Entropy optimized magneto-thermo-diffusive transport in a chemically reactive unsteady third grade nanofluid flow...

The purpose of this study is to investigates the complex magneto-thermo-diffusive transport and entropy generation characteristics in unsteady third-grade nanofluid flow over a stretching surface, driven by the need for accurate prediction of mixed convective heat-mass transfer mechanisms in advanced thermal systems. This work aims to quantify how magnetohydrodynamic behavior under the simultaneous influences of Cattaneo-Christov heat and mass diffusion, viscous dissipation, thermal radiation, nonuniform heat generation/absorption, Brownian motion, thermophoresis, and activation energy influences thermal performance within the Buongiorno nanofluid framework. The governing nonlinear partial differential equations are transformed into non-dimensional ordinary forms and solved numerically via a fourth-order Runge-Kutta method integrated with the shooting algorithm. To enhance predictive fidelity, the resulting datasets are trained through advanced ANN algorithms, and model accuracy is verified using regression metrics, error histograms, and mean square error analysis. The obtained graphical results evaluations reveal that intensified magnetic field intensity and unsteadiness significantly suppress fluid velocity, whereas thermal radiation, Eckert number, Brownian motion, and thermophoretic diffusion substantially enhance heat transport. Entropy generation increases significantly with higher Brinkman and radiation parameters. Quantitatively, increasing radiation parameter from 0.2 to 1.0 elevates the Nusselt number by 14.28%, while higher activation energy parameter from 0.5 to 2.0 suppresses the thermal transport rate by 12.63% and amplifying the mass transfer rate by 29.9%. The ANN framework achieves superior predictive accuracy and computational stability, enabling a robust platform for optimizing thermal systems and supporting advanced biomedical diagnostics such as early stage cancer detection and tumor classification.