Journal of Magnetics 22(4), 642-648 (2017) https://doi.org/10.4283/JMAG.2017.22.4.642 © 2017 Journal of Magnetics Magnetic Field and Permeability Effects on Jeffrey Fluid in Eccentric Tubes Having Flexible Porous Boundaries Arshad Riaz 1 * , Abdul Razaq 1 , and Aziz Ullah Awan 2 1 Department of Mathematics, University of Education Lahore, Jauharabad Campus 41200, Jauharabad, Pakistan 2 Department of Mathematics, University of the Punjab Lahore, Pakistan (Received 23 September 2017, Received in final form 3 November 2017, Accepted 6 November 2017) In the present study, we recapitulated the magnetic field and porous medium effects on the peristaltic mecha- nism of a Jeffrey fluid model observed between two electrically conducting eccentric annuli. The inner annulus is assumed to be rigid and to contain constant velocity across the longitudinal direction of the enclosure; the outer one is considered to be flexible and to experience peristaltic waves travelling down its walls. Moreover, the magnetic field is examined in the direction normal to the pattern in the presence of a porous medium. The flow, meanwhile, is incompressible and follows in an unsteady format. The flow’s descriptive equations are reduced by anticipation of long wave length and small Reynolds number approximations. The resulting governing equa- tions are then handled using analytical techniques. The achieved expressions for the considerable functions are manipulated graphically to determine the influences of various appertaining parameters. Finally, the results are compared with those of previous studies to confirm the validity of the present solutions through tables and graphs. The graphs indicated that the magnetic field increases the pumping rate but that the porosity reduces it. Keywords : peristaltic transport, porous medium, eccentric cylinders, Jeffrey fluid, magnetohydrodynamics 1. Introduction The peristaltic mechanism of fluids in three-dimensional geometries (tubes/ducts) has a special allure among to researchers. Peristalsis suggests a wave-like phenomenon that occurs due to involuntary expansion and contraction of a lissome wall. A large number of applications of peristaltic flow have been proved in different fields such as physiology, engineering and medicine. In many surgical processes for example, it is applied to circulate the blood in heart-lung machines. Naturally too, this process pro- pagates to the intestines, stomach and esophagus. Many scientists and engineers have explored varieties of pumping machines very similar to roller pumps. The peristaltic mechanism of a toxic liquid is employed in the nuclear industry to retrieve penetration of the external environment [1]. The variable magnetic field acting on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls has been investigated by Bhatti et al. [2]. Bhatti et al. [3] have examined the heat and mass transfer of two-phase flow with electric double-layer effects induced due to peristaltic propulsion in the presence of a transverse magnetic field. An extensive literature is available for analysis of the peristaltic transport of Newtonian and non-Newtonian fluids in various flow patterns [4-7]. Reddy et al. [8] have discussed the influence of lateral walls on the peristaltic flow in a rectangular duct. And, In order to simplify the problem, they have measured the results under the implementation of long wavelength and low Reynolds number. After a thorough review of the literature, it is found that only a few studies have analyzed the effect of the eccentricity attribute [9- 11]. In recent years, the peristaltic flow of non-Newtonian fluids through eccentric cylinders has been investigated by some researchers. Recently, a mathematical model of peristaltic transport through eccentric cylinders was presented by Mekheimer et al. [12], who [13] have also executed the particulate suspension flow induced by sinusoidal peristaltic waves through eccentric cylinders with thread annular. Ellahi et al. [14] presented a series of solutions for the magnetohydrodynamic peristaltic flow of a Jeffrey fluid in eccentric cylinders. ©The Korean Magnetics Society. All rights reserved. *Corresponding author: Tel: 03006076036 Fax: 03455992002, e-mail: arshadriaz26@gmail.com ISSN (Print) 1226-1750 ISSN (Online) 2233-6656