Steady states, oscillations and heat explosion in a combustion problem with convection

The effect of convection on the heat generated by an exothermic reaction is considered within a square reactor bounded by constant temperature walls. The fluid flow and heat transfer equations are solved numerically for a range of values of the Rayleigh Ra and Frank-Kamenetskii K numbers. From these solutions, boundaries between bounded solutions and thermal runaway are determined, with the range of K for bounded solutions increasing as Ra is increased. The system is capable of sustaining both steady and oscillatory behaviour, including simple periodic as well as both chaotic and period-three responses. A parametric region where there is hysteresis is found with either oscillations or steady states seen at the same parameter values, dependent on the initial configuration of the system.