Experiments were performed to study freezing on a finned vertical tube when either conduction in the solid or natural convection in the liquid controls the heat transfer. Conduction is the controlling mode when the liquid is at its fusion temperature, whereas natural convection controls when the liquid temperature is above the fusion value. The phase change medium was a paraffin, 99% pure n-eicosane, with a fusion temperature of 36.4°C. Auxiliary experiments were also performed with an unfinned tube to obtain comparison data. For conduction control, the enhancement of freezing due to finning is less than the area ratio of the finned and unfinned tubes, whereas for natural-convection control the enhancement is very nearly equal to the area ratio. The liquid-solid interface is a thicket of whisker-like crystals when conduction controls but is straight (i.e. vertical). On the other hand, the interface is smooth but tapered when natural convection controls-yielding bottom-heavy frozen specimens. When conduction controls, freezing continues more or less indefinitely, whereas natural convection severely retards the freezing and ultimately terminates it altogether.