This paper presents a numerical simulation of the flow structure, flow topology, and heat transfer of an isothermal cylinder with variable corner radius ratio (r/R) = 0, 0.1, 0.25, 0.5, 0.75, and 1.0, for two different flow regimes. One is steady and the other is pulsating flow. Here, r is the corner radius and R is the cylinder half-width. The air stream flow has a low Reynolds number Re of 100 and Prandtl number Pr = 0.7. The dimensionless amplitude of the velocity oscillations (A * ) is 40% relative to the free-stream velocity, and the dimensionless frequency is 7. The governing equations were solved using the ANSYS-FLUENT 19.2 package. The Pressure implicit with the splitting of the operator algorithm PISO is used for the pressurevelocity coupling. The results from the models agree with those in the literature. The effect of r/R on the flow structure around the cylinder is investigated for steady and pulsating flow regimes. Increasing r/R leads to the appearance of two major flow patterns around the cylinder. Pattern A appears at r/R < 0.1, which has leading-corner separation and two secondary bubbles appear on the sides of the cylinder. Pattern B appears at r/R ˃ 0.1, which has trailing-corner separation. The time-mean drag coefficient ( D ) for the pulsating flow is higher than that of the steady flow overall r/R. For the pulsating flow, D increases by about 5.37% overall r/R. The surface-and time-averaged Nusselt number increases with increasing r/R for both flow regimes.