<p>This study investigates the thermal performance of inclined porous moving fins with trapezoidal, dovetail, and rectangular profiles under combined convective–radiative heat transfer conditions in a fully saturated porous medium. The fins are mounted on an inclined surface, and fluid–solid interactions are modeled using Darcy’s law. The analysis incorporates temperature-dependent convective and radiative heat transfer coefficients. The governing equations are nondimensionalized and solved using a combination of the Fibonacci wavelet method (FWM) and Physics-Informed Neural Networks (PINNs). The study meticulously examines the impact of several critical parameters, including tip tapering, inclination angle, porosity, internal heat generation, magnetic field influence, and the power-law index, on the thermal distribution and fin performance. Findings indicate that the dovetail fin profile achieves the highest thermal distribution, followed by the rectangular and trapezoidal profiles, especially under conditions of low internal heat generation. Furthermore, an increase in the power-law index results in a reduction of fin efficiency, and with the dovetail profile consistently exhibiting superior efficiency compared to the others. The findings offer valuable guidance for the thermal design of extended surfaces in applications such as heat exchangers, electronic cooling systems, and energy conversion devices.</p>