Mixed heat convection inside annular spaces occurs in many engineering technology applications. This study aims to determine the effect of the sinusoidal surface parameters of an outer cylinder, which are represented by variations in the undulation number and amplitude of the wavy surface, on flow structure and thermal fields for different values of the Reynolds number (Re; from 0 to 600) and Rayleigh number (Ra; from 10³ to 10⁶). A horizontal annular space bounded by two concentric cylinders contained air with a Prandtl number that equaled 0.7. The sinusoidal surface of the fixed circular outer cylinder was maintained at a constant cold temperature (T^c), whereas the surface of the circular inner cylinder was set at a constant hot temperature (T^h) and rotated in counter-clockwise direction at constant angular velocity. Calculations were performed under steady-state conditions. A computational procedure based on the finite volume technique was implemented using the software ANSYS Fluent (version 16.1). Results indicate that the heat transfer from the inner cylinder increased with a rise in the surface amplitudes and undulation numbers with a fixed Re. The average Nusselt number increased with an increase in Ra and reduced when the undulation number increased from one to two. In summary, the heat transfer of the cylinder with the sinusoidal outer surface is better by 7.3% than that of the conventional cylinder.