Analytical solution of moistened trapezoidal porous fins considering all nonlinear effects

The primary objective of this study is to conduct a detailed investigation of the performance of a porous trapezoidal fin subjected to coupled sensible and latent heat transfer at its surface. The comprehensive literature survey reveals that, despite studies on other fin shapes, no previous research has tackled a porous trapezoidal-fin configuration. Assuming linear temperature dependence of thermal conductivity, Darcy’s law is used to describe flow within the porous fin. Employing the differential transformation method, the efficiency of a moisture-absorbing fin has been computed. To model the condensation process, the humidity ratio is approximated as a cubic polynomial function of the porous fin surface temperature, with its relationship obtained through regression-based psychrometric correlations. A comparative investigation has been conducted into the effects of parameters such as relative humidity, trapezoidal expansion ratio, and thermal conductivity coefficient on temperature variation and efficiency of porous fins with specified porosity and permeability. The numerical scheme and resulting outputs were validated through detailed comparisons with available benchmark results. A strong agreement was observed between the DTM-based solutions, the high-precision finite difference method, and existing literature results. The analysis shows that along a dry fin, the maximum temperature difference between the base and tip is approximately 1.5 °C for an expansion ratio of − 0.5 and 2.5 °C for an expansion ratio of + 0.5. When the fin surface is wet, these values increase significantly to 4.76 °C and 7.76 °C, respectively. The results indicate that variations in specific design parameters of porous trapezoidal fins, across different expansion ratios, cause notable changes in fin efficiency. The efficiency of a trapezoidal porous fin is influenced by its geometric expansion ratio, with maximum efficiency occurring at negative expansion ratios. From a comparative perspective, wet porous fins are less efficient than dry fins.