Abstract
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, two dimensional flow of a viscous nanofluid is observed in an annulus with ciliated tips. The current theoretical model may be supposed as mathematical illustration to the movement of ciliary motion in the presence of an endoscopic tube (or catheter tube). The inner tube is rigid, while the outer tube takes a metachronal wave. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. Exact solutions have been established for both velocity and temperature profiles, which include nanoparticle effects. The features of the ciliary motion are analyzed by plotting graphs and discussed in detail.