A Study on Nonlinear Wet Fin Problem Using Homotopy Analysis Method

Abstract

Homotopy analysis method (HAM) is used to study a rectangular wet fin with variable thermal conductivity. Unlike most theoretical investigations which have been carried out by considering a constant thermal conductivity and a linear relationship between the specific humidity of air and temperature, in this work, thermo-geometric and psychrometric variations are assumed to be nonlinear. The above considerations make the fin problem highly nonlinear due to nonlinearities in the governing equation as well as in the boundary conditions. HAM is used to determine the closed-form solution (i.e., temperature field) and the efficiency of the fin. It is noticed that the fin efficiency is obtained as a function of thermo-geometric fin parameter. The effects of the wet surface and variable conductivity on the temperature field as well as on the fin efficiency are analyzed. The present results of HAM are found to be in very good agreement with the available results of relevant literature. It is shown that the thermo-geometric fin parameter has a significant role on the fin efficiency. The present study reveals that the simultaneous heat and mass transfer across the fin surface is thermally less efficient compared to the fin surface involving heat transfer only.