Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-18T09:17:10.025Z Has data issue: false hasContentIssue false
  • English
  • Français

MHD Peristaltic Flow in a Curved Channel with Convective Condition

Published online by Cambridge University Press:  19 September 2016

T. Hayat ,
S. Farooq  and
A. Alsaedi
T. Hayat
Affiliation:
Department of MathematicsQuaid-I-Azam UniversityIslamabad, Pakistan Nonlinear Analysis and Applied Mathematics Research GroupDepartment of MathematicsKing Abdulaziz UniversityJeddah, Saudi Arabia
S. Farooq*
Affiliation:
Department of MathematicsQuaid-I-Azam UniversityIslamabad, Pakistan
A. Alsaedi
Affiliation:
Nonlinear Analysis and Applied Mathematics Research GroupDepartment of MathematicsKing Abdulaziz UniversityJeddah, Saudi Arabia
*
*Corresponding author (farooq.fmg89@yahoo.com)
Get access

Abstract

This attempt addresses the peristaltic transport of Jeffrey fluid in a curved channel. Heat transfer is discussed employing convective condition at the channel walls. Effects of radial applied magnetic field and Joule heating are retained. Convective boundary conditions at both walls with different temperature are also accounted. The relevant equations are modeled in view of lubrication approach. Closed form expression for stream function is constructed. Numerical solution of stream function, velocity and temperature is obtained via shooting method in Mathematica with the help of NDSolve command. It is observed that curvature has opposite effects on the lower and upper walls of channel. However temperature is an increasing function of curvature parameter. Temperature also decreases in presence of heat transfer convective parameter naturally the Biot number.

