Study of MHD effects on the cilia-induced flow of a Newtonian fluid through a cylindrical tube

A. M. Siddiqui¹ - A. A. Farooq^{2, 3} - M. A. Rana²

¹ Department of Mathematics, York Campus, Pennsylvania State University, 1031 Edge comb Avenue York, PA 17403, USA
² Department of Basic Sciences, Riphah International University, Islamabad, Pakistan
³ COMSATS Institute of Information Technology, University road, Tobe Camp, Abbottabad, KPK,Pakistan

Abstract
In this paper, we investigate a fluid-mechanical model describing the role of ciliary beating in terms of the metachronal wave on the transport of a magnetohydrodynamic fluid in a tube. The nonlinear equations and the relevant boundary conditions governing the flow of a Newtonian fluid under the influence of a transverse magnetic field are formulated in a cylindrical coordinate system. Exact solutions for velocities, axial pressure gradient and stream function are obtained using the long wavelength and creeping flow approximations. The influence of pertinent parameters on the pumping and the trapping characteristics are discussed through graphs. Analysis is also applied and compared with the observed value of the flowrate of epididymal fluid in the ductus efferents of the male reproductive tract. It is found that the pumping due to ciliary activity has to work more efficiently for pushing the MHD fluid if compared with a simple Newtonian fluid. It is also observed that the trapping can be reduced significantly by increasing the magnetic field strength. Figs 8, Refs 16.