Transient characteristics are presented for the solidification process of Phase Change Material (PCM) in a triplex tube with circular fins and a triplex tube with longitudinal fins. The phase change time of PCM in a triplex tube with circular fins was compared with that of a triplex tube with longitudinal fins during the solidification process. The comparison was performed for the same tube dimensions and fin surface area. To make the comparison, new correlations of the solidification time for two types of fin configurations were developed using the method of asymptotes. We found that a triplex tube with longitudinal fins had a better performance during solidification in most practical applications. On the other hand, a triplex tube with circular fins performed much better when a small solidification time is required.