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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
*
1[email protected], [email protected]
2[email protected], [email protected]
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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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References

1.Latham, T. W., “Fluid Motion in a Peristaltic Pump,” M.Sc. Thesis, MIT, Cambridge, MA (1966).Google Scholar
2.Zien, T. F. and Ostrach, S. A., “A Long Wave Approximation to Peristaltic Motion,” Journal of Biomechanics, 3, pp. 63–75 (1970).Google Scholar
3.Lee, J. S. and Fung, Y. C., “Flow in Non-Uniform Small Blood Vessels,” Microvascular Research, 3, pp. 272–287 (1971).Google Scholar
4.Srivastava, L. M., Srivastava, V. P. and Sinha, S. N., “Peristaltic Transport of a Physiological Fluid: Part I. Flow in Non-Uniform Geometry,” Biorheology, 20, pp. 153–166 (1983).CrossRefGoogle ScholarPubMed
5.Takabatake, S., Ayukawa, K. and Mori, A., “Peristaltic Pumping in Circular Cylindrical Tubes: A Numerical Study of Fluid Transport and Its Efficiency,” Journal of Fluid Mechanics, 193, pp. 267–283 (1988).Google Scholar
6.Srivastava, L. M. and Srivastava, V. P., “Peristaltic Transport of a Power-Law Fluid: Application to the Ductus Efferentes of the Reproductive Tract,” Rheology Acta, 27, pp. 428–433 (1988).Google Scholar
7.Elshehawey, E. F. and Mekheimer, Kh. S., “Couple-Stresses in Peristaltic Transport of Fluids,” Journal of Physics D: Applied Physics, 27, pp. 1163–1170 (1994).Google Scholar
8.Ramachandra, R. A. and Usha, S., “Peristaltic Transport of Two Immiscible Viscous Fluids in a Circular Tube,” Journal of Fluid Mechanics, 298, pp. 271–285 (1995).Google Scholar
9.Misra, J. C.Pandey, S. K., “Peristaltic Transport in a Tapered Tube,” Mathematical and Computer Modelling, 22, pp. 137–161 (1995).CrossRefGoogle Scholar
10.Mekheimer, Kh. S., “Peristaltic Transport of a Couple-Stress Fluid in a Uniform and Nonuniform Channels,” Biorheology, 39, pp. 755–765 (2002).Google Scholar
11.Vajravelu, K., Sreenadh, S. and Babu, V. R., “Peristaltic Transport of a Herschel-Bulkley Fluid in an Inclined Tube,” International Journal of Non-Linear Mechanics, 40, pp. 83–90 (2005).Google Scholar
12.Mekheimer, Kh. S. and Abd Elmaboud, Y., “The Influence of Heat Transfer and Magnetic Field on Peristaltic Transport of a Newtonian Fluid in a Vertical Annulus: Application of an Endoscope,” Physics Letters A, 372, pp. 1657–1665 (2008).Google Scholar
13.Mekheimer, Kh. S.Abd Elmaboud, Y., “Peristaltic Flow of a Couple Stress Fluid in an Annulus: Application of an Endoscope,” Physica A, 387, pp. 2403–2415 (2008).Google Scholar
14.De., Vries K., Lyons, E. A., Ballard, J., Levi, C. S. and Lindsay, D. J., “Contractions of the Inner Third of Myometrium,” America Journal of Obstetrics Gynecol, 162, pp. 679–682 (1990).Google Scholar
15.Eytan, O., Jaffa, A. J. and Elad, D., “Peristaltic Flow in a Tapered Channel: Application to Embryo Transport Within the Uterine Cavity,” Medical Engineering & Physics, 23, pp. 475–484 (2001).Google Scholar
16.Eytan, O., Jaffa, A. J. and Elad, D., “Peristaltic Transport in an Asymmetric Channel Through a Porous Medium,” Applied Mathematics and Computers, 182, pp. 140–150 (2006).Google Scholar
17.Subba Reddy, M. V., Rao, A. R. and Sreenadh, A., “Peristaltic Motion of a Power-Law Fluid in an Asymmetric Channel,” International Journal of Non-Linear Mechanics, 42, pp. 1153–1161 (2007).Google Scholar
18.Ebaid, A., “Effects of Magnetic Field and Wall Slip Conditions on the Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel,” Physics Letters, Section A: General, Atomic and Solid State Physics, 372, pp. 4493–4499 (2008).Google Scholar
19.Sobh, A. M., “Slip Flow in Peristaltic Transport of a Carreau Fluid in an Asymmetric Channel,” Canadian Journal of Physics, 87, pp. 957–965 (2009).CrossRefGoogle Scholar
20.Shit, G. C., Roy, M. and Ng, E. Y. K., “Effect of Induced Magnetic Field on Peristaltic Flow of a Micropolar Fluid in an Asymmetric Channel,” International Journal for Numerical Methods Biomedical Engineering, 26, pp. 1380–1403 (2010).Google Scholar
