The speed law for highly radiative flames in a gaseous mixture with large activation energy

We study a thermodiffusive combustion model for premixed flames propagating in reactive gaseous mixtures which contain inert dust. As observed by Joulin, radiative transfer of heat may significantly enhance the flame temperature and its propagation speed. The Joulin effect is at its most pronounced in the parameter regime where the medium is very transparent while radiative flux dominates convection. In this asymptotic regime, where in the limit the flame temperature achieves its upper bound, we determine the law that describes the relation between the propagation speed of the flame and the control parameters. Finally, we present strong numerical evidence for the validity of the asymptotic analysis. © 2005 Society for Industrial and Applied Mathematics.