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The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid

Author

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  • S. M. Khaled
  • Abdelhalim Ebaid
  • Fahd Al Mutairi

Abstract

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.

Suggested Citation

  • S. M. Khaled & Abdelhalim Ebaid & Fahd Al Mutairi, 2014. "The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:367526
    DOI: 10.1155/2014/367526
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    1. Emad H. Aly & Abdelhalim Ebaid, 2014. "Effect of the Velocity Second Slip Boundary Condition on the Peristaltic Flow of Nanofluids in an Asymmetric Channel: Exact Solution," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, March.
    2. Abdelhalim Ebaid & S. M. Khaled, 2014. "An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    3. Abdelhalim Ebaid & S. M. Khaled, 2014. "An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Emad H. Aly & Abdelhalim Ebaid, 2014. "Effect of the Velocity Second Slip Boundary Condition on the Peristaltic Flow of Nanofluids in an Asymmetric Channel: Exact Solution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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