Biomimetic-driven electro-osmotic flow of a fractional second-grade fluid in a convergent–divergent channel considering the influence of hall current and ion slip under a periodic magnetic field

This work investigates biomimetic peristaltic transport of a fractional second-grade fluid in a convergent/divergent channel under complex wave propagation, motivated by applications in microfluidic and biomedical systems. The objective is to analyze the combined effects of electro-osmosis, porous media, Hall current, ion-slip conditions, andperiodic magnetic fields on flow, heat, and mass transfer characteristics. The governing equations are non-dimensionalized and extended using a modified Caputo fractionalderivative, and analytical solutions are obtained via the Homotopy Perturbation Method under long-wavelength and low-Reynolds-number assumptions. The results reveal that ion slip and Hall current enhance axial velocity at the channel center while suppressing it near the walls, with stronger velocity retardation observed for non-periodic magnetic fields. Temperature decreases with Hall current but increases with ion-slip effects, whereas the Sherwood number increases with Brownian motion and decreases with thermophoresis. Comparisons with existing literature validate the accuracy of the solutions. The outcomes of this investigation offer valuable insights for applications in microfluidic and biomedical systems, where electro-osmotic transport, Hall current, and ion-slip effects play a crucial role in regulating fluid motion. The results are particularly relevant for understanding blood-flow behavior, optimizing targeted drug-delivery processes, and designing efficient lab-on-chip devices. Moreover, the analysis contributes to industrial applications involving heat-transfer enhancement and precise control of non-Newtonian fluids under oscillatory magnetic fields.