An Artificial Neural Network Model for Predicting the Nanofluids’ Optimal Velocity and Skin Friction in a Convergent Channel

This work purveys an artificial neural network (ANN) model for the steady two-dimensional viscous incompressible radial flow of $Au - Water$ (a mixture composed of water as base fluid and nanoparticles of Gold (Au)) and $Ag - Water$ (a mixture composed by water as base fluid and nanoparticles of Silver (Ag)) nanofluids between plane walls which converge in the presence of the MHD effect. The governing partial differential equations of the present physics and their appropriate boundary conditions are initially cast into dimensionless forms to reduce into the ordinary differential equation. The resulting equation thus formed is worked out by adopting the superior numerical simulation, namely, successive linearization method (SLM) to get the accurate solution, and used to generate the data set of size $1502\times 4$ . A great agreement of the numerical simulation is achieved with the existing results. Two ANN models (Model 1 and Model 2) with two hidden layers were proposed. In Model 1 first hidden layer consists of 5 neurons and the second hidden layer consists of 3 neurons, whereas Model 2 consists of 10 neurons in the first hidden layer and 5 neurons in the second hidden layer. The results showed that the proposed ANN model can predict the velocity with high accuracy, and helps to predict the velocity/skin friction for any combination of the values of the proposed fluid’s physical parameters. An R-squared value reaching 0.99 can be obtained using an artificial neural network with the Stochastic Gradient Descent (SGD) optimizer, with a momentum of 0.8, and a learning rate of 0.02.