Design of neural networks for second-order velocity slip of nanofluid flow in the presence of activation energy

Abstract

<abstract> <p>The research groups in engineering and technological fields are becoming increasingly interested in the investigations into and utilization of artificial intelligence techniques in order to offer enhanced productivity gains and amplified human capabilities in day-to-day activities, business strategies and societal development. In the present study, the hydromagnetic second-order velocity slip nanofluid flow of a viscous material with nonlinear mixed convection over a stretching and rotating disk is numerically investigated by employing the approach of Levenberg-Marquardt back-propagated artificial neural networks. Heat transport properties are examined from the perspectives of thermal radiation, Joule heating and dissipation. The activation energy of chemical processes is also taken into account. A system of ordinary differential equations (ODEs) is created from the partial differential equations (PDEs), indicating the velocity slip nanofluid flow. To resolve the ODEs and assess the reference dataset for the intelligent network, Lobatto IIIA is deployed. The reference dataset makes it easier to compute the approximate solution of the velocity slip nanofluid flow in the MATLAB programming environment. A comparison of the results is presented with a state-of-the-art Lobatto IIIA analysis method in terms of absolute error, regression studies, error histogram analysis, mu, gradients and mean square error, which validate the performance of the proposed neural networks. Further, the impacts of thermal, axial, radial and tangential velocities on the stretching parameter, magnetic variable, Eckert number, thermal Biot numbers and second-order slip parameters are also examined in this article. With an increase in the stretching parameter's values, the speed increases. In contrast, the temperature profile drops as the magnetic variable's value increases. The technique's worthiness and effectiveness are confirmed by the absolute error range of 10<sup>-7</sup> to 10<sup>-4</sup>. The proposed system is stable, convergent and precise according to the performance validation up to E<sup>-10</sup>. The outcomes demonstrate that artificial neural networks are capable of highly accurate predictions and optimizations.</p> </abstract>