Thermal runaway in a system with a constant power source

A model appropriate to chemical self-heating for an exothermic gas-phase reaction zone with a constant power source provided at the center is analyzed. Criticality is shown to be a feature, with ignition and extinction accompanying changes in the power. As the size of the power source at the center of the reaction zone is reduced, however, there is a transition process to a continuous variation of the steady-state temperature with the power. The relevance of this model to technically important applications is discussed.