Table of Contents Author Guidelines Submit a Manuscript
Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 825376, 8 pages
http://dx.doi.org/10.1155/2013/825376
Research Article

Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment

1Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt

Received 31 May 2013; Accepted 3 August 2013

Academic Editor: Gabriel Turinici

Copyright © 2013 Abdelhalim Ebaid and Emad H. Aly. 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.

Linked References

  1. T. W. Latham, Fluid motion in a peristaltic pump [M.S. thesis], MIT, Cambridge, UK, 1966.
  2. T.-F. Zien and S. Ostrach, “A long wave approximation to peristaltic motion,” Journal of Biomechanics, vol. 3, no. 1, pp. 63–75, 1970. View at Google Scholar · View at Scopus
  3. J.-S. Lee and Y.-C. Fung, “Flow in nonuniform small blood vessels,” Microvascular Research, vol. 3, no. 3, pp. 272–287, 1971. View at Google Scholar · View at Scopus
  4. L. M. Srivastava, V. P. Srivastava, and S. N. Sinha, “Peristaltic transport of a physiological fluid. Part I. Flow in non-uniform geometry,” Biorheology, vol. 20, no. 2, pp. 153–166, 1983. View at Google Scholar · View at Scopus
  5. S. Takabatake, K. Ayukawa, and A. Mori, “Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency,” Journal of Fluid Mechanics, vol. 193, pp. 267–283, 1988. View at Google Scholar · View at Scopus
  6. E. F. El Shehawey and K. S. Mekheimer, “Couple-stresses in peristaltic transport of fluids,” Journal of Physics D, vol. 27, no. 6, pp. 1163–1170, 1994. View at Publisher · View at Google Scholar · View at Scopus
  7. R. A. Ramachandra and S. Usha, “Peristaltic transport of two immiscible viscous fluids in a circular tube,” Journal of Fluid Mechanics, vol. 298, pp. 271–285, 1995. View at Google Scholar · View at Scopus
  8. K. S. Mekheimer, “Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels,” Biorheology, vol. 39, no. 6, pp. 755–765, 2002. View at Google Scholar · View at Scopus
  9. K. Vajravelu, S. Sreenadh, and V. R. Babu, “Peristaltic transport of a Herschel-Bulkley fluid in an inclined tube,” International Journal of Non-Linear Mechanics, vol. 40, no. 1, pp. 83–90, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. K. S. Mekheimer and Y. Abd elmaboud, “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, vol. 372, no. 10, pp. 1657–1665, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. K. S. Mekheimer and Y. Abd elmaboud, “Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope,” Physica A, vol. 387, no. 11, pp. 2403–2415, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. K. De Vries, E. A. Lyons, G. Ballard, C. S. Levi, and D. J. Lindsay, “Contractions of the inner third of the myometrium,” American Journal of Obstetrics and Gynecology, vol. 162, no. 3, pp. 679–682, 1990. View at Google Scholar · View at Scopus
  13. O. Eytan, A. J. Jaffa, and D. Elad, “Peristaltic flow in a tapered channel: application to embryo transport within the uterine cavity,” Medical Engineering and Physics, vol. 23, no. 7, pp. 473–482, 2001. View at Google Scholar · View at Scopus
  14. E. F. Elshehawey, N. T. Eldabe, E. M. Elghazy, and A. Ebaid, “Peristaltic transport in an asymmetric channel through a porous medium,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 140–150, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. M. V. Subba Reddy, A. Ramachandra Rao, and S. Sreenadh, “Peristaltic motion of a power-law fluid in an asymmetric channel,” International Journal of Non-Linear Mechanics, vol. 42, no. 10, pp. 1153–1161, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Ebaid, “Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel,” Physics Letters A, vol. 372, no. 24, pp. 4493–4499, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. A. M. Sobh, “Slip flow in peristaltic transport of a Carreau fluid in an asymmetric channel,” Canadian Journal of Physics, vol. 87, no. 8, pp. 957–965, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. G. C. Shit, M. Roy, and E. Y. K. Ng, “Effect of induced magnetic field on peristaltic flow of a micropolar fluid in an asymmetric channel,” International Journal for Numerical Methods in Biomedical Engineering, vol. 26, no. 11, pp. 1380–1403, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. K. S. Mekheimer, S. Z. A. Husseny, and Y. Abd Elmaboud, “Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel,” Numerical Methods for Partial Differential Equations, vol. 26, no. 4, pp. 747–770, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Srinivas and R. Muthuraj, “Effects of chemical reaction and space porosity on MHD mixed convective flow in a vertical asymmetric channel with peristalsis,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1213–1227, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Srinivas, R. Gayathri, and M. Kothandapani, “Mixed convective heat and mass transfer in an asymmetric channel with peristalsis,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 1845–1862, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Das, “Influence of slip and heat transfer on mhd peristaltic flow of a jeffrey fluid in an inclined asymmetric porous channel,” Indian Journal of Mathematics, vol. 54, pp. 19–45, 2012. View at Google Scholar
