Numerical calculations have been carried out for the mixed convection flow in a concentric curved annulus with constant heat flux boundary condition at inner wall. The flow is assumed to be fully developed so as to maintain a constant streamwise pressure and temperature gradient. Computations have been performed for flows of radius ratio 0.2 and 0.5 with the Dean number lying in the range 0<k<900, and Grashof numbers of 8000 and 80000. The second flow patterns and heat flux profiles are presented. The friction ratio and heat transfer properties for curved annular duct flows are explained in comparison with those for straight annular duct flows. It is found that the friction ratio and the Nusselt number ratio are proportional to $K^{1/2}$ for the wide range of the Dean number considered here.