AI-Driven FEM Analysis of Marangoni Convection in Carreau Nanofluids

This study examines the influence of nonlinear thermal radiation on Carreau nanofluid flow over a wedge under Marangoni boundary conditions. The model incorporates thermophoresis and Brownian motion effects, with governing partial differential equations reduced to ordinary differential form via similarity transformations. The analysis focuses on velocity, temperature, and concentration distributions, alongside key transport parameters: Nusselt number (Nu_x), Sherwood number (Sh_x), and skin friction coefficient (Cf_x). To enhance predictive capability, a supervised artificial neural network (ANN) based on the Levenberg–Marquardt algorithm is implemented in MATLAB. Trained on simulation data, the ANN demonstrates high regression accuracy with a mean squared error (MSE) below 0.001. Results indicate that Nu_x increases by 12% as the magnetic parameter rises from 0.5 to 2, while Sh_x decreases by 9% as thermophoresis increases from 0.1 to 0.6. This hybrid FEM–ANN framework offers new insights into Marangoni-driven nanofluid dynamics and provides a robust surrogate modeling approach for optimizing complex thermal transport systems.