In this study, the thermal properties of a fully wetted and movable longitudinal fin made of linear functionally graded material (FGM) are investigated. The thermal behavior of the fin under radiative and convective conditions is analyzed for three different material scenarios: a homogeneous material (HM), FGM I with higher thermal conductivity near the base, and FGM II with increasing thermal conductivity towards the tip. The resulting energy equation, a secondorder nonlinear differential equation, is primarily solved using the Akbari-Ganji method (AGM) and a numerical approach, while the Adomian decomposition method (ADM) is employed as a secondary check for the specific case. The thermal properties of the fin are analyzed graphically for the thermal conductivity grading parameter (β), the Peclet number (Pe), and other relevant parameters. Results indicate that the temperature distribution along the fin is highest for FGM II, intermediate for FGM I, and lowest for HM.
Ramezani et al. (Thu,) studied this question.