction and by natural convection. Also, the approach is easily generalised to more complex reactions and flow systems.

No abstract

No abstract

During an exothermic reaction in a fluid, convection may ensue on a local scale and then develop to the scale of the entire vessel. In this work, we study the effects of both localised and global convection on thermal explosions occurring between parallel plates. Analytical relations are derived for the various transitions in regimes of convective and thermal behaviours. We show that these relations agree well with previous numerical work and with new simulations in the present investigation. We also determine analytically the time for onset of convection, as well as the temperature increase at that time, for stable and explosive systems. The effects of the Prandtl number of the fluid on the transitions between regimes are noted.