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Journal of Engineering
Volume 2016, Article ID 9718786, 10 pages
http://dx.doi.org/10.1155/2016/9718786
Research Article

Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

Young Researchers and Elites Club, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received 19 November 2015; Revised 9 March 2016; Accepted 24 April 2016

Academic Editor: Oronzio Manca

Copyright © 2016 Meysam Mohamadali and Nariman Ashrafi. 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. L. T. Wardhaugh and D. V. Boger, “Flow characteristics of waxy crude oils: application to pipeline design,” AIChE Journal, vol. 37, no. 6, pp. 871–885, 1991. View at Publisher · View at Google Scholar · View at Scopus
  2. S. G. Hatzikiriakos, G. Heffner, D. Vlassopoulos, and K. Christodoulou, “Rheological characterization of polyethylene terephthalate resins using a multimode Phan-Tien-Tanner constitutive relation,” Rheologica Acta, vol. 36, no. 5, pp. 568–578, 1997. View at Publisher · View at Google Scholar · View at Scopus
  3. V. Ngamaramvaranggul and M. F. Webster, “Simulation of pressure-tooling wire-coating flow with Phan-Thien/Tanner models,” International Journal for Numerical Methods in Fluids, vol. 38, no. 7, pp. 677–710, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar · View at Scopus
  5. K. V. Prasad, S. R. Santhi, and P. S. Datti, “Non-Newtonian power-law fluid flow and heat transfer over a non-linearly stretching surface,” Applied Mathematics, vol. 3, no. 5, pp. 425–435, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. H. Xu and S.-J. Liao, “Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet,” Computers & Mathematics with Applications, vol. 57, no. 9, pp. 1425–1431, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. S. Abel, P. S. Datti, and N. Mahesha, “Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source,” International Journal of Heat and Mass Transfer, vol. 52, no. 11-12, pp. 2902–2913, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. C. Wang, “Analytic solutions for a liquid film on an unsteady stretching surface,” Heat and Mass Transfer, vol. 42, no. 8, pp. 759–766, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. K. Atalık, “Group theoretical analysis and similarity solutions for stress boundary layers in viscoelastic flows,” Journal of Non-Newtonian Fluid Mechanics, vol. 153, no. 1, pp. 62–71, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. I. A. Hassanien, “Flow and heat transfer from a continuous surface in a parallel free stream of viscoelastic second-order fluid,” Applied Scientific Research, vol. 49, no. 4, pp. 335–344, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. H. Schichting, Boundary Layer Theory, chapter 97, McGraw Hill, New York, NY, USA, 6th edition, 1964.
  12. T. Hayat, C. Fetecau, Z. Abbas, and N. Ali, “Flow of a Maxwell fluid between two side walls due to a suddenly moved plate,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 2288–2295, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. S. Shateyi, “A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction,” Boundary Value Problems, vol. 2013, article 96, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Fetecau, M. Jamil, C. Fetecau, and I. Siddique, “A note on the second problem of Stokes for Maxwell fluids,” International Journal of Non-Linear Mechanics, vol. 44, no. 10, pp. 1085–1090, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. M. B. Ashraf, T. Hayat, S. A. Shehzad, and A. Alsaedi, “Mixed convection radiative flow of three dimensional Maxwell fluid over an inclined stretching sheet in presence of thermophoresis and convective condition,” AIP Advances, vol. 5, no. 2, Article ID 027134, pp. 761–768, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Awais, T. Hayat, A. Alsaedi, and S. Asghar, “Time-dependent three-dimensional boundary layer flow of a Maxwell fluid,” Computers and Fluids, vol. 91, pp. 21–27, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. K. R. Rajagopal, “Boundary layers in non-linear fluids,” in Trends in Applications of Mathematics to Mechanics, M. D. P. Monteivo Marques and J. F. Rodriques, Eds., vol. 77 of Pittman Monographs and Surveys in Pure and Applied Mathematics, Longman, 1995. View at Google Scholar
  18. D. V. Boger and K. Walters, Rheological Phenomena in Focus, Elsevier Science, Amsterdam, Netherlands, 1993.
  19. M. Renardy and X. Wang, “Boundary layers for the upper convected Maxwell fluid,” Journal of Non-Newtonian Fluid Mechanics, vol. 189-190, pp. 14–18, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Renardy, “High Weissenberg number boundary layers for the upper convected Maxwell fluid,” Journal of Non-Newtonian Fluid Mechanics, vol. 68, no. 1, pp. 125–132, 1997. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Hagen and M. Renardy, “Boundary layer analysis of the Phan-Thien-Tanner and Giesekus model in high Weissenberg number flow,” Journal of Non-Newtonian Fluid Mechanics, vol. 73, no. 1-2, pp. 181–189, 1997. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Renardy, “Prandtl boundary layers for the Phan-Thien TANner and Giesekus fluid,” Zeitschrift für angewandte Mathematik und Physik, vol. 66, no. 3, pp. 1061–1070, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. Renardy, “Wall boundary layers for Maxwell liquids,” Archive for Rational Mechanics and Analysis, vol. 152, no. 2, pp. 93–102, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. M. Renardy and X. Wang, “Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids,” Journal of Mathematical Fluid Mechanics, vol. 16, no. 1, pp. 179–191, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. M. Renardy, “The initial value problem for creeping flow of the upper convected Maxwell fluid at high Weissenberg number,” Mathematical Methods in the Applied Sciences, vol. 38, no. 5, pp. 959–965, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. G. I. Ogilvie and M. R. Proctor, “On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities,” Journal of Fluid Mechanics, vol. 476, pp. 389–409, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  27. R. B. Bird and R. C. Armstrong, Dynamics of Polymeric Liquids, vol. 1, John Wiley & Sons, New York, NY, USA, 2nd edition, 1987.
  28. H. I. Andersson and V. Kumaran, “On sheet-driven motion of power-law fluids,” International Journal of Non-Linear Mechanics, vol. 41, no. 10, pp. 1228–1234, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. J. D. Evans, “Re-entrant corner flows of the upper convected Maxwell fluid,” Proceedings of The Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, vol. 461, no. 2053, pp. 117–142, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. M. Renardy, “A matched solution for corner flow of the upper convected Maxwell fluid,” Journal of Non-Newtonian Fluid Mechanics, vol. 58, no. 1, pp. 83–89, 1995. View at Publisher · View at Google Scholar · View at Scopus
  31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, vol. 77 of Fortran, Cambridge University Press, New York, NY, USA, 2nd edition, 2007.