Delivered by Ingenta to: Rice University IP: 146.185.205.116 On: Sun, 12 Jun 2016 11:52:35 Copyright: American Scientific Publishers RESEARCH ARTICLE Copyright © 2014 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 11, 1040–1048, 2014 Peristaltic Flow in Cylindrical Tubes with an Endoscope Subjected to Effect of Rotation and Magnetic Field A. M. Abd-Alla 1 2 ∗ , S. M. Abo-Dahab 1 3 , and R. D. El-Semiry 1 1 Faculty of Science, Mathematical Department, Taif University, 888, Saudi Arabia 2 Faculty of Science, Mathematical Department, Sohag 82524, Egypt 3 Faculty of Science, Mathematical Department, SVU, Qena 83523, Egypt This study examines peristaltic flow problem in a tubes subjected to rotation and magnetic field with an endoscope. The analytical expressions for the pressure gradient, velocity, pressure rise and friction force on the inner and outer tubes and shear stress are obtained in the analytical form. The effect of the non-dimensional wave amplitude, the magnetic field, the rotation and the non- dimensional volume flow are analyzed theoretically and computed numerically. Comparison was made with the results obtained in the presence and absence of magnetic field and rotation. The results indicate that the effect of the non-dimensional wave amplitude, magnetic field, rotation and non-dimensional volume flow on peristaltic flow are very pronounced. Keywords: Peristaltic Flow, Jeffrey Fluid, Rotation, Magnetic Field. 1. INTRODUCTION Peristalsis is defined as a wave of relaxation/contraction imparted to the walls of a flexible conduit, thereby pump- ing the enclosed material. Physiological flows, e.g., in the ureter and the esophagus, utilize this method of transport. Also, peristaltic finger and roller pumps are frequently used for corrosive or very pure materials so as to prevent direct contact of the fluid with the pump’s internal sur- faces. The mechanics of peristalsis have been examined by a number of investigators. Abd-Alla et al. 1 investigated the effect of the rotation, magnetic field and initial stress on peristaltic motion of micropolar fluid. Mahmoud et al. 2 discussed the effect of the rotation on wave motion through cylindrical bore in a micropolar porous medium. Hayat et al. 3 studied peristaltic transport of viscous fluid in a curved channel with compliant walls. Akbar et al. 4 pointed out the effects of heat and mass transfer on the peristaltic flow of hyperbolic tangent fluid in an annulus. Nadeem and Akbar 5 investigated the influence of heat and chem- ical reactions on Walter’s B fluid model for blood flow through a tapered artery. Ali et al. 6 studied the peristaltic flow of a Maxwell’s fluid in a channel with compliant walls. Srinivas and Kothandapani 7 discussed the influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls. Jiménez-Lozano and Sen 8 studied streamline topologies of two-dimensional ∗ Author to whom correspondence should be addressed. peristaltic flow and their bifurcations. Maiti and Misra 9 explained the peristaltic flow of a fluid in a porous chan- nel: A study having relevance to flow of bile within ducts in a pathological state. Koshel 10 made comments on “Peri- staltic flow of a Williamson fluid in an asymmetric chan- nel.” Yldrm and Sezer 11 investigated the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. Shkolnikov et al. 12 discussed a self- priming, roller-free, miniature, peristaltic pump operable with a single. Koch et al. 13 studied the PDMS and tubing- based peristaltic micropumps with direct actuation. Ali et al. 14 discussed Non-Newtonian fluid flow induced by peristaltic waves in a curved channel. Hayat et al. 15 stud- ied three-dimensional flow of a Jeffery fluid over a linearly stretching sheet. Nadeem and Akbar 16 discussed the influ- ence of heat transfer on a peristaltic transport of Herschel– Bulkley fluid in a non-uniform inclined tube. Hayat and Noreen 17 studied the peristaltic transport of fourth grade fluid with heat transfer and induced magnetic field. Hayat et al. 18 studied the effect of the induced magnetic field on peristaltic transport of a Carreau fluid. Tripathi 19 investi- gated a mathematical model for swallowing of food bolus through the esophagus under the influence of heat transfer. Abd-Alla et al. 20 investigated the wave propagation mod- eling in cylindrical human long wet bones with cavity. The extensive literature on the topic is now available and we can only mention a few recent interesting investigations in Refs. [21–29]. 1040 J. Comput. Theor. Nanosci. 2014, Vol. 11, No. 4 1546-1955/2014/11/1040/009 doi:10.1166/jctn.2014.3460