ANN-based analysis of MHD third-grade hybrid nanofluid flow over a thin needle with fuzzy volume fraction under nonlinear radiation and heat generation

This investigation examines the magnetohydrodynamic (MHD) flow and heat transfer characteristics of a third-grade hybrid nanofluid (HNF) containing $${\text{Al}}_{{2}} {\text{O}}_{{3}}$$ and $${\text{TiO}}_{2}$$ nanoparticles suspended in sodium alginate over a horizontally translating thin needle under the influence of viscous dissipation, nonlinear thermal radiation, and internal heat generation effects. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) via similarity transformations and solved numerically using the bvp4c finite-difference method. For uncertainty analysis and comparison through the triangular membership function, the volume fractions of nanosized materials have been taken as triangular fuzzy numbers (TFNs) [0, 10%, 20%]. The TFNs are controlled with the help of the $$\zeta {\text{ - cut}}$$ approach. Additionally, Artificial Neural Networks (ANNs), trained via Bayesian Regularization (BRS) and Levenberg–Marquardt (LMS) algorithms, are developed for predictive modelling of skin friction and heat flux coefficients. Parametric analysis reveals that the flow gradient decreases as the volume fraction and the magnetic factor increase. The thermal gradient of the liquid and HNF rises with larger values of the thermal ratio factor, volumetric fraction, and Eckert number. The HNF demonstrates superior thermal performance compared to conventional third-grade fluid. According to the fuzzy analysis, the HNF exhibits the highest thermal energy transmission compared to both nanofluids (NFs). The ANN models show excellent agreement with numerical solutions, exhibiting low mean squared errors (MSE) across training, testing, and validation datasets. This integrated fuzzy-neural framework provides a novel approach for uncertainty quantification in HNF applications, with direct relevance to biomedical devices, aerospace thermal management, and renewable energy systems.