Mathematical analysis for the efficiency of a semi-spherical fin with simultaneous heat and mass transfer

In this paper an analytical solution for the efficiency of a semi-spherical fin when subjected to simultaneous heat and mass transfer mechanisms is studied. For the mathematical analysis of a wet fin equation, a relationship between humidity ratio and temperature of the saturation air is needed. The driving forces for the heat and mass transfer are the temperature and humidity ratio differences, respectively. Analytical solutions are obtained for the temperature distribution over the fin surface when the fin is fully wet. It is observed that in humid conditions the fin has high efficiency to be used in industry. The variation effects of these parameters have been considered. Finally linear relation has been proposed for humidity and temperature on the fin surface.