Artificial neural network with incompressible smoothed particle hydrodynamics for exothermic chemical reaction on heat and mass transfer in a rectangular annulus

Abstract

This work aims to simulate the impacts of exothermic reaction and Soret–Dufour numbers on the double diffusion of Nano Enhanced Phase Change Materials (NEPCM) inside a porous annulus. The complex rectangular annulus contains two ellipses and two triangles on the walls’ vertical sides. The complex proposals of closed domains during heat/mass transfer of NEPCM can be used in energy savings, cooling electronic devices, and heat exchangers. The fractional-time derivative of the governing systems is solved numerically based on the ISPH method. The artificial neural network (ANN) is combined with the ISPH results to predict the average Nusselt number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}

$$\begin{document}$$\overline{Nu }$$\end{document}$$ and Sherwood number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Sh }$$\end{document}$$ . The main objective of establishing the ANN model in this investigation is to create a reliable predictive instrument capable of estimating the values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Nu }$$\end{document}$$ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Sh }$$\end{document}$$ . The results described the impacts of dimensionless Frank-Kamenetskii number ( Fk = 0–1), Darcy number ( Da = 10 ⁻²–10 ⁻⁵), Dufour number ( Du = 0–0.1), buoyancy ratio ( N = − 2 to 5), Rayleigh number ( Ra = 10 ³–10 ⁶), Lewis number ( Le = 1–20), Soret number ( Sr = 0–0.2) , fusion temperature ( θ _f  = 0.05–0.9) , and fractional order parameter ( α = 0.9–1) on thermosolutal convection of a suspension. The overall heat/mass transition as well as the velocity field are dramatically enhanced when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$Ra$$\end{document}$$ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$N$$\end{document}$$ were boosted. The fractional time derivative helps reach a steady state in less time instants. The phase change material (PCM) is always changed when temperature distribution changes and is controlled by a fusion temperature. The porous struggled with nanofluid flow at a lower Darcy number. Frank-Kamenetskii number is a promising factor in enhancing the temperature distributions in an annulus. As a result, this work may be applied in various engineering and industrial fields because it contains significant terms in improving heat/mass transmission as well as a phase change material. The ANN model introduced a precise agreement of the prediction values with the actual values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Nu }$$\end{document}$$ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Sh }$$\end{document}$$ . Then, the present ANN model can accurately estimate the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Nu }$$\end{document}$$ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\begin{document}$$\overline{Sh }$$\end{document}$$ values.