Natural and mixed convection heat transfer from a horizontal cylinder placed in a vented square enclosure has been investigated using numerical method with ANSYS Fluent 16.1 software for laminar and turbulent flow. Navier- Stokes equations and energy equation with standard k-? transport equation turbulence model have been used to simulate both flow and thermal behaviors. The operating conditions covered a range of the Rayleigh number from 103 to 106 and the Richardson number range between 0.1 and 100 at variable sizes of the lower open vent with constant upper opening size. The Nusselt numbers, velocity lines and isotherms are presented to display the flow and thermal behaviors. The results displayed that the average Nusselt number is affected by Rayleigh number, Richardson number, enclosure width and lower opening size. The Nusselt number is enhanced by controlling the lower opening size. The maximum enhancement range for Nusselt number is between 20-85% depending on the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size. The velocity lines and isotherms are directly affected by the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size.