Flow of MHD Nanofluids over a Nonlinear Stretchable Sheet: Artificial Neural Network Approach

The authors develop a innovative hybrid numerical simulation scheme combining numerical discretization technique through the fourth order polynomial collection (bvp4c), and artificial neural networks (ANNs), to model magnetohydrodynamics (MHD) of a nano liquid flowing over a nonlinear expanding sheet. They use the physical laws that govern the flow of the liquid to create the coupled partial differential equations (PDEs) of the problem. Then, applied similarity transformations to turn these into ordinary differential equations and use the bvp4c technique in MATLAB to find the results. To predict the velocity, temperature, and concentration of nanoparticles in nanofluids, the feedforward neural network (FFNN) used to approximate their solutions and thereby improve their predictions. The multi-layered perceptron (MLP) neural network is utilized to acquire the testing functions. The optimized algorithm, adaptive movement estimation (ADAMS) is used to get the adjustable values. The ANNs show remarkable coherence with the numerical results achieved from solving the ODEs and demonstrate strong extrapolation capabilities, good generalization performance, and a low computational cost. In addition to predicting how the various parameters (Brownian diffusion, thermophoresis, and magnetic field) affect the convection of the fluid's heat, this study investigates how the Brownian diffusion and thermophoretic forces interact to disperse nanoparticles throughout the fluid and to facilitate heat transfer in nanofluids. The results indicate that ANNs can be used as an alternative to address the complexities of nanofluid-based boundary layer problems affected by MHD conditions; the proposed method could also be used for designing and simulating high-order systems in thermal applications.