Computational Modeling of Magnetohydrodynamic Non‐Newtonian Fluid Transport With Coupled Thermal–Solutal Exchange and Entropy Generation in Wavy Channel

We employ a rigorous analytical framework to investigate ciliary motion coupled with heat and mass transfer, an approach essential for understanding the fundamental biological processes that govern airway physiology. This work offers a computational tool for modeling non‐Newtonian mucus transport and thermodynamic irreversibility in the human airway mucociliary clearance, which will aid in the development of biomedical modeling tools for analysis of respiratory physiology and design of microfluidics‐based therapeutic systems. A two‐region description of cilia‐driven motion in a Ree–Eyring liquid is formulated here, retaining magnetic, thermal, and species‐transport mechanisms simultaneously. Balance laws for mass, momentum, energy, and species furnish the field equations; these are reduced under slender‐channel and creeping‐flow assumptions and subsequently integrated in closed form. Losses stemming from frictional heating and conductive exchange are measured through the local rate at which entropy is produced. The role of the governing nondimensional groups is then examined in depth, including the Hartmann number, viscosities, thermal conductivities, and other material constants, whose effects on the flow, thermal, and solutal fields are illustrated through line graphs and contour maps. Computations indicate that the largest speeds and temperatures arise inside the periciliary region, whereas solute accumulates most strongly in the outer mucus region. Imposing the magnetic field markedly alters transport behavior and increases irreversibility throughout the channel. Quantitatively, raising the Ree–Eyring parameter from to reduces the axial velocity from u ≈ 1.9 near the channel centreline to at , that is, a complete reversal of the cilia‐driven stream.