Metachronal Wave Impact in a Channel Flow in the Presence of Prandtl Fluid Model

Motile cilia are tiny, hair-like structures originate in many different types of biological processes. They produce directed flow to allow fluid transport. Cilia are important for locomotion and play a dynamic part in animal and human growth and in everyday life. It may help to remove contaminants from organs or tissue by facilitating the flow of fluids over the cell. The intention of our theoretical study is to inspect the physical and computational aspects of applied magnetic field on Prandtl (non-Newtonian) ciliated fluid flow, that moves through a uniform ciliated channel. This flow is the conduct for symmetrical wave circulation and is frequently observed during the expansion and contraction of concentrical cilia. The problem is first formulated mathematically, which results in a highly nonlinear system of PDEs. Equations are transformed into ODEs using a scaling group of transformations. Second, approximation of wavelength is long and Reynolds number is low used to analyze the flow motion caused by metachronal waves. The emerging equation is solved numerically using the bvp4c method. Dimensionless velocity, temperature, pressure rise, and pressure gradient expressions are engendered and graphical comprehensive illustrations of all these in relation to various factors are also provided. Also, streamlines are fabricated to exhibit the flow phenomenon of ciliary motion.