21.Yildirim, A. and Sezer, S. A., “Effects of Partial Slip on the Peristaltic Flow of a MHD Newtonian Fluid in an Asymmetric Channel,” Mathematical and Computer Modelling, 52, pp. 618–625 (2010).Google Scholar
22.Mekheimer, Kh. S., Husseny, S. Z. A. and Abd Elmaboud, Y., “Effects of Heat Transfer and Space Porosity on Peristaltic Flow in a Vertical Asymmetric Channel,” Numerical Methods for Partial Differential Equations, 26, pp. 747–770 (2010).CrossRefGoogle Scholar
23.Mekheimer, K. S., Husseny, S. Z.-A. and Abd El Lateef, A. I., “Effect of Lateral Walls on Peristaltic Flow Through an Asymmetric Rectangular Duct,” Applied Bionics Biomechanics, 8, pp. 295–308 (2011).Google Scholar
24.Eytan, O., Jaffa, A. J. and Elad, D., “Effects of Chemical Reaction and Space Porosity on MHD Mixed Convective Flow in a Vertical Asymmetric Channel with Peristalsis,” Mathematics Computer Modeling, 54, pp. 1213–1227 (2011).Google Scholar
25.Pandey, S. K. and Chaube, M. K., “Peristaltic Transport of a Maxwell Fluid in a Channel of Varying Cross Section Induced by Asymmetric Waves: Application to Embryo Transport Within Uterine Cavity,” Journal of Mechanics Medicine Biology, 11, pp. 675–690 (2011).CrossRefGoogle Scholar
26.Srinivas, S., Gayathri, R. and Kothandapani, M., “Mixed Convective Heat and Mass Transfer in an Asymmetric Channel with Peristalsis,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 1845–1862 (2011).Google Scholar
27.Das, K., “Influence of Slip and Heat Transfer on Mhd Peristaltic Flow of a Jeffrey Fluid in an Inclined Asymmetric Porous Channel,” Indian Journal of Mathematics, 54, pp. 19–45 (2012).Google Scholar
28.Abd Elmaboud, Y., Mekheimer, Kh. S. and Abdellateef, A. I., “Thermal Properties of Couple-Stress Fluid Flow in an Asymmetric Channel with Peristalsis,” Journal of Heat Transfer, 135, art. no. 044502 (2013).Google Scholar
29.Eytan, O., Jaffa, A. J. and Elad, D., “Endoscopic Effects on Peristaltic Flow of a Nanofluid,” Communications in Theoretical Physics, 56, p. 761 (2011).Google Scholar
30.Akbar, N. S., Nadeem, S., Hayat, T. and Hendi, A. A., “Peristaltic Flow of a Nanofluid in a Non-Uniform Tube,” Heat and Mass Transfer, 48, pp. 451–459 (2012).Google Scholar
31.Akbar, N. S. and Nadeem, S., “Peristaltic Flow of a Phan-Thien-Tanner Nanofluid in a Diverging Tube,” Heat Transfer, 41, pp. 10–22 (2012).Google Scholar
32.Mustafa, M., Hina, S., Hayat, T. and Alsaedi, A., “Influence of Wall Properties on the Peristaltic Flow of a Nanofluid: Analytic and Numerical Solutions,” International Journal of Heat and Mass Transfer, 55, pp. 4871–4877 (2012).Google Scholar
33.Akbar, N. S., Nadeem, S., Hayat, T. and Hendi, A. A., “Peristaltic Flow of a Nanofluid with Slip Effects,” Meccanica, 47, pp. 1283–1294 (2012).Google Scholar
34.Bég, O. A. and Tripathi, D., “Mathematica Simulation of Peristaltic Pumping with Double-Diffusive Convection in Nanofluids: A Bio-Nano-Engineering Model,” Journal of Nanoengineering Nanosystems, DOI: 10.1177/1740349912437087 (2012).Google Scholar
35.Choi, S. U. S., “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, U.S.A., ASME, FED 231/MD 66, p. 99 (1995).Google Scholar
36.Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E. and Grulke, E. A., “Anomalously Thermal Conductivity Enhancement in Nanotube Suspension,” Applied Physics Letters, 79, pp. 2252–2254 (2001).Google Scholar
37.Pankhurst, Q. A., Connolly, J., Jones, S. K. and Dobson, J., “Applications of Magnetic Nanoparticles in Biomedicine,” Journal of Physics D: Applied Physics, pp. 167–181 (2003).Google Scholar
38.Habibi, M. R., Ghassemi, M. and Hamedi, M. H., “Analysis of High Gradient Magnetic Field Effects on Distribution of Nanoparticles Injected Into Pulsatile Blood Stream,” Journal of Magnetism Magnetic Materials, 324, pp. 1473–1482 (2012).CrossRefGoogle Scholar
39.Mishra, M. and Rao, A. R., “Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel,” ZAMP, 53, pp. 532–550 (2003).Google Scholar