Neural network modeling of heat transfer on transient curved stretching surface with slip dynamics

This study investigates nanofluids for energy transfer across a curve stretching sheet. The integration of nanofluids markedly improves thermal management and lubrication efficiency across diverse engineering domains. This analysis focuses on the transport and heat exchange behavior of water based nanofluid interacting with an unsteady nonlinear curved plate in slip conditions. Gold and silver nanoparticles are dispersed separately in water, forming two distinct nanofluids. A curvilinear coordinate structure is employed to capture the geometric complexity of the modeled system for accurate representation. The governing equations are solved using physics‑informed neural network (PINN) and finite difference method (FDM), ensuring both data‑driven adaptability and discretization accuracy to simplify computation. Numerical simulations are carried out to evaluate velocity fields, and temperature distribution under controlled factors. The flow resistance is observed at elevated levels for the silver-water nanofluid, in comparison with the gold-water formulation demonstrating increased performance. In contrast, thermal exchange reveals that gold nanoparticles deliver enhanced outcomes in energy transfer efficiency across multiple cases. Among the parameters considered, the Biot number has the most pronounced effect on heat transfer, producing an approximately 58% variation in the heat transfer rate relative to other factors.