Machine-learning prediction of Williamson nanofluid flow over a nonlinear stretching sheet with velocity and concentration slip and melting effects using nonlinear activation function

This study investigates the heat-transfer and flow behavior of an MHD Williamson nanofluid over a nonlinear stretching sheet within a porous medium, considering velocity and concentration slip, melting effects, internal heat generation and thermal radiation. The parameter analysis shows that magnetic forces suppress velocity and increase temperature, radiation enhances both fields, thermophoresis strengthens velocity and concentration, while Brownian motion raises temperature but lowers concentration. Higher Schmidt and chemical-reaction parameters reduce both velocity and concentration and mixed-convection parameters increase velocity but decrease temperature. Skin friction rises with the Williamson, radiation and thermophoresis parameters; the Nusselt number increases with radiation but decreases with Brownian motion, Schmidt number and magnetic effects, whereas the Sherwood number grows with Brownian motion, Schmidt number and chemical reaction. A two-layer feed-forward neural network was implemented for this study and the network was trained using the Levenberg-Marquardt backpropagation algorithm. The artificial neural network employs a nonlinear activation function (hyperbolic tangent) in the hidden layer and a linear activation in the output layer to effectively learn the nonlinear relationships between the governing input parameters and the resulting velocity, temperature and concentration profiles of the Williamson nanofluid system. A key contribution is the application of an artificial neural network (ANN) to predict velocity, temperature and concentration profiles. The ANN achieves high accuracy with MSE values of about 10−9 to 10−11, gradient values near 10−8 and Mu between 10−9 and 10−8, confirming stable training and precise prediction. The findings offer valuable insights for systems involving nanofluid-based heat and mass transfer, including cooling technologies, heat exchangers and polymer-processing operations.