Analytical study of stretched ultra-lean premixed flames within porous inert media

It has been shown both theoretically and experimentally that combustion within porous inert media can extend the flammability limits of reactant mixtures for unstretched stationary premixed flames. However little attention has been given to flames within porous media submitted to stretch conditions. This work presents a closed form approximate analytical solution for the problem of ultra-lean premixed flames within porous inert media subjected to small stretch rates in an impinging flow configuration against a constant temperature wall. The solution is obtained using the method of matched asymptotic expansions taking advantage of the large difference between the solid- and gas-phase thermal conductivities. The model allows for thermal nonequilibrium between the phases and is able to predict the flame temperature, velocity and position as function of the stretch rate. The results show that within porous media low stretch rates may increase the flame temperature, further extending the lean flammability limit of the reactant mixture when compared to planar flames. The model is restricted to low porosities, low stretch rates, low heat losses and intense interphase heat transfer.