Stochastic procedures to solve the nonlinear mass and heat transfer model of Williamson nanofluid past over a stretching sheet

Abstract

The stochastic procedures ANNs-LMB are provided with three categories of sample statistics, testing, training and verification. The nonlinear mass and heat transfer of Williamson nanofluid (MHTWF) on a stretched surface is divided into three profiles, dimensionless stream, concentration and temperature. The statistics, 10 %, 15 % and 75 % for testing, validation and training are provided to solve the nonlinear MHTWF past over a stretched surface. The solutions of the MHTWF are provided using the artificial neural networks (ANNs) together with the novel geographies of Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. A reference data set is designed for the comparison of the obtained and proposed solutions for the fluid system. The absolute error is used to check the accuracy and precision of the nonlinear MHTWF past over a stretched surface, which have been provided around 10−05-10−08, 10−05-10−07 and 10−05-10−06 for each case of the model. The obtained numerical solutions of the nonlinear fluid dynamics system have been considered for the reduction of mean square error (MSE). The capability and dependability of the stochastic procedure are authenticated using the relative arrangements of MSE, error histograms (EHs), state transitions (STs), correlation and regression.