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Exact Analytical Solution for the Peristaltic Flow of Nanofluids in an Asymmetric Channel with Slip Effect of the Velocity, Temperature and Concentration

Published online by Cambridge University Press:  13 March 2014

E. H. Aly  and
A. Ebaid
E. H. Aly*
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia Department of Mathematics, Faculty of Education, Ain Shams University, Roxy 11757, Cairo, Egypt
A. Ebaid*
Affiliation:
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
*
1efarag@kau.edu.sa, emad-aly@hotmail.com
2aebaid@ut.edu.sa, halimgamil@yahoo.com
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Abstract

The peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.

In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

Keywords

NanofluidPeristaltic flowAsymmetric channelExact solutionSlip model
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 4 , August 2014 , pp. 411 - 422
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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