A single-variable model for the temperature in an ignition process is known to exhibit blow-up (or thermal runaway) if the usual Frank-Kamenetskii approximation is made. This occurs both for ODE and for PDE models (i.e. with or without diffusion). When a second dependent variable, representing the concentration of a depleted species, is included in an ODE model, although the temperature can get large, it is now bounded (by the initial concentration). Work, in conjunction with J.Bebernes and with M.Herrero and J.Velazquez, discusses the consequences, for thermal runaway, of including concentration in a reaction diffusion model and the role of boundary conditions, Lewis number and limiting cases.
Connect With Us: