This paper reports the effect of the position of a cooled cylinder in a rectangular cavity on the cooling process of water around the cylinder. The governing equations are solved by a finite difference method, and the flow structure and temperature distributions are predicted. The initial water temperature, T-i, is varied at 4, 6, 8 and 12 degrees C, while the temperature of the cylinder surface is fixed at 0 degrees C. The obtained timewise variations of the temperature field and the velocity held as well as the mean Nusselt number over the cylinder surface are compared. The changes in the position of the cylinder and the initial water temperature largely affect fluid flows. Only an upward flow appears along the cylinder for T-i = 4 degrees C, while for T-i > 4 degrees C a downward flow is observed in early stages, and then the flow direction is changed to upward. Therefore, an averaged Nusselt number over the cylinder surface and averaged water temperature vary in a complicated manner with time for T-i > 4 degrees C. The cooling rate of water is largely affected by the change of the position of the cylinder.