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This study presents the design of an artificial neural network (ANN) to evaluate and predict the viscosity behavior of Al 2 O 3 /10W40 nanofluid at different temperatures, shear rates, and volume fraction of nanoparticles. Nanofluid viscosity (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\mu }_{nf}$$\end{document}    μ   nf) is evaluated at volume fractions (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\varphi$$\end{document}   φ=0.25% to 2%) and temperature range of 5 to 55 °C. For modeling by ANN, a multilayer perceptron (MLP) network with the Levenberg–Marquardt algorithm (LMA) is used. The main purpose of this study is to model and predict the    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\mu }_{nf}$$\end{document}    μ   nfof Al 2 O 3 /10W40 nanofluid through ANN, select the best ANN structure from the set of predicted structures and manage time and cost by predicting the ANN with the least error. To model the ANN,    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\varphi$$\end{document}   φ, temperature, and shear rate are considered as input variables, and    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\mu }_{nf}$$\end{document}    μ   nfis considered as output variable. From 400 different ANN structures for Al 2 O 3 /10W40 nanofluid, the optimal structure consisting of two hidden layers with the optimal structure of 6 neurons in the first layer and 4 neurons in the second layer is selected. Finally, the R regression coefficient and the MSE are 0.995838 and 4.14469E−08 for the optimal structure, respectively. According to all data, the margin of deviation (MOD) is in the range of less than 2% < MOD < + 2%. Comparison of the three data sets, namely laboratory data, correlation output, and ANN output, shows that the ANN estimates laboratory data more accurately.

scientific reports

An optimal feed-forward artificial neural network model and a new empirical correlation for prediction of the relative viscosity of Al2O3-engine oil nanofluid