The present article presents a parametric study on the forced convection heat transfer from a heated rotating inner cylinder with the stationary outer cylinder in the presence of an axial flow. Both laminar and turbulent flows of air are considered. The following parameters were considered in the present research work: Reynolds number, the rotational speed of the inner cylinder, heat flux dissipated from the inner cylinder in addition to the annulus gap width. The results are presented to show the variation of the Nusselt number with the governing parameters for both laminar and fully turbulent flow. The results of the present study show that increasing either the Reynolds number, rotation speed, and/or the gap distance, leads to improve the cooling and enhancing the heat dissipation from the inner cylinder for both laminar and turbulent flows. The present numerical results show also that various heat flux values from the inner rotating cylinder have a negligible effect on the rate of the cooling process.