A Parametric Study of Functionally Graded Variable Thickness Longitudinal Fin Under Fully Wet Condition

Thermal analysis and comparison of the functionally graded longitudinal fin, having a different profile with an insulated tip in fully wet condition, are reported in the present work. In many air-conditioning and refrigeration equipments, the performance of the cooling coil is affected due to vapor condensation on its surface. In this work, the thermal conductivity of the longitudinal fin is varied with exponential law. For analysis and comparison of a fin having different profiles, their weight is assumed to be constant. With the help of the psychometric chart, a nonlinear cubic polynomial relationship is established between specific humidity and corresponding fin surface temperature. Considering a volume element of fin under steady state, energy balance concept is used to derive nonlinear differential heat transfer equation. This differential equation is solved using bvp4c command in MATLAB^®. This technique is very useful to solve boundary value problems by collocation method. Further for a different combination of grading parameters, geometry parameters, and relative humidity, a differential equation is solved and results are shown in graphical form. The formulation is verified with standard results, and relative error obtained between these two results is negligible. These results give a better understanding of the thermal performance of functionally graded longitudinal wet fin, and generated data can be used for design purpose.