- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 209678, 15 pages
Exact Solutions for the Axial Couette Flow of a Fractional Maxwell Fluid in an Annulus
1Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan
2Department of Mathematics, University of Education, Lahore 54000, Pakistan
3Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt 47040, Pakistan
Received 10 October 2011; Accepted 3 November 2011
Academic Editors: M. Rasetti, A. Sanyal, and G. F. Torres del Castillo
Copyright © 2012 M. Imran et al. 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.
- S. F. Han, Constitutive Equation and Computational Analytical Theory of Non-Newtonian Fluids, Science Press, Beijing, China, 2000.
- G. G. Stokes, On the Effect of the Rotation of Cylinders and Spheres about Their Axis in Increasing the Logarithmic Decrement of the Arc of Vibration, Cambridge University Press, Cambridge, UK, 1886.
- G. I. Taylor, “Stability of a viscous liquid contained between two rotating cylinders,” Philosophical Transactions of the Royal Society A, vol. 223, pp. 289–298, 1923.
- G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK, 1967.
- T. W. Ting, “Certain non-steady flows of second-order fluids,” Archive For Rational Mechanics And Analysis, vol. 14, no. 1, pp. 1–26, 1963.
- P. N. Srivastava, “Non-steady helical flow of a viscoelastic liquid,” Archiwum Mechaniki Stosowanej, vol. 18, pp. 145–150, 1966.
- N. D. Waters and M. J. King, “The unsteady flow of an elastico-viscous liquid in a straight pipe of circular cross section,” Journal of Physics D, vol. 4, no. 2, article 304, pp. 204–211, 1971.
- K. Q. Zhu, Y. J. Lu, P. P. Shen, and J. L. Wang, “A study of start-up pipe flow of Maxwell fluid,” Acta Mechanica Sinica, vol. 35, p. 218, 2003 (Chinese).
- D. Yang and K. Q. Zhu, “Start-up flow of a viscoelastic fluid in a pipe with a fractional Maxwell's model,” Computers and Mathematics with Applications, vol. 60, no. 8, pp. 2231–2238, 2010.
- W. Tan and M. Xu, “Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model,” Acta Mechanica Sinica/Lixue Xuebao, vol. 18, no. 4, pp. 342–349, 2002.
- T. Wenchang, P. Wenxiao, and X. Mingyu, “A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates,” International Journal of Non-Linear Mechanics, vol. 38, no. 5, pp. 645–650, 2003.
- T. Hayat, S. Nadeem, and S. Asghar, “Periodic unidirectional flows of a viscoelastic fluid with the fractional Maxwell model,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 153–161, 2004.
- D. Tong and Y. Liu, “Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe,” International Journal of Engineering Science, vol. 43, no. 3-4, pp. 281–289, 2005.
- D. Tong, R. Wang, and H. Yang, “Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe,” Science in China G, vol. 48, no. 4, pp. 485–495, 2005.
- H. Qi and H. Jin, “Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders,” Acta Mechanica Sinica, vol. 22, no. 4, pp. 301–305, 2006.
- H. Qi and M. Xu, “Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channel,” Mechanics Research Communications, vol. 34, no. 2, pp. 210–212, 2007.
- W. P. Wood, “Transient viscoelastic helical flows in pipes of circular and annular cross-section,” Journal of Non-Newtonian Fluid Mechanics, vol. 100, no. 1-3, pp. 115–126, 2001.
- C. Fetecau, C. Fetecau, and D. Vieru, “On some helical flows of Oldroyd-B fluids,” Acta Mechanica, vol. 189, no. 1-2, pp. 53–63, 2007.
- D. Vieru, W. Akhtar, C. Fetecau, and C. Fetecau, “Starting solutions for the oscillating motion of a Maxwell fluid in cylindrical domains,” Meccanica, vol. 42, no. 6, pp. 573–583, 2007.
- M. Khan, S. Hyder Ali, and H. Qi, “Exact solutions of starting flows for a fractional Burgers' fluid between coaxial cylinders,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1775–1783, 2009.
- C. Fetecau, A. U. Awan, and C. Fetecau, “Taylor-couette flow of an Oldroyd-B fluid in a circular cylinder subject to a time-dependent rotation,” Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, vol. 52, no. 2, pp. 117–128, 2009.
- M. Athar, C. Fetecau, and A. U. Awan, “Exact solutions for the flow of a generalized second grade fluid due to a longitudinal quadratic time-dependent shear stress,” International Journal of Industrial Mathematics, vol. 2, no. 3, pp. 153–165, 2010.
- W. Akhtar, C. Fetecau, and A. U. Awan, “Exact solutions for the axial Couette flow of generalized Maxwell fluid induced by time dependent shear stress,” Australian and New Zealand Industrial and Applied Mathematics Journal. In press.
- M. Athar, A. U. Awan, and C. Fetecau, “A note on the unsteady flow of a fractional Maxwell fluid through a circular cylinder,” Acta Mechanica Sinica. In press.
- M. Kamran, M. Athar, and M. Imran, “Critical study on rotational flow of a fractional Oldroyd-B fluid induced by a circular cylinder,” ISRN Mathematical Physics, vol. 2012, Article ID 835398, p. 15, 2012.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC Press, Boca Raton, Fla, USA, 2nd edition, 2007.
- C. F. Lorenzo and T. T. Hartley, “Generalized functions for fractional calculus,” NASA/TP 1999-209424, 1999.