The analysis of fins using arc length to determine the minimum volume for a given heat transfer rate is demonstrated by a unified formulation for fully and partially wet surfaces of longitudinal and pin fins. The shape of the optimum profile, a circular arc, was identical for both fin geometries under the same surface conditions. The optimum shape for partially wet surfaces had two different circular arcs for dry and wet surfaces. Unlike the previous study, the base thickness of circular profiles was less than that of parabolic profiles, regardless of the surface conditions. The minimum fin volume for the circular profile was always less than the corresponding parabolic profile. The difference in volume between these profiles reached a maximum for fully wet surfaces, and was also dependent upon the psychrometric properties and heat rate constraint. The optimum wet circular arc resulted in a maximum 156% savings in fin material, compared with the parabolic arc for pin fins; this percentage was up to 135% for longitudinal fins. Nevertheless, the savings for longitudinal and pin fins were only 25.9% and 22.0%, respectively, for dry surfaces; these results differed from published values. (c) 2013 Elsevier Ltd. All rights reserved.