This work presents a numerical study of the fluid flow over a superelliptic cylinder body by applying a finite volume method with an adaptive mesh refinement technique. The influence of the Reynolds number (Re), incidence angle (theta) and shape index (n) on the detailed kinetics of the flow and the macroscopic properties (drag coefficient C-d and surface mean Nusselt number Nu) have been examined over wide ranges of conditions as: 0.3 <= Re <= 200, 0 degrees <= theta <= 45 degrees and 1/2 <= n <= 5. The critical Reynolds numbers, corresponding to the onset of flow separation and the onset of the laminar unsteady regime, have been identified. The results show that the characteristics of flow and heat transfer of the fluids are affected in an intricate manner by Re, theta and n. Based on the simulated results, new equations have been proposed to estimate the C-d and Nu. (C) 2019 Elsevier B.V. All rights reserved.