Hydromagnetic flow of Newtonian fluid due to ciliary motion in a channel

A. M. Siddiqui¹ , A. A. Farooq^{2, 3} , M. A. Rana³

¹ Department of Mathematics, York Campus, Pennsylvania State University, USA
² Department of Basic Sciences, Riphah International University, Islamabad, Pakistan
³ COMSATS Institute of Information Technology, Abbottabad, Pakistan

Abstract
This study is concerned with a cilia-induced magnetohydrodynamic (MHD) flow of an incompressible Newtonian fluid in a channel. The governing equations for the two dimensional hydromagnetic flows are modelled and then simplified by using long wavelength and creeping flow approximations. Exact solutions for velocities, stream function and axial pressure gradient are derived as a function of the cilia and metachronal wave velocity. However, the expression for pressure rise per wavelength is found numerically. Effects of various physical parameters on the computational results are discussed through graphs. It is found that the magnetic field and the volume flow rate are inversely proportional to each other. The present study also reveals that the trapping of Newtonian fluid in a ciliated channel can be diminished by increasing the strength of magnetic field. Finally, the analysis is applied and compared with the observed value of flow rate of spermatic fluid in the ductus efferents of the male reproductive tract. Tables 1, Figs 11, Refs 18.