Modeling of Soret and Dufour’s Convective Heat Transfer in Nanofluid Flow Through a Moving Needle with Artificial Neural Network

In this study, forced convective heat and mass transfer of a nanofluid using the Buongiorno model and moving radially through a thin needle has been analyzed using the Runge–Kutta fourth-order technique with shooting approach. In order to analyze the thermo-diffusion and diffusion-thermoeffects on the flow, Dufour and Soret effects have been investigated and the mass transport phenomenon has also been investigated by activation energy. Partial differential systems of the flow model have been obtained with the boundary-layer approach and modified by using the appropriate transformations to be connected to nonlinear ordinary differential systems. The Runge–Kutta technique is the most popular methodology for obtaining the numerical results to solve the differential equations. It can evaluate higher-order numerical solutions and provide answers that are as close to correct solution. Therefore, using the Runge–Kutta fourth-order strategy with a shooting strategy, a data set has been created for different flow scenarios of the interesting and comprehensive model for nanofluid (Boungiorno’s model), which incorporates Brownian motion and thermophoresis. Using this data set, an artificial neural network model has been developed to predict skin friction coefficient, Sherwood number and Nusselt number values. Seventy percentage of the data used in ANN models developed with different numbers of datasets have been used for training, 15%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$15\%$$\end{document} for validation and 15%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 15\%$$\end{document} for testing. The results show that ANN models can predict skin friction coefficient, Sherwood number and Nusselt number values with error rates of -0.33%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\,0.33\%$$\end{document}, 0.08%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.08\%$$\end{document} and 0.03%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.03\%$$\end{document}, respectively.