Supervised machine learning computing paradigm of energy activation for magnetic nanofluid flow via porous surface with nonlinear variant viscosity

In industries like chemical processing, energy systems, metallurgy, filtration, and electronics cooling, activation energy in magneto-nanofluid flow with variant viscosity is essential for regulating reaction rates, maximizing heat and mass transfer, enhancing energy efficiency, and guaranteeing safe operation. This work is important because it advances our knowledge of heat and mass transmission in magnetized nanofluid flows, where the fluid viscosity varies nonlinearly with temperature or other physical parameters. The study's primary goal is to create a numerical model capable of precisely analyzing the intricate relationship between magnetic forces, nonlinear viscosity, porous media, and nanoparticle transport. To get the perfect predictions, the governing model employed the efficacy of artificial neural networks with Levenberg Marquardt structure back propagation (ANN-LMSB), which is designed to investigate energy activation with exponential viscosity variant with temperature on magneto-hydrodynamic nanofluid flow past porous plate (MHD-NFPP). To articulate mathematical modeling, the Reynolds exponential model is used. By employing the model of Darcy–Brinkman–Forchheimer, the momentum equation is additionally formulated. Thermophoresis force and Brownian diffusion have been inspected by implementing Buongiorno model. Along with magnetic body force, mass conservation, nanoparticle concentration, momentum, and energy equations are expressed. Initially, the flow of fluid is denoted by the scheme of PDEs, which are transformed into the structure of ODEs. By employing Adams numerical method, a data set for suggested ANN-LMSB is produced for diverse scenarios by alteration of stretching parameter, the Hartmann number, the thermal and concentration Grashof numbers, the thermophoresis, the Brownian motion, Prandtl number, the chemical reaction constant, Schmidt number, and relative temperature parametric number. By training, testing, and validation procedures of ANN-LMSB, estimated solution of distinct cases is verified, and for the perfection of the suggested model, the comparison for verification is carried out. Afterwards, execution of suggested ANN-LMSB was validated by regression evaluation, mean square error, and histogram studies. Correctness level in range from 10–9 to 10–11 approves distinction of suggested methodology established on the closeness of the recommended and reference results.