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 splitting of operator algorithm PISO is used for the pressure-velocity 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 – 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 (C̄D) for the pulsating flow is higher than that of the steady flow overall r/R. For the pulsating flow, C̄D increases about 5.37% overall r/R. The surface- and time-averaged Nusselt number increases with increasing r/R for both flow regimes.