Optimal Design of Constructal T-Shaped Fin Under Partially Wet Condition for Enhanced Thermal Performance: An Analytical Approach

Abstract

In refrigeration and air conditioning systems, the fin surface may become dry, fully wet or partially wet depending upon the psychometric, thermo-physical and geometric parameters. The current work is intended to determine the length of the dry portion, temperature distribution, performance and optimum design parameters of a T-shaped fin under partially wet condition. Temperature dependent thermal conductivity of the fin material is taken and the humidity ratio of saturated air is considered to vary linearly with the corresponding fin surface temperature. Considering these the governing equation of T-shaped fin becomes nonlinear and it has been solved analytically by using Homotopy Perturbation Method. The point of separation between the dry and wet portions of a T-shaped fin may be located either in the stem or flange part and hence, two cases having different governing equations and boundary conditions are analyzed in the current study. For the optimization study, Lagrange multiplier technique is employed and the results are obtained by maximizing the heat transfer rate for a constant fin volume. Further, a comparative study is presented between insulated and convective fin tip conditions.