Cilia-driven magnetohydrodynamic transport of Carreau-Buongiorno nanofluid in a converging elliptical duct with temperature-dependent properties

The main focus of past research on cilia-driven transport and nanofluid flow has been on planar or circular channels, without accounting for realistic duct geometries, variable fluid properties, or magnetic-field effects. Within these constraints, the present work aims to develop a complete mathematical model of magnetohydrodynamic Carreau-Buongiorno nanofluid flow in an elliptical converging duct driven by metachronal ciliary motion. The nonlinear governing equations, including variable viscosity and thermal conductivity, Brownian motion, thermophoresis, viscous dissipation, and Lorentz force effects, are reduced into a wave frame and simplified through the lubrication approximation. The Homotopy Perturbation Method is used to obtain semi-analytical solutions. The findings indicate that momentum redistribution in variable viscosity decreases the axial velocity along the major axis and increases core flow in the minor axis. The magnetic fields increase flow along the major axis by transferring momentum via the Lorentz force, but they reduce motion along the minor axis in the core region. Increased thermal conductivity improves heat diffusion, whereas thermophoresis and Brownian motion play important roles in the transport and thermal mixing of nanoparticles. The novelty of this study is that the combined modelling of cilia-driven propulsion, non-Newtonian nanofluid interactions, magnetic control, and converging geometry (elliptical) is performed. The results are useful in focused drug delivery, microfluidic cooling, and the bio-inspired pump design.