Levenberg-Marquard Analysis of Electrically Conducting Prandtl–Eyring Nanofluid Flow Driven by Thermophoretic and Thermodynamic Processes

• The thermophysical behavior of electrically conducting viscoelastic (Prandtl–Eyring) nanoliquid flow (TAEC-VNF) past a stretchable surface is analyzed. • Use backpropagation Levenberg–Marquardt-optimized neural networks to assess the governing model for accurate predictions. • Employing the Adams numerical method for various situations, the variable factors. • With a degree of perfection from 10 −8 to 10 −9 , the proposed technique matches reference results closely. In modern industrial and engineering processes, efficient control of solutal and thermal transport in nanoliquid systems improves thermal performance, energy utilization, and process reliability. This paper gives a numerical analysis of electrically conducting Prandtl-Eyring fluid flow containing nanoparticles under the influence of thermophoresis and thermodynamic mechanisms. The fluid model contains magnetohydrodynamic (MHD) effects to account for the action of an applied magnetic field. The research offers valuable insights for commercial and engineering applications such as cooling technologies, polymer processing, biomedical systems, and energy devices. Inspired by such impactful applications, this study investigates the thermophysical behavior of electrically conducting Prandtl–Eyring nanoliquid flow (TAEC-VNF) past a stretchable surface. Use backpropagation Levenberg–Marquardt-optimized neural networks to assess the governing model for accurate predictions. To measure thermal and solutal transport parameters in the flow system, the Buongiorno nano paradigm was used. To accelerate the computation process, the issue in the partial differential system has been transformed into a non-dimensional ordinary differential form. Employing the Adams numerical method for various situations, the variable factors include Hartmann number M , fluid parameters α and β , Brownian diffusion coefficient N b , thermophoresis coefficient N t , Lewis L e and Prandtl P r numbers, respectively. The suggested paradigm is linked to the optimization of the intended solver's application, and the approximate solutions for different cases are validated by the NN-BLMS training, testing, and validation approach. Additionally, the regression analysis, mean square error, and histogram examination of NN-BLMS were used to verify the proposed solution. With a degree of perfection from 10 −8 to 10 −9 , the proposed technique matches reference results closely. The effects of flow regulating limitations on concentration, heat, and momentum are shown graphically.