An approximate model for the ignition of reactive materials by a hot spot with reactant depletion

In this paper, we present a mathematical model to describe the ignition of a reactive material subject to a known heat input at a given radius. By current methods, the full solution is not readily solvable analytically. The main purpose of this work is to pose the right questions for this complex phenomenon, which is yet some way from total solution. An approximate solution to the model equations is presented, and a possible physical explanation for the finding that ignition behaviour is suppressed for small radius hot spots.