Using the Method of Lines to determine critical conditions for thermal ignition

Abstract

There are many situations in which the critical conditions for thermal ignition cannot be determined analytically. These include cases where the chemistry needs to be properly considered, where the geometry is not just the simplest and where other processes must be included. In these circumstances, numerical (or at least semi-analytical) means are used to determine critical conditions for thermal ignition. Once confronted with a numerical approach to solving a problem, it is necessary to be a little circumspect about the results and seek independent means to corroborate them. For this reason, the present paper reports on the Method of Lines to investigate a recent reactive hotspot problem which has previously been shown to display unexpected behaviour and demonstrates the use of sensitivity analysis to rigourously determine criticality in such a dissipative system.