Numerical and machine learning data driven analysis of thermo-magnetic Eyring-Powell rheological nanomaterial flow past a vertical porous surface

Motivated by developments in electromagnetic nanomaterials coating processes, a mathematical and computational study is presented of the nonlinear magnetohydrodynamic (MHD) free convection boundary layer flow, as well as the heat transfer, of a non-Newtonian Eyring–Powell ternary fluid from a vertical plate. A non-Darcy, isotropic, homogeneous porous medium is considered, and the effects of thermal radiation and heat source/sink are included. In this work, water acts as the suspension medium for the ternary nanoparticles. Rosseland’s algebraic diffusion flux model is adopted for radiative effects and is valid for optically thick nanofluids. The dimensional form of the governing equations is transformed into dimensionless form by manipulating non-similar solutions. The numerical solution of the transformed conservation equations with physically realistic boundary conditions employs the Keller Box technique, a second-order implicit finite-difference method known for its versatility. The numerical code's validity is confirmed through comparison with results from existing literature. Velocity and temperature distributions within the boundary layer are considered for the effects of the Eyring–Powell rheological parameter, a local non-Newtonian parameter based on length scale, magnetic parameter, Darcy number, Forchheimer parameter, the Biot number, radiation parameter, heat source/sink parameter and dimensionless streamwise coordinate. The relative performance of ternary water nanofluid, binary water nanofluid, and mono water nanofluid is computed. The computations provide some insight into the behavior of non-Newtonian nanofluids of relevance to coating flows with nanomaterials. In this research paper, an ANN architecture for the Eyring-Powell ternary nanofluid is proposed using neural network techniques. The numerical dataset is utilized to train a feedforward backpropagation neural network (FFBPNN) employing the Levenberg-Marquardt (LM) algorithm, facilitating rapid convergence and optimal weight adjustment. The trained artificial neural network attains minimal mean squared error values and a high coefficient of determination, demonstrating prediction accuracy and underscoring its reliability and efficiency. It provides cooling effects, and this model showed high accuracy, with less than 0.05% deviation from CFD results, and improved heat transfer efficiency.