Theory of Ignition Considered as a Thermal Reaction

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Abstract
The history of a family of exothermally reactive solids is studied theoretically with the help of analytical and numerical calculations. The different members of this family of nonisothermal solids are obtained, by changing scales and values of parameters, from the basic model which describes a zero‐order reaction of a semi‐infinite slab of material subjected at its surface to heat transfer from a gas. For low initial temperatures of the solid, the heat transfer rate determines the ignition time while for high initial temperatures, this heating parameter is less important than the initial temperature, which controls the adiabatic ignition time. For the model used, the ignition time is generally quite sensitive to the duration of the external heating. Within the solid, it is found that the inner boundary of the region in which the chemical heat production is negligible moves inward along a diffusional type of path x ∝ t½ but that the point of maximum temperature, which develops after interruption of the external heating, follows a much different path. An analytical, approximate method of estimating minimum ignition time was tested by making comparison with numerical integrations and is probably accurate to 25 percent in the ignition time. The computational side of the theory presented here may be regarded as essentially complete for practical purposes until greater accuracy and detail are required by more critical applications than are now in prospect. Meaningful utilization of the computations in practical applications will not however be possible until reliable measurements have been made of certain of the parameters for the solid—namely, activation energy, frequency factor and thermal conductivity—and for the external heating— namely, gas temperature and heat transfer coefficient. In the course of the computations, many mathematical questions arose which are fundamental to the investigation of this and more realistic models of ignition but which remain to be answered.

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