Hybrid analysis of deep learning and statistical approach in predicting heat transfer rate of radiative polar nanofluid flow with inertial drag

The synergy of nanotechnology and magnetic fields in hybrid-nanofluid (HNF) flow opens new pathways for addressing complex problems. These driving innovations across a wide range of fields in several areas of engineering as well as biomedical applications. The study aims to analyze an HNF flow through a stretching surface while micropolar rotation is present, which improves the heat transfer coefficient. The present investigation shows the behavior of the Gold and Copper in water-based HNF flow through a porous stretching surface with a second-order slip condition. Further, the heat transport phenomenon is enriched due to the inclusion of Joule and Darcy dissipation, thermal radiation, and heat generation in the present analysis. Moreover, the equations undergo similarity transformations to become ordinary differential equations. Shooting-based Runge–Kutta Felhberg method numerically solves the controlling partial differential equations. The qualitative behavior of each of the factors is presented through graphs and described briefly. Furthermore, a robust statistical analysis is presented for optimizing the heat transfer rate utilizing response surface methodology (RSM) embedding central composite design, which is validated through an analysis of variance test. Also a comparative analysis of the result is obtained employing an artificial neural network for the same response consisting of the proposed factors. Finally, the result of R2 (coefficient of determination) obtained by utilizing RSM shows a good accuracy level with 99.74%. The current study's contributing results include improved thermal profile and a lower momentum field due to a stronger magnetic field.