Thermal radiation and activation energy effects on MHD mixed-convective Carreau nanofluid stagnation-point flow over a stretchable sheet: Levenberg-Marquardt neural-network analysis

This paper discusses the nonlinear mixed-convective stagnation-point flow, heat transfer, and species transport of a Carreau fluid on a stretchable sheet in the existence of thermal radiation, activation energy, Brownian motion, thermophoresis, and magnetohydrodynamic effects. The governing equations of the system of equations of the coupled nonlinear system of ordinary differential equations of the fields of velocity, temperature and concentration are derived by the use of suitable similarity transformations. The nonlinear fluid-flow analysis is approximated using an LMS-BPNN surrogate trained on bvp4c reference solutions. with a backpropagation neural network to give an accurate and computationally efficient framework of the transformed system. The small mean squared errors of the proposed model of order 10 −9 to 10 −10 and the near-unity regression coefficients (R ≈ 1) confirm that the proposed model has strong predictive capability. It is found that the Hartmann number inhibits the velocity field due to the retarding Lorentz force and the temperature ratio parameter boosts the thermal boundary layer and decreases the local Nusselt number. The higher the Schmidt number, the lower the concentration profile and the higher the Sherwood number. The parameters of thermophoresis and Brownian motion contribute to the increase of the thermal transport whereas the Weissenberg number modulates greatly the momentum boundary layer by the shear-thinning characteristic of the Carreau fluid. The results indicate that the LMS-BPNN framework serves as a computationally efficient surrogate for traditional solvers within the sampled parameter space; however, its predictive reliability beyond the trained parameter range requires further validation before broader generalization can be claimed. The novelty of this work lies in integrating Carreau rheology, mixed convection, MHD, thermal radiation, activation energy, Brownian motion, thermophoresis, and LMS-BPNN prediction within a unified stagnation-point flow model.