The theory of self-heating leading to explosion in a closed system

2 THE THEORY OF SELF-HEATING LEADING TO EXPLOSION IN A CLOSED SYSTEM 

The theory of self-heating leading to explosion has been developed by the Russian workers, Semenov [13] and Frank-Kamenetskii [14], There is an excellent review of the early work and developments up to about 1966 by Gray and Lee [15]. 

Consider an exothermic reaction taking place at a rate r in a batch reactor. The reactants are assumed to be at a uniform temperature Tk-The rate of heat generation is 

In the simplest form of the theory, reactant consumption is ignored, i.e. [A] = [A]q. This is often a reasonable assumption, but allowance can be made for depletion of reactant by reaction before explosion if necessary [16-18], 

Heat will be lost from the system by conduction, convection and radiation. If the temperature difference between the reactants and their surroundings is not too great, the rate of heat loss, Ql, is given by 

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