Numerical investigation of eringen number effects on magneto–micropolar channel flow with a cuboid obstacle using FreeFEM++

Magneto-micropolar flows arise in microfluidic transport, electromagnetic pumping, and thermal management systems involving complex fluids. This study numerically examines magneto-micropolar channel flow past a cuboid obstacle, with a specific focus on the previously unexplored influence of the Eringen number in the presence of micromagnetorotation. The governing equations, formulated using Eringen’s micropolar theory, are solved through a finite element scheme implemented in FreeFEM++. The analysis highlights how microstructural inertia influences separation, wake recovery, and vortex-magnetic interactions. A comprehensive parametric study is conducted by varying the Eringen and Reynolds numbers along with the spin magnetization and magnetic coupling parameters. The results show that low strengthens microrotation and produces larger, persistent wakes, whereas high suppresses rotational effects and restores near-Newtonian behavior. Magnetic parameters (Ms, α, β) further regulate vortex size and microrotation intensity. Overall, the Eringen number emerges as a key control parameter for optimizing flow stability in microfluidics, pumping devices, and heat-transfer systems.