Determination of Critical Ambient Temperatures for Thermal Ignition

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Abstract
The theory of thermal ignition, whether or not consumption and diffusion of reactant is taken into account, has usually been analysed using the traditional grouping of dimensionless parameters suggested by Frank-Kamenetskii (1955). This particular grouping has the effect of complicating the role of the most practically significant control variable, namely the ambient temperature. This paper investigates the single heat-balance equation (with temperature, rescaled to make it dimensionless without using the ambient temperature). Here reactant consumption has been neglected, and this means that the upper branches of steady solutions are of less physical interest. It transpires that the nature of the bifurcation diagram for this case, with the dimensionless ambient temperature as ‘eigenparameter’, can be explained, with precise results being possible for the multiplicity and stability of these steadystates. These results parallel with those obtained in the traditional variables. Computation of the bifurcation diagram in these variables gives immediate access to the critical ambient temperature rather than through an iterative process as required with the Frank-Kamenetskii formulation.

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