Metachronal wave form analysis on cilia-driven flow of non-Newtonain Phan–Thien–Tanner fluid model: A physiological mathematical model

Abstract

The Phan–Thien–Tanner non-Newtonian model of fluid flow is considered to mathematically model the cilia governed flow inside the human body. The collective action of cilia generates a rhythmic motion in form of metachronal wave traveling along the wall of channel. We have utilized the necessary assumptions to non-dimensionalize this complex problem and the exact solutions are obtained for the cilia governed flow problem. The graphical results are also incorporated to further discuss these solutions in detail. The wavy movements developed due to rhythmic actions of cilia are clearly evident in pressure gradient graphs. Further, a parabolic flow pattern is also observed in this ciliated channel flow problem. Streamlines disclose the trapping phenomenon and the multiple pumping regions can be seen in intrigued pressure rise graphical solutions.