Keywords

Jeffrey fluidJoule heatingConvective conditionRadial applied magnetic field
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 4 , August 2017 , pp. 483 - 499
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Latham, T. W., “Fluid motion in peristaltic pump,” M. S Thesis, Massachusetts Institute of Technology, Cambridge Massachusetts, U.S.A (1966).Google Scholar
2. Shapiro, A. H., Jaffrin, M. Y. and Weinberg, S. L., “Peristaltic pumping with long wavelength at low Reynolds number,” Journal of Fluid Mechanics, 37, pp. 799–825 (1969).CrossRefGoogle Scholar
3. Shapiro, A. H., “Pumping and retrograde diffusion in peristaltic waves,” Proceedings of the Workshop Ureteral Reftm Children, National Academy of Science, Washington, D.C., U.S. (1967).Google Scholar
4. Fung, Y. C., “Peristaltic pumping: a bio engineering model,” Proceedings of the Workshop Ureteral Reftm Children, National Academy of Science, Washington, D.C., U.S. (1971).Google Scholar
5. Hayat, T., Ali, N. and Asghar, S., “An analysis of peristaltic transport for flow of a Jeffrey fluid,” Acta Mechanica, 193, pp. 101–112 (2007).CrossRefGoogle Scholar
6. Hayat, T., Yasmin, H., Alhuthali, M. S. and Kutbi, M. A., “Peristaltic flow of a non-Newtonian fluid in an asymmetric channel with convective boundary conditions,” Journal of Mechanics, 29, pp. 599–607.Google Scholar
7. Ebaid, A., “Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with nano-particles in an asymmetric channel,” Computers & Mathematics with Applications, 68, pp. 77–85 (2014).Google Scholar
8. Nadeem, S. and Akram, S., “Peristaltic flow of a Jeffrey fluid in a rectangular duct,” Nonlinear Analysis: Real World Applications, 11, pp. 4238–4247 (2010).Google Scholar
9. Kothandapani, M. and Srinivas, S., “Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel,” International Journal of Non-Linear Mechanics, 43, pp. 915–924 (2008).Google Scholar
10. Hayat, T. and Ali, N., “Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube,” Communications in Nonlinear Science and Numerical Simulation, 13, pp. 1343–1352 (2008).Google Scholar
11. Hayat, T., Ahmad, N. and Ali, N., “Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid” Communications in Nonlinear Science and Numerical Simulation, 13, pp. 1581–1591 (2008).Google Scholar
12. Tripathi, D. and Beg, O. A., “A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping,” Proceedings of the institution of mechanical Engineers, Part H: Journal of Engineering in Medicine, DOI: 10.1177/0954411912449946 (2012).CrossRefGoogle Scholar
13. Jalilian, E., Onen, D., Neshev, E. and Mintchev, M. P., “Implantable neural electrical stimulator for external control of gastrointestinal motility,” Medical Engineering & Physics, 29, pp. 238–252 (2007).CrossRefGoogle ScholarPubMed
14. Wang, Y., Ali, N., Hayat, T. and Oberlack, M., “Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube,” Applied Mathematical Modelling, 35, pp. 3737–3750 (2011).CrossRefGoogle Scholar
15. Hayat, T., Nisar, Z., Ahmad, B. and Yasmin, H., “Simultaneous effects of slip and wall properties on MHD peristaltic motion of nanofluid with Joule heating,” Journal of Magnetism and Magnetic Materials, 395, pp. 48–58 (2015).Google Scholar
16. Srinivas, S., Gayathri, R. and Kothandapani, M., “The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport,” Journal of Magnetism and Magnetic Materials, 180, pp. 2115–2122 (2009).Google Scholar
17. Hayat, T. and Hina, S., “The influence of wall properties on the MHD peristaltic flow of a Maxwell fluid with heat and mass transfer,” Nonlinear Analysis: Real World Applications, 11, pp. 3155–3169 (2010).Google Scholar
18. Srinivas, S. and Muthuraj, R., “Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis” Mathematical and Computer Modelling, 54, pp. 1213–1227 (2011).Google Scholar
19. Hina, S., “MHD peristaltic transport of Eyring--Powell fluid with heat/mass transfer, wall properties and slip conditions,” Journal of Magnetism and Magnetic Materials, 404, pp. 148–158 (2016).Google Scholar
20. Hayat, T., Noreen, S., Alhothuali, M. S., Asghar, S. and Alhomaidan, A. “Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer,” International Journal of Heat and Mass Transfer, 55, pp. 443–452 (2012).CrossRefGoogle Scholar
21. Naby, Abd El., Hakeem, Abd El., El Misery, A. E. M., and Abd El Kareem, M. F., “Effects of a magnetic field on trapping through peristaltic motion for generalized Newtonian fluid in channel,” Physica A: Statistical Mechanics and its Applications, 367, pp. 79–92 (2006).Google Scholar
22. Hayat, T., Iqbal, M., Yasmin, H., Alsaadi, F. and Alotaibi, N., “Nonlinear peristaltic flow of a Carreau fluid in the presence of hall current and convective effect,” The European Physical Journal Plus, 129, pp. 1–16 (2014).Google Scholar
23. Hayat, T., Yasmin, H., Ahmad, B. and Chen, B., “Simultaneous effects of convective conditions and nanoparticles on peristaltic motion,” Journal of Molecular Liquids, 193, pp. 74–82 (2014).Google Scholar
24. Awais, M., Farooq, S., Yasmin, H., Hayat, T. and Alsaedi, A., “Convective heat transfer analysis for MHD peristaltic flow of Jeffrey fluid in an asymmetric channel,” International Journal of Biomathematics, 7, 1450023 (2014).Google Scholar
25. Hayat, T., Bibi, S., Rafiq, M., Alsaedi, A. and Abbasi, F. M., “Effect of an inclined magnetic field on peristaltic flow of Williamson fluid in an inclined channel with convective conditions,” Journal of Magnetism and Magnetic Materials, 401, pp. 733–745 (2016).Google Scholar
26. Abbasi, F. M., Hayat, T. and Ahmad, B., “Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating,” Journal of Central South University, 21, pp. 1411–1416 (2014).Google Scholar
27. Sato, H., Kawai, T., Fujita, T. and Okabe, M., “Two dimensional peristaltic flow in curved channels,” The Japan Society of Mechanical Engineers B, 66, pp. 679–685 (2000).CrossRefGoogle Scholar
28. Ali, N., Sajid, M. and Hayat, T., “Long wavelength flow analysis in a curved channel,” Zeitschrift für Naturforschung A, 65, pp. 191–196 (2010).CrossRefGoogle Scholar
29. Ali, N., Sajid, M., Javed, T. and Abbas, Z., “Non-Newtonian fluid flow induced by peristaltic waves in a curved channel,” European Journal of Mechanics - B/Fluids, 29, pp. 387–394 (2010).CrossRefGoogle Scholar
30. Hayat, T., Quratulain, ., Rafiq, M., Alsaadi, F. and Ayub, M., “Soret and Dufour effects on peristaltic transport in curved channel with radial magnetic field and convective conditions,” Journal of Magnetism and Magnetic Materials, 405, pp. 358–369 (2016).Google Scholar
31. Hayat, T., Abbasi, F. M., Ahmed, B. and Alsaedi, A., “Peristaltic transport of Carreau-Yasuda fluid in a curved channel with slip effects,” PLOS ONE, 9, e95070 (2014).Google Scholar
32. Hina, S., Mustafa, M., Hayat, T., and Alotaibi, N. D., “On peristaltic motion of pseudoplastic fluid in a curved channel with heat/mass transfer and wall properties,” Applied Mathematics and Computation, 263, pp. 378–391 (2015).Google Scholar
33. Hayat, T., Tanveer, A. and Alsaadi, F., “Simultaneous effects of radial magnetic field and wall properties on peristaltic flow of Carreau-Yasuda fluid in curved flow configuration,” AIP Advances, 5, 127234 (2015).Google Scholar