Fractional order analysis of radiating couple stress MHD nanofluid flow in a permeable wall channel

This study explores the entropy analysis of a radiating couple stress magnetohydrodynamic (MHD) nanofluid flow using a time-fractional order approach within a permeable vertical wall channel. The nanofluid's behavior is influenced by various factors, including thermal radiation, thermophoresis, Brownian motion of nanoparticles, suction/injection, viscous dissipation, Joule heating, buoyancy forces, heating couple stress effects, and an applied magnetic field, resulting in a highly nonlinear system. Accounting for memory-dependent behavior, the Caputo time-fractional derivative is introduced into the governing equations. The study evaluates entropy generation due to heat transfer, viscous dissipation, nanoparticle mass transport, and magnetic influences. An implicit finite difference method is employed to solve the governing equations, analyzing the impact of key parameters. The findings reveal that decreasing the fractional parameter enhances the local entropy generation rate and Bejan number, signifying greater thermodynamic irreversibility. These insights contribute to optimizing energy efficiency in industrial and biomedical applications involving MHD nanofluids.