A Galerkin spectral method has been applied to solve numerically the problem of fully developed laminar mixed convection in horizontal concentric annuli with axially uniform heat flow per unit length, uniform temperature along the periphery of the heated wall, thermal insulation on the remaining surface. Results have been obtained for PeRa values up to 107, for Pr ¼ 0.7, 5 and ∞, for inner to outer diameter ratio h ¼ 0.2 in case of inner wall heated and for h ¼ 0.2, 0.4 and 0.6 in case of outer wall heated. Compu- tations allow understanding the onset of secondary flows and their influence on both fluid dynamics and heat transfer. In particular, the distortion of the axial shear stress effects the reduction of the mass flow rate at a given axial pressure gradient. On the other hand, boundary layer thinning determines an in- crease in the Nusselt number up to a factor 2.5 on average in the investigated range as summarized by suitable correlations. Eventually, results have been compared with other numerical computations and experimental data only available for restricted ranges of the governing parameters.