Entropy generation in time-fractional magnetohydrodynamic nanofluid Couette flow between permeable walls

This study investigates entropy generation in magnetohydrodynamic radiative nanofluid Couette flow through a permeable channel using the Caputo time-fractional derivative framework. The model incorporates thermal radiation, magnetic field effects, viscous and Joule heating, nanoparticle volume fraction, and wall suction/injection, with the upper permeable wall moving and subject to convective heat exchange with its surroundings. The fractional derivative captures memory-dependent transport processes, extending classical models of transient nanofluid flow and heat transfer. The governing fractional partial differential equations for velocity and temperature are solved numerically via a hybrid Euler wavelet collocation method for spatial discretization and a fractional finite difference scheme for temporal discretization, with Newton's method employed for nonlinear resolution. Key thermophysical quantities such as Bejan number, entropy generation rate, skin friction and Nusselt number are analyzed to assess irreversibilities and transport mechanisms. The parametric results reveal that increasing the fractional-order parameter and nanoparticles volume fraction enhances thermal performance but also augment entropy generation , while stronger magnetic fields and wall permeability significantly alter momentum transport and entropy distribution. These findings provide valuable guidelines for entropy management in nanofluid-based thermal–fluid systems with applications in energy conversion, microfluidics, and advanced cooling technologies.