A method based on the variational principle is used to determine a minimum shape of wet fins for effective transfer of heat in fins. In many air-cooling applications, fin surface becomes wet as the surface is lower than the dewpoint temperature of the surrounding air. On the wet surface, both the sensible and latent heat transfer take place due to an existence of respective driving forces. The fin temperature is also dependent upon the latent heat released on its surface from the condensed moisture. The humidity ratio of air adjacent to the fin surface for the latent heat transfer is a psychrometric function with temperature. Due to this, the analysis of wet fins is always difficult as the governing fin equation is complex in nature. A simple model based on a linearity function between humidity ratio and temperature has been an alternative approximate model. The present analysis is attempted to estimate an envelope shape of wet fins by minimising fin volume for a constraint heat transfer rate for an actual variation of humidity ratio with temperature. The effect of psychrometric properties of air on the minimum shape of wet fins has been studied in the present work. The fin performance for the least envelope shape of wet fins is proposed with the variation of thermo-psychrometric parameters. A comparison of results for the variation of linear and nonlinear humidity ratio with temperature on the analysis of the minimum envelope shape has been systematically investigated. This study is also highlighted errors in connection with the linear model to determine the least fin shape for efficient heat transfer. This analysis may be extremely important in those augmentation heat transfer apparatuses where a gain in weight creates always an excessive overburden. Due to this, the selection of the function of humidity ratio as a fin surface temperature may be extremely important for calculating minimum weight of a fin for the same heat transfer duty. (C) 2015 Elsevier Ltd. All rights reserved.