We study in this paper the combined effect of heat loss and reversibility on the propagation of planar flames formed within the counterflow configuration. The problem has been formulated first using the thermodiffusive model with constant density and then solved numerically using finite elements. The impact of four main parameters, namely the reversibility r, the heat loss κ, the strain rate ε, and the activation energy β, on the propagation of planar flames has been discussed in details. The study has shown that planar flames under reversible conditions behave qualitatively similar to those observed for irreversible reactions, which agree with the asymptotic findings. In the presence of heat loss, the problem exhibits multiplicity of solutions whose number and stability were found to vary according to the strain rate ε. In addition, the study has predicted the existence of a certain value of the reversibility parameter r beyond which the impact of reversibility becomes negligible. Finally, we have examined the stability of the solutions and determined the domain of stability of solutions and their multiplicity for this problem.

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