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.

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1 Sal'nikov's chemical reaction is very simple; it consists of two consecutive first-order steps, producing a product B from a precursor P via an active intermediate A, in P → A → B. The first step is assumed to be thermoneutral, with zero activation energy, whilst the second step is exothermic and has a positive activation energy. These properties make this mechanism one of the simplest to display thermokinetic oscillations, as seen in cool flames. We consider a pure gas, P, undergoing Sal'nikov's reaction in a closed spherical vessel, whose walls are held at a constant temperature. Natural convection becomes significant once the temperature is high enough for the Rayleigh

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