Heat and mass transfer analysis on magnetohydrodynamics Powell–Eyring nanofluid flow with Hall current, thermal radiation, Brownian motion, and thermophoresis effects over a stretched surface

Abstract This study primarily explores the influence of the Hall current on Powell–Eyring nanofluid within the framework of magnetohydrodynamic (MHD) flow over an extending surface. The research comprehensively explores critical factors, including heat source, radiation, thermophoresis, and Brownian motion, utilizing a combination of partial differential equations (PDEs) and ordinary differential equations (ODEs). Subsequently, these equations are mathematically elucidated using the fourth‐order Runge–Kutta method in MATLAB under specified boundary conditions. The study aims to provide new insights into the complex interplay among the Hall current, heat source, radiation, thermophoresis, and Brownian motion. Within the MHD framework, the equations for momentum, energy, and nanoparticle concentration are systematically derived. Major findings reveal the significant influence of the Hall current and magnetic field strength on fluid flow behavior, indicating potential control mechanisms for optimizing heat transfer in nanofluid‐based industrial processes. That nanoparticle distribution also offers valuable insights for tuning nanofluid properties. The study emphasizes the importance of visual representation through graphs and tables. These outcomes contribute to a more comprehensive consideration of nanoparticle behavior, with practical implications for optimizing complex industrial systems using nanofluid.