Neuro-computing for third-grade nanomaterial flow under impacts of activation energy and mixed convection along rotating disk

This paper examines the activation energy influence in third-grade nanoparticle flow model (TG-NPFM), which is nonlinear mixed convective flow over a spinning disk under the influence of heat sink/source as well as viscous dissipation by utilizing Bayesian Regulation Method with backpropagated Artificial Neural Networks (BRM-BPANN). Nonlinear thermal radiation is also involved in the considered flow dynamics to obtain the approximated numerical solutions. The nonlinear PDEs of TG-NPFM are then transformed into nonlinear ODEs by implementing the corresponding transformation. We solved these ODEs by Optimal Homotopy Analysis Method (OHAM) to explain the dataset used as a reference for BRM-BPANN for different scenarios of TG-NPFM. This reference dataset is then exported to MATLAB to compute the results. The outcomes of TG-NPFM are figured by adopting the procedures of testing, validation and training. Moreover, approximated solution is compared with standard solution and the efficacy examination of TG-NPFM is authenticated by the studies of MSE, error histogram and regression plots. These soft computation frameworks provide incentive to use an efficient and dependable alternative paradigm built on soft computing environments to solve problems by doing a descriptive analysis to mitigate the impacts of different physical features. It is a new implementation of intelligent computational system of artificial intelligence introduced by incorporating the solver BRM-BPANN for interpreting the TG-NPFM. The absolute error values lie between 10-8 to 10-5, 10-10 to 10-5, 10- to 10-4, 10- to 10-3, 10- to 10-5, 10-9 to 10, 10- to 10- and 10- to 10-3, which show the reliability and accuracy of the technique. The convergence and precision of the algorithm can easily be seen through the results of per- formance, training state and fitness plot, along with the regression value of R = 1.

Automated summary

This paper examines the influence of activation energy in third-grade nanoparticle flow model (TG-NPFM) using Bayesian Regulation Method with backpropagated Artificial Neural Networks (BRM-BPANN). The nonlinear thermal radiation and viscous dissipation are considered in the model to obtain the numerical solutions. The nonlinear partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using the Optimal Homotopy Analysis Method (OHAM). The results of TG-NPFM are obtained through testing, validation, and training processes, and compared with standard solutions using MSE, error histogram, and regression plots for validation. The reliability and accuracy of the technique are demonstrated through the absolute error values and convergence and precision of the algorithm.