Ignition and Extinction of a Reaction in the Presence of Increasing External Temperature: General Results and Slow Temperature Rise

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, du/dt = v exp [u/(1+ɛ u)]-c(u-β t), dv/dt = - ɛ Av exp [u/(1+ɛ u)]. We examine the conditions under which the temperature u attains a local maximum and minimum, or alternatively is always increasing with time t.