In the present paper,by performing a two-dimensional simulation,the heat transfer from a hot cylinder to a cold square enclosure has been studied parametrically and the consequent effect of changing in cylinder diameter has been investigated. The 2-D governing equations have been solved using the finite volume method and TDMA in an ADI procedure for different diameters of cylinder inside a square enclosure with a constant characteristic length for two different Rayleigh numbers of 104 and 105.Results showed that the patterns of streamlines, isotherms and the Nusselt number values depend strongly on the Rayleigh number and also ratio of cylinder diameter to characteristic length of enclosure (2R/H). In this case, the centers of vortices created around the cylinder appear in bottom half of enclosure in 2R/H=0.4 for Ra=104 and in 2R/H= 0.5 for Ra=105. Moreover, it is observed that increasing the Rayleigh number and 2R/H ratio, the heat transfer rate from the enclosure is also increased.For example,in 2R/H=0.5, by increasing the Rayleigh number from 104 to 105, the average Nusselt enhances about 30 percent of its initial value and in Ra=105, by changing the 2R/H ratio from 0.2 to 0.5, the average Nusselt climbs almost 35 percent of its initial value.