Inclined magnetic force impact on cross nanoliquid flowing with widening shallow and heat generating by using artificial neural network (ANN)

Artificial neural networks (ANNs) have a wide range of applications in science and technology. Artificial neural networks (ANNs) widely utilized in image and speech recognition, neural language processing, drug discovery, genomics and bioinformatics, Robotics and control systems, material science and energy and power system. Due to the above applications, the main focus of this article is to scrutinize the impact of inclined magnetic field on a cross nanofluid flow with slip velocity and convective boundary conditions over a variable porosity. Gold (Au) nanoparticles are suspended in base liquid blood. Thermal stratification and heat generation with joule heating impact is taken in the energy equation in order to see the heat transfer. To transform the non-linear partial differential equations (PDE's) into non-linear ordinary differential equations (ODE's) utilized the von-Karman similarity transformation parameters. For the solutions of the non-linear ODE's, the 4th- order Runge-Kutta numerical method is employed. A dataset for the employed neural network back propagated Levenberg-Marquard scheme (NN-BLMS) is generated for various estimations of the embedded parameters like Weissenberg number, magnetic parameter, angle of inclination, porosity and permeability parameters, thermal stratification parameter by utilizing the 4th-order Runge-Kutta numerical scheme. The testing, validation and training methods of NN-BLMS are utilized to scrutinize the approximate solution of cross nanofluid with slip velocity and convective boundary conditions. The performance of the proposed NN-BLMS to successfully solved the cross nanofluid model is endorsed via mean squared error, error histogram and regression analysis. Streamlines and heatlines are plotted for different parameters including in velocity and temperature equations.