Mucociliary transport is a fundamental physiological process that ensures the clearance of inhaled pathogens, particulates, and excess secretions from the respiratory tract. It is driven by the coordinated beating of cilia embedded in a viscoelastic mucus layer that overlies a watery periciliary fluid. Over the past several decades, mathematical and biomechanical models have been developed to elucidate the fluid mechanical principles governing this transport mechanism, incorporating increasingly sophisticated descriptions of mucus rheology, ciliary kinematics, and geometrical constraints. In parallel, advances in magnetohydrodynamics and non Newtonian fluid theory have opened new avenues for understanding how external fields and complex material responses can modulate microscale transport phenomena. The present study synthesizes and extends these lines of inquiry by developing a unified theoretical framework for cilia driven flow in channels that accounts simultaneously for rheological complexity and magnetohydrodynamic effects. Drawing strictly on established results from the literature, including the foundational work on mucociliary transport, viscoelastic fluid mechanics, fractional and second grade models, and magnetically influenced channel flows, this article constructs a detailed conceptual model of how metachronal ciliary waves interact with electrically conducting mucus to generate transport under physiological and pathological conditions. Particular attention is paid to the role of epithelial health, mucus viscoelasticity, and external magnetic fields in altering flow resistance, transport efficiency, and mixing. By interpreting the classical and contemporary studies within a common theoretical language, the article highlights previously underexplored synergies between biological transport and applied magnetofluid dynamics. The results provide a descriptive yet rigorous account of how modifications in cilia density, beat frequency, mucus rheology, and magnetic field strength collectively shape the velocity profiles, shear distributions, and clearance rates within airway like channels. This integrative perspective not only deepens our understanding of normal mucociliary function but also offers insight into disease states such as severe asthma, chronic infection, and impaired epithelial function, where deviations in any of these parameters can lead to compromised clearance and tissue damage.