Travelling Combustion Waves in a Porous Medium. Part II—Stability

Abstract

The linear stability properties of the travelling combustion waves found in Part I are examined. The key parameters which determine the stability properties of the waves are found to be the (scaled) driving velocity and the solid specific heat. In particular, the destabilising influence of increasing either of these two parameters is demonstrated. The results indicate that travelling combustion waves whose reaction is turned off because the solid temperature becomes too low are always unstable, whereas travelling waves whose reaction is turned off due to depletion of solid reactant can be stable. Global techniques are employed to prove that, for large enough values of the scaled solid specific heat, combustion cannot be sustained in any form, and all initial conditions lead to extinction.