Entropy generation minimisation in Darcy–Forchheimer flow of a micropolar hybrid nanofluid over a stretching sheet with activation energy and Joule heating

This study investigates the thermodynamic irreversibility of a micropolar hybrid nanofluid (Cu–Al2O3/water) over a stretching sheet in a Darcy–Forchheimer porous medium. The objective is to analyse entropy generation minimisation under magnetohydrodynamics (MHD), Joule heating, viscous dissipation and Arrhenius activation energy. The transformed dimensionless ordinary differential equations are solved numerically using the MATLAB bvp4c algorithm and validated against classical analytical solutions. Key quantitative findings indicate that increasing the micropolar vortex viscosity parameter (K from 0 to 1) enhances the skin friction coefficient by 54% while suppressing the local Nusselt number by nearly 78%. Crucially, strong magnetic fields (M≥3.0) and viscous dissipation trigger a heat transfer reversal (Nux=−1.0213), directing heat from the fluid into the wall. Thermodynamic analysis reveals that entropy generation is predominantly driven by fluid friction and Joule heating near the boundary, shifting to heat transfer irreversibility in the far-field. Ultimately, these findings provide a critical thermodynamic framework for optimising advanced thermal management systems, polymer extrusion processes and active flow-control devices.