The aim of this study is to find optimum values of design parameters of annular flow with outer grooved cylinder and rotating inner cylinder in the presence of axial flow by using Response surface Method (RSM). This configuration is popular in cooling of electric generators and rotating machineries. Groove aspect ratio (0 < b/c < 1.5), number of grooves (0 < N-g < 20), Taylor number (0 < Ta < 2.24 x 10(6)) and axial Reynolds number (4437 < Re-a < 14,297) are selected as design parameters while the Nusselt number (Nu) and pressure drop (Delta P) are selected as responses. Firstly, the effect of b/c and N-g on pressure drop, friction factor and heat transfer enhancement inside grooved channel is investigated. In the next step, RSM has been employed to construct correlations required in optimization. The accuracy of correlations is proved experimentally. Finally optimization based on heat transfer to pressure drop ratio has been employed to determine optimum values of design parameters to maximize heat transfer and minimize pressure drop of Couette-Taylor-Poiseuille flow inside the grooved channels. Heat transfer to pressure drop ratio is maximum at b/c = 1.42 and N-g = 19. This optimization gives a lot of freedom to designers to choose the optimal geometric parameters of electric motors. (C) 2017 Elsevier Ltd. All rights reserved.