  23. Y. Abd Elmaboud, S. Kh. Mekheimer, and A. I. Abdellateef, “Thermal properties of couple-stress fluid flow in an asymmetric channel with peristalsis,” Journal of Heat Transfer, vol. 135, no. 4, 8 pages, 2013. View at Publisher · View at Google Scholar
  24. N. S. Akbar and S. Nadeem, “Thermal and velocity slip effects on the peristaltic flow of a six constant Jeffrey's fluid model,” International Journal of Heat and Mass Transfer, vol. 55, no. 15-16, pp. 3964–3970, 2012. View at Publisher · View at Google Scholar · View at Scopus
  25. N. S. Akbar and S. Nadeem, “Numerical and analytical simulation of the peristaltic flow of Jeffrey fluid with Reynold’s model of viscosity,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22, pp. 458–472, 2012. View at Google Scholar
  26. N. S. Akbar, S. Nadeem, T. Hayat, and A. A. Hendi, “Analytical and numerical analysis of Vogel's model of viscosity on the peristaltic flow of Jeffrey fluid,” Journal of Aerospace Engineering, vol. 25, no. 1, pp. 64–70, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. N. S. Akbar and S. Nadeem, “Analytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope,” Chinese Physics B, vol. 22, no. 1, Article ID 014703, 2013. View at Publisher · View at Google Scholar
  28. N. S. Akbar and S. Nadeem, “Mixed convective magnetohydrodynamic peristaltic flow of a Jeffrey nanofluid with Newtonian heating,” Zeitschrift für Naturforschung, vol. 68, pp. 433–441, 2013. View at Google Scholar
  29. N. S. Akbar and S. Nadeem, “Endoscopic effects on peristaltic flow of a nanofluid,” Communications in Theoretical Physics, vol. 56, no. 4, pp. 761–768, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. N. S. Akbar, S. Nadeem, T. Hayat, and A. A. Hendi, “Peristaltic flow of a nanofluid in a non-uniform tube,” Heat and Mass Transfer/Waerme-und Stoffuebertragung, vol. 48, no. 2, pp. 451–459, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. N. S. Akbar and S. Nadeem, “Peristaltic flow of a Phan-Thien-Tanner nanofluid in a diverging tube,” Heat Transfer, vol. 41, no. 1, pp. 10–22, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. M. Mustafa, S. Hina, T. Hayat, and A. Alsaedi, “Influence of wall properties on the peristaltic flow of a nanofluid: analytic and numerical solutions,” International Journal of Heat and Mass Transfer, vol. 55, pp. 4871–4877, 2012. View at Google Scholar
  33. N. S. Akbar, S. Nadeem, T. Hayat, and A. A. Hendi, “Peristaltic flow of a nanofluid with slip effects,” Meccanica, vol. 47, pp. 1283–1294, 2012. View at Google Scholar
  34. O. A. Bég and D. Tripathi, “Mathematica simulation of peristaltic pumping with double-diffusive convection in nanofluids: a bio-nano-engineering model,” Journal of Nanoengineering and Nanosystems, 2012. View at Publisher · View at Google Scholar
  35. S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in The Proceedings of the ASME International Mechanical Engineering Congress and Exposition, ASME, San Francisco, Calif, USA.
  36. S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood, and E. A. Grulke, “Anomalous thermal conductivity enhancement in nanotube suspensions,” Applied Physics Letters, vol. 79, no. 14, pp. 2252–2254, 2001. View at Publisher · View at Google Scholar · View at Scopus
  37. Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” Journal of Physics D, vol. 36, no. 13, pp. R167–R181, 2003. View at Publisher · View at Google Scholar · View at Scopus
  38. M. R. Habibi, M. Ghassemi, and M. H. Hamedi, “Analysis of high gradient magnetic field effects on distribution of nanoparticles injected into pulsatile blood stream,” Journal of Magnetism and Magnetic Materials, vol. 324, no. 8, pp. 1473–1482, 2012. View at Publisher · View at Google Scholar · View at Scopus
  39. M. Majumder, N. Chopra, R. Andrews, and B. J. Hinds, “Nanoscale hydrodynamics: enhanced flow in carbon nanotubes,” Nature, vol. 438, no. 7064, p. 44, 2005. View at Publisher · View at Google Scholar · View at Scopus
  40. M. Mishra and A. R. Rao, “Peristaltic transport of a Newtonian fluid in an asymmetric channel,” Zeitschrift fur Angewandte Mathematik und Physik, vol. 54, no. 3, pp. 532–550, 2003. View at Publisher · View at Google Scholar · View at Scopus