Steady-state laminar mixed convection of Newtonian fluids in a square cross-sectioned cylindrical annular enclosure with rotating inner wall and heated top cover has been numerically analysed based on axisymmetric incompressible flow simulations. Richardson number, Reynolds number and 𝑟𝑖/𝑅 effects on heat and momentum transport have been investigated for the range of Richardson number 0 ≤ 𝑅𝑖 ≤ 1, Reynolds number 500 ≤ 𝑅𝑒 ≤ 2000 and 0.25≤𝑟𝑖/𝑅≤8 at a representative value of Prandtl number (i.e. 𝑃𝑟=1.0). A scaling analysis has been also carried out in order to elucidate the possible influences of Reynolds, Richardson and Prandtl numbers and 𝑟𝑖/𝑅 on the mean Nusselt number. It has been found that the mean Nusselt number 𝑁𝑢̅̅̅̅ demonstrates a monotonically decreasing trend with increasing 𝑅𝑖 whereas 𝑁𝑢̅̅̅̅ increases with increasing 𝑟𝑖/𝑅 and 𝑅𝑒 which is consistent with scaling estimation. It is also observed that the flow pattern in the case of purely forced convection (i.e. 𝑅𝑖 = 0) is significantly different from those in mixed convection (i.e. 𝑅𝑖> 0). In the case of 𝑅𝑖 = 0 (i.e. purely forced convection), a one-cell flow structure with two small vortexes on the top corners is observed for 𝑟𝑖/𝑅≤1, whereas a second cell appears in the flow field for 𝑟𝑖/𝑅> 1 at 𝑅𝑒 = 1000. On the other hand, in the case of mixed convection (i.e. 𝑅𝑖> 0), two-cell and four-cell flow structures occur in the flow field depending on 𝑅𝑖 and 𝑟𝑖/𝑅 for the range of 𝑅𝑖, Re and 𝑟𝑖/𝑅 considered here at 𝑃𝑟=1.0. Based these observations, a flow regime diagram has been proposed here for mixed convection (i.e. 𝑅𝑖> 0) for the range of 𝑅𝑖, 𝑅𝑒 and 𝑟𝑖/𝑅 analysed in this study.