Biomimetic elasticity effects on EMHD Sutterby fluid flow through an elastic wavy channel interacting with a porous medium

This work investigates the biomimetic elasticity effects on EMHD Sutterby fluid flow through an elastic wavy channel interacting with a porous medium. The potential, continuity, and momentum equations are formulated for sinusoidal wall corrugations, and the perturbation method is employed to derive semi-analytical expressions for the velocity component and volumetric flux. The influence of corrugation amplitude, wall elasticity, magnetic induction, Darcy permeability, elastic gradient, and magnetic Reynolds effects is examined through analytical solutions and graphical results. The velocity profiles demonstrate that wall corrugation significantly alters fluid motion, where small amplitudes weaken the wave influence. The axial velocity decreases with increasing Hartmann number due to Lorentz damping, whereas higher Darcy number increases the flow rate through enhanced permeability. Increasing the elastic gradient reduces velocity magnitude and intensifies magnetic coupling, and wall stiffness and tension parameters stabilize the velocity field and suppress oscillations. The induced magnetic potential increases with the magnetic Reynolds number. The obtained results show good agreement with special limiting cases reported previously, confirming the validity of the formulation. The study suggests that modulation of wall elasticity and magnetic parameters enables precise control of EMHD non-Newtonian flows in flexible channels and offers potential applications in drainage, irrigation, and liquid transport systems.