Homotopy analysis method in thermal profiling of porous fin: A comparison of rectangular and triangular configurations

This research investigates the thermal behavior of a porous longitudinal fin under fully wet condition, focusing on the impacts of convection and radiation. Varying fin thickness along the length of the fin prompts a comparative analysis of fin profiles such as rectangular and triangular shapes. Recent studies on porous fin thermal analysis using traditional methods often struggle with solution convergence in complex nonlinear equations. This study overcomes these issues by applying the Homotopy Analysis Method (HAM). HAM has emerged as a powerful alternative due to its flexibility in controlling convergence through the auxiliary parameter h, offering a significant improvement over conventional technique. Graphical representations of the fin thermal profile evaluate the effects of convective, radiative, and wet porous parameters. Comparative assessments of rectangular and triangular fin profiles reveal that the rectangular fin exhibits the highest temperature distribution, whereas the triangular fin shows the lowest. Furthermore, the efficiency of the fin (eta) indicates that the triangular fin is less efficient compared to rectangular ones. The results obtained from HAM have been validated with established studies and show good alignment. The use of HAM offers precise solutions for heat transfer, enhancing fin designs to maximize heat dissipation and advance thermal management.