Thermal performance of moving rectangular fins: comparative analysis of insulated and convective tip conditions via PINNs and hermite wavelet method

This study analyzes the thermal behavior of a fully wetted moving rectangular fin under combined effects of natural convection, thermal radiation, internal heat generation, and a uniform magnetic field. Fluid flow is modeled using Darcy’s law, and two tip conditions insulated (Case 1) and convective (Case 2) are investigated. The governing nonlinear ordinary differential equations are solved using Physics-Informed Neural Networks (PINNs) and the Hermite wavelet method. Results indicate that convective tips significantly improve heat dissipation compared to insulated tips. Increasing the convective heat transfer coefficient reduces the temperature distribution. As the internal heat generation parameter (Q) increases from 0 to 0.5, temperature rises by about 12.5% in Case 1 and 13.1% in Case 2. In contrast, increasing the Hartmann number (H) from 0 to 0.5 decreases temperature by approximately 12.7% and 11%, respectively. Fin efficiency (η) increases notably with higher internal heat generation, improving by 34–43% in Case 1 and 31–36% in Case 2, especially at higher generation parameters. However, efficiency declines with increasing power index (n), dropping by 4–14% (Case 1) and 6–20% (Case 2), with stronger effects at larger wet parameters. These findings support optimized fin design for enhanced thermal management.