Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling

• Published in: Scientific reports Vol. 11; no. 1; p. 14509
• Main Authors: Shafiq, Anum, Çolak, Andaç Batur, Sindhu, Tabassum Naz, Al-Mdallal, Qasem M, Abdeljawad, T
• Format: Journal Article
• Language: English
• Published: England Nature Publishing Group 15.07.2021; Nature Publishing Group UK; Nature Portfolio
• Subjects: Absorption; Algorithms; Boundary conditions; Fluid flow; Heat; Neural networks
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-021-93790-9

In current investigation, a novel implementation of intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural networks (ANN) with the Levenberg-Marquard algorithm is provided to interpret heat generation/absorption and radiation phenomenon in unsteady electrically conducting Williamson liquid flow along porous stretching surface. Heat phenomenon is investigated by taking convective boundary condition along with both velocity and thermal slip phenomena. The original nonlinear coupled PDEs representing the fluidic model are transformed to an analogous nonlinear ODEs system via incorporating appropriate transformations. A data set for proposed MLP-ANN is generated for various scenarios of fluidic model by variation of involved pertinent parameters via Galerkin weighted residual method (GWRM). In order to predict the (MLP) values, a multi-layer perceptron (MLP) artificial neural network (ANN) has been developed. There are 10 neurons in hidden layer of feed forward (FF) back propagation (BP) network model. The predictive performance of ANN model has been analyzed by comparing the results obtained from the ANN model using Levenberg-Marquard algorithm as the training algorithm with the target values. When the obtained Mean Square Error (MSE), Coefficient of Determination (R) and error rate values have been analyzed, it has been concluded that the ANN model can predict SFC and NN values with high accuracy. According to the findings of current analysis, ANN approach is accurate, effective and conveniently applicable for simulating the slip flow of Williamson fluid towards the stretching plate with heat generation/absorption. The obtained results showed that ANNs are an ideal tool that can be used to predict Skin Friction Coefficients and Nusselt Number values.