It is shown that a variable grouping containing a logarithmic time-dependent factor is required for the development of a coordinate-perturbation expansion which realistically describes the spatially varying thermal-runaway process. The resulting solution is in good agreement with careful numerical computations. It describes a self-focusing temperature growth, the form and behavior of which are remarkably independent of both the conditions leading to thermal runaway and the topology of the thermal-runaway region. The detailed solution also reveals an underlying structure in the temperature development, in which a strongly supercritical thermal runaway is found to be very much like a less strongly supercritical, but more highly-developed, thermal runaway. Some numerically computed results are presented, detailing the Ignition Kernel formed as a result of supercritical thermal runaway in a fixed-temperature symmetric container.
|Number of pages
|Quarterly Journal of Mechanics and Applied Mathematics
|Published - Aug 1985