Numerical computations are conducted for turbulent mixed convection of air in a horizontal concentric annulus between a cooled outer cylinder and a heated, rotating, inner cylinder. Time-averaged equations of turbulent fluid motion and heat transfer are solved using the Launder-Shanna low-Re eddy-viscosity two-equation model coupled with the Yap correction and the Kato-Launder modification. Numerical results are obtained for the Rayleigh number, Ra, ranging from 10(7) to 10(10), the Reynolds number, Re, from 0 to 10(5) and the radius ratio, RR, from 2.6 to 10 for a constant Prandtl number of 0.7. The effects of these parameters on the flow and heat transfer characteristics are discussed in detail. Predictions are also compared with published studies of other investigators. A good agreement with the results from the published experimental data and other computations is found. A comprehensively comparative analysis shows that the Kato-Launder modification is an essential ingredient, which can effectively reduce the unrealistic turbulence energy at impingement regions. Therefore, the modification can return more satisfactory prediction for the considered cases, Results show that the mean Nusselt number. Nu, increases with an increase in Ra. but decreases with an increase in Re or RR. When Ra > 10(9), a crucial phenomena, the peak value of local Nusselt number occurring in the vicinity of thermal plume region, is first discovered and discussed. For the centrifugal configurations, it is found that rotation has caused significant reduction in the mean heat transfer and it generally increases the strength of the secondary flows.