Computational analysis of Powell-Eyring nanomaterials flow: mixed convection dynamics, metachronal wave phenomenon and Buongiorno model

Cilia-driven flow plays a crucial role in biological transport, facilitating mucus clearance, development, and microfluidic applications. The integration of nanofluids and mixed convection further enhances heat and mass transfer unlocking new possibilities in biomedical and industrial fields. This study presents a comprehensive computational analysis of Powell-Eyring nanomaterial flow through a ciliated curved channel under the influence of metachronal wave phenomena. The influences of mixed convection, viscous dissipation, chemical reactions, activation energy, and thermophoresis on heat and mass transfer are extensively analyzed. The porous medium is modeled using the modified Darcy law and Darcy-Forchheimer formulation. The governing equations are simplified using the lubrication approach and solved numerically through the implicit finite difference method (FDM). The analysis includes detailed evaluations of velocity, skin friction, temperature, heat transfer rate, concentration, Sherwood number, and streamlines. Key findings reveal that velocity increases with the Grashof number but decreases with the cilia length parameter in the central region of the channel. Additionally, temperature and concentration show opposite behaviors in response to the Brownian and thermophoresis parameters. Streamlines illustrate the flow dynamics driven by ciliated motion within a curved channel.