Multi-nanoparticle-induced enhancement of heat and mass transfer in non-Newtonian cross fluid under MHD and Ohmic dissipation effects: FEM analysis

Industrial fluids with shear-dependent viscosity, such as polymer melts, biological fluids and nanoparticle suspensions, play a vital role in engineering applications, including electromagnetic flow control, electronic cooling, metallurgical processes, magnetohydrodynamics (MHD) pumps and energy systems. To achieve realistic modeling, this study aims to investigate simultaneous heat and mass transfer in a non-Newtonian cross fluid containing mono-, di- and tri-nanoparticles over a heated stretching surface. Key engineering indicators – skin friction coefficient, Nusselt number and Sherwood number – are analyzed to support the design of efficient thermal systems. The effects of Joule heating, viscous dissipation, free-stream velocity and homogeneous chemical reaction on flow, thermal and concentration fields are also examined. The governing equations are formulated using boundary layer approximations and transformed into similarity-based boundary value problems. These are solved numerically using the finite element method (FEM) because of its robustness, accuracy and suitability for nonconservative systems. The original two-dimensional problem is reduced to a one-dimensional form, ensuring computational efficiency. The results demonstrate that tri-nanofluids provide superior heat transfer performance, yielding the maximum wall heat flux. In contrast, di-nanofluids exhibit the highest wall shear stress compared to mono- and tri-nanofluids. Joule heating significantly increases fluid temperature and deteriorates thermal efficiency, highlighting the importance of minimizing Ohmic dissipation in magnetically influenced thermal systems. This study presents a novel FEM-based comparative framework to distinguish the thermal and hydrodynamic behaviors of mono-, di- and tri-nanoparticle-enhanced Cross fluids under MHD conditions. The findings offer quantitative insights into heat and mass transfer enhancement and provide practical guidance for optimizing advanced cooling and electromagnetic fluid systems.