Neural network analysis of ternary hybrid nanofluid flow with Darcy-Forchheimer effects

The study develops an advanced supervised learning algorithm integrating an artificial recurrent neural network (ARNN) with the Levenberg-Marquardt method (ARNN-LMM) to model the two-dimensional nonlinear convective flow of a ternary hybrid nanofluid over a nonlinear stretching surface (2D-NCFTNSS). The research addresses a critical gap in predictive modeling by introducing a ternary hybrid nanofluid (THNF) system, incorporating Brownian motion, thermophoresis, nonlinear thermal radiation, and Darcy-Forchheimer effects into the governing equations, which are transformed into a dimensionless form for numerical analysis. The proposed ARNN-LMM framework provides an intelligent computing approach for approximating numerical solutions with high accuracy. The study's novelty lies in the first-time application of ARNN-LMM to solving complex nonlinear transport phenomena and analyzing the impact of physical parameters on flow, thermal, and concentration profiles. Results reveal that velocity decreases with increasing nanoparticle concentration, porosity, and inertia factors, while thermal characteristics improve with higher radiation, Brownian motion, thermophoresis, and heat generation. The percentage increase in the Nusselt number is demonstrated through a statistical chart to support the study. The model's accuracy is validated using regression (RG) index measurements, error histograms (EH), auto-correlation (AC) analysis, and convergence curves, achieving a minimal mean square error (MSE) ranging between E−10 and E−3. Future prospects include extending the model to three-dimensional geometries, experimental validation, and real-time applications in thermal energy systems, biomedical cooling, and aerospace heat management. The study highlights the potential of ARNN-LMM for solving nonlinear fluid dynamics problems with superior precision and computational efficiency.