Linear stability analysis of a fully developed mixed convection flow of air in an annular horizontal duct is numerically investigated for the radius ratio R=1.2, a Péclet and a Rayleigh number less than 200 and 6000, respectively. An iterative method is developed to enable the convergence of the dimensionless parameters to their marginal values at the transition. New mixed convection flows are highlighted that are highly correlated with those obtained in natural convection problems under the assumption of two dimensionality. The synthesis of our results on the transitions permits us to build the map of stability for the steady and established mixed convection flows and clearly shows the occurrence of multiplicity of solutions for some couples of Rayleigh and Péclet numbers.