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Journal of Applied Mathematics
Volume 2014, Article ID 367526, 11 pages
Research Article

The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid

1Department of Mathematics, Faculty of Sciences, Helwan University, Cairo, Egypt
2Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Saudi Arabia
3Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
4Department of Chemical Engineering, Faculty of Engineering, University of Tabuk, Saudi Arabia

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. This 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.


The problem of the peristaltic flow of a nanofluid under the effect of an endoscope is reinvestigated. The mathematical model is governed by a system of linear and nonlinear partial differential 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 different 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 effect of various parameters on the temperature distribution, the nanoparticle concentration, the pressure gradient, and the pressure rise has been also discussed through graphs.