Eur. Phys. J. Plus (2014) 129: 176
https://doi.org/10.1140/epjp/i2014-14176-1

Regular Article

Metachronal beating of cilia under influence of Hartmann layer and heat transfer

¹ DBS&H CEME, National University of Sciences and Technology, Islamabad, Pakistan
² School of Mathematical Sciences, Peking University, 100871, Beijing, P.R. China
³ Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan
⁴ Department of Mathematics, Quaid-i-Azam University 45320, 44000, Islamabad, Pakistan

^* e-mail: drsnqau@gmail.com

Received: 20 June 2014
Revised: 28 June 2014
Accepted: 3 July 2014
Published online: 22 August 2014

Abstract

The propulsion system of cilia motion is investigated considering a viscous fluid model. The problem of the two-dimensional fluid motion in a symmetric channel with ciliated walls is considered. The features of ciliary structures are resolved by the supremacy of viscosity effects over inertial control by the long-wavelength and low-Reynolds-number approximation. Exact solutions for the longitudinal pressure gradient, temperature and velocities are obtained. The pressure gradient and volume flow rate for different values of the flow parameters are also predicted. The flow possessions for the viscous fluid are solved as a function of the cilia and metachronal wave velocity.