Analytic solution for heat transfer of wet fins on account of all nonlinearity effects

Like dry surface fins, development of the boundary layer over a wet fin causes the heat transfer coefficient to vary over the fin surface. The present study analytically determines the performance of different fins geometries by analyzing the temperature-dependent thermal conductivity of the fin material and the variable heat transfer coefficient under wet surface conditions. Rectangular, triangular, convex (parabolic), and exponential geometric longitudinal fins were analyzed by the differential transform method under dehumidifying surface conditions. The mass transfer process was calculated by adopting the humidity ratio as a polynomial function with fin surface temperature, which was determined from the psychrometric correlation using regression analysis. The effect of the wet surface, the variable conductivity, and the heat transfer coefficient of different profiles on the temperature and fin efficiencies were studied comparatively. A new expression based on the transformed method was formulated appropriately to determine the heat transfer rate as nonlinear terms associated with it. Optimum design analysis was also carried out, and from these results, fin performance and optimization parameters were identified for variations of the same design constants with different geometric fins.