Biomechanical analysis of cilia-induced liquid propulsion in rough porous passageway under magnetic field control: MATLAB- and Mathematica-based simulations

Biological processes like mucus movement in the respiratory tract, circulation of cerebrospinal liquid, and sperm cell propulsion all rely on cilia-driven flow. Understanding the importance of the cilia-driven flow of generalized Newtonian fluid with surface roughness is critical for determining the biomechanics of these mechanisms and their consequences for several kinds of diseases. Motivated by these important applications, this article aims to examine the impact of surface roughness along with magnetic field inside horizontal passage using the Carreau–Yasuda (C.Y) model. Moreover, the effect of the porous medium is also considered. The flow equations are developed using the lubrication approximation. The MATLAB bvp5c and Mathematica NDSolve are utilized to solve boundary value problems. The validation of the numerical approach is made with a limiting case. The impact of various parameters on streamlines, velocity, and pressure gradient are shown graphically. This analysis reveals that surface roughness, magnetic field, and porous medium strongly impact streamline topologies, velocity, and pressure gradient. For accuracy, surface roughness plays a crucial role in developing various medical devices.