Research Article The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid S. M. Khaled, 1,2 Abdelhalim Ebaid, 3 and Fahd Al Mutairi 4 1 Department of Mathematics, Faculty of Sciences, Helwan University, Cairo, Egypt 2 Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Saudi Arabia 3 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia 4 Department of Chemical Engineering, Faculty of Engineering, University of Tabuk, Saudi Arabia Correspondence should be addressed to Abdelhalim Ebaid; aebaid@ut.edu.sa Received 17 July 2014; Revised 16 October 2014; Accepted 26 October 2014; Published 18 November 2014 Academic Editor: Nicolae Herisanu Copyright © 2014 S. M. Khaled et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te problem of the peristaltic fow of a nanofuid under the efect of an endoscope is reinvestigated. Te mathematical model is governed by a system of linear and nonlinear partial diferential equations with prescribed boundary conditions. Really, the exact solution for any physical problem, if available, is of great importance which inevitably leads to a better understanding of the behaviour of the involved physical phenomena. An attempt for doing so has been done in the present paper, where the temperature equation is solved exactly by the help of Laplace transform and, accordingly, the exact expressions for the nanoparticle concentration, the axial velocity, the pressure gradient, and the pressure rise are established. Furthermore, it is showed in this paper that the physical interpretations of some involved phenomena are found totally diferent than those previously obtained by the approximate solutions using the homotopy perturbation method. In addition, several comparisons between the current results and the approximate ones have been displayed. Finally, the efect of various parameters on the temperature distribution, the nanoparticle concentration, the pressure gradient, and the pressure rise has been also discussed through graphs. 1. Introduction Te subject of peristaltic fow of classical Newtonian and non-Newtonian fuids has a long history [1–7]. It was and is still of interest to many researchers because of its medical and engineering applications. For example, Mekheimer and Abd elmaboud [8] showed that the peristaltic fow of blood with bioheat transfer is of great importance in destroying undesirable tissues, such as cancer. It was also clarifed in [9] that, in the case of hyperthermia, the tissue can be destroyed when heated to 42–45 ∘ C. In addition, peristaltic fow occurs widely in the functioning of the ureter, chyme movement in the intestine, movement of eggs in the fallopian tube, the transport of the spermatozoa in cervical canal, transport of bile in the bile duct, transport of cilia, circulation of blood in small blood vessels, and the transport of intrauterine fuid within the cavity of the uterus. Nowadays, nanotechnology is widely used in industry since materials with sizes of nanometers possess unique physical and chemical properties. Normally, if the particle sizes are in the 1–100 nm ranges, they are generally called nanoparticles, 1 nm (nano-meter) = 10 −9 meters. Nanoscale particle added fuids are called nanofuid. Te term nanofuid was frst used by Choi [10] to describe a fuid in which nanometer-sized particles are suspended in conventional heat transfer basic fuids. Fluids such as oil, water, and ethylene glycol mixture are poor heat transfer fuids, since the thermal conductivity of these fuids plays an important role in the heat transfer coefcient between the heat transfer medium and the heat transfer surface. Numerous methods have been followed to improve the thermal conductivity of these fuids by suspending nano/micro or larger-sized particle materials in liquids. An innovative technique to improve heat transfer is by using nanoscale particles in the base fuid [10]. Choi et al. [11] showed that the addition of a small amount (less than 1% by volume) of nanoparticles to conventional heat transfer liquids increased the thermal conductivity of the fuid up to approximately two times. Tis Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 367526, 11 pages http://dx.doi.org/10.1155/2014/367526