A design of an intelligent computing networks to study impacts of porous dissipation and slip for boundary layer flow along Darcy-Brinkman porous media

Abstract

In this article we observed the Darcy-Brinkman flow model in the existence of frictional heating and porous dissipation (DBFM) over a stretching sheet by employ the neural network backpropagated with Bayesian regularization technique (NNBP-BRT). NNBP-BRT has the ability to exhibit relatively complex relationships, which implies it can be used in numerical investigations to construct a robust framework. Bayesian regularization is a mathematical procedure that converts a nonlinear regression into a “well-posed” statistical equation in the ridge regression methodology. Partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by employ appropriate similarity transformation. The resulting system of nonlinear equations was numerically solved using the fourth-order Runge–Kutta approach with velocity and thermal slip assumptions. Here we utilized ND-Solve method to solve the ordinary differential equations and clarify the reference dataset for NNBP-BRT for different scenarios of DBFM by varying parameters. To compute the approximated solutions and error analysis plots of different scenarios of DBFM the reference dataset is utilized in MATLAB software using the command ‘nftool’. The performance of NNBP-BRT is observed and obtained by observing the regression curves, histograms and MSE outcomes. The solution of DBFM is obtained by testing, validation and training process. Figures depict velocity profiles and temperature profiles for different variations of parameters. The effect of different flow parameters Brinkmann parameter, porosity parameter, Prandtl number and Eckert number on velocity profile and temperature profile are discussed and the results are presented graphically.