Ignition and extinction of a reaction in the presence of increasing external temperature: general results and slow temperature rise

Abstract

We consider a homogeneous model for a first order, exothermic chemical reaction subjected to a linearly increasing external temperature. With u and v representing dimensionless internal temperature and concentration respectively, d u /d t ═ v exp [ u /( 1 + ∊ u )] – c ( u – βt ), d v /d t ═ – ∊ A v exp [ u /(1 + ∊ u )]. We examine the conditions under which the temperature u attains a local maximum and minimum, or alternatively is always increasing with time t .