The influence of reactant consumption on the critical conditions for thermal ignition

Abstract

The differential equations giving the temperature and reactant concentration as functions of time in a simple exothermic reaction cannot be solved explicitly. We can, however, identify critical values of the physical parameters governing the reaction that indicate the threshold of a large temperature rise. When the temperature rise is sufficiently large the material may ignite or explode. When reactant consumption is neglected there is a well known definition of the critical value of the parameter controlling heat loss. This critical value is defined by the discontinuity in the lowest available steady state temperature. When reactant consumption is included in the equations different definitions of the critical relationships between the parameters become possible. In this thesis three different critical criteria and their connections with the steady state criterion are examined. The first examines points of inflexion in the graph of reactant concentration versus temperature. Secondly points of inflexion in the temperature-time curve are studied. The third criterion is concerned with points of inflexion in the graph of the maximum temperature against the parameter controlling heat loss.