Designing Hyperbolic Tangent Sigmoid Function for Solving the Williamson Nanofluid Model

Abstract

This study shows the design of the novel hyperbolic tangent sigmoid function for the numerical treatment of the Williamson nanofluid model (WNM), which is categorized as velocity, concentration, and temperature. A process of a deep neural network using fifteen and thirty neurons is presented to solve the model. The hyperbolic tangent sigmoid transfer function is used in the process of both hidden layers. The optimization is performed through the Bayesian regularization approach (BRA) to solve the WNM. A targeted dataset through the Adam scheme is achieved that is further accomplished using the procedure of training, testing, and verification with ratios of 0.15, 0.13, and 0.72. The correctness of the deep neural network along with the BRA is performed through the overlapping of the solutions. The small calculated absolute error values also enhance the accurateness of the designed procedure. Moreover, the statistical observations are authenticated to reduce the mean square error for the nonlinear WNM.