Bounds for the speed of combustion flames: The effect of mass diffusion

In this paper we analyze the speed of gas flames in a combustion premixed model that consists of two species (fuel and non-fuel). The main novelty with respect to recently published papers is that here we take into account the effect of the diffusion velocities in the energy equation. This means that the speed of the traveling wave obtained by numerically solving the combustion model (i.e., a system of two coupled one-dimensional partial differential equations) is a function of the Lewis number. New bounds for the propagation speed of the combustion flame are derived here by performing a mathematical procedure that reduces the full combustion model into a single reaction-diffusion equation of a single variable. The new expressions derived here predict bounds that agree well with the flame speeds obtained from simulations of the full combustion model. We finally analyze the case that includes the effect of radiative losses. Now, pulses rather than fronts propagate, whose speeds are also correctly predicted by the new expressions derived here.