Transient natural convection in water around a cooled horizontal cylinder placed in a rectangular enclosure has been studied. The governing equations were solved by a finite difference method, and the flow structure and temperature distributions have been predicted. The purpose of the present study is to examine the effects of the position of the cylinder and the initial temperature of water on the cooling process of water. The initial water temperature was varied at 4,6,8 and 12℃, and timewise variations of the temperature field and the velocity field as well as the mean Nusselt number on the cylinder surface were compared. The changes in the position of the cylinder and the initial water temperature largely affect fluid flows due to the density inversion of water. Complicated flow patterns are observed for initial water temperatures larger than 4℃. Therefore, the cooling rate of water is largely changed with the change in the position of the cylinder for initial water temperatures larger than 4℃.