Skip to main content
SpringerLink
Log in

Some duct flows of a fractional Maxwell fluid

  • Applications
  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract.

The aim of this paper is to establish the analytical solutions corresponding to two types of unsteady flows of fractional Maxwell fluid in a duct of rectangular cross-section. The fractional calculus approach is used in solving the problems. With the help of the methods of separation of variables and Laplace transforms, the expressions for the velocity field and the volume flux are presented under series forms in terms of the generalized G functions. Similar solutions for Newtonian and ordinary Maxwell fluids, performing the same motions, are also obtained as the limiting cases of our solutions. Furthermore, the influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.C. Maxwell, Phil. Trans. Roy. Soc. Lond. 157, 49 (1867)

    Article  Google Scholar 

  2. J.J. Choi, Z. Rusak, J.A. Tichy, J. Non-Newtonian Fluid Mech. 85, 165 (1999)

    Article  MATH  Google Scholar 

  3. C. Friedrich, Rheol. Acta 30, 151 (1991)

    Article  Google Scholar 

  4. D.Y. Song, T.Q. Jiang, Rheol. Acta 37, 512 (1998)

    Article  Google Scholar 

  5. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)

  6. R. Hilfer, Applications of Fractional Calculus in Physics (World Scientific Press, Singapore, 2000)

  7. M.Y. Xu, W.C. Tan, Sci. China Ser. G 46, 145 (2003)

    Article  Google Scholar 

  8. M.Y. Xu, W.C. Tan, Sci. China Ser. G 49, 257 (2006)

    Article  MATH  Google Scholar 

  9. A. Heibig, L.L. Palade, J. Math. Phys. 49, 043101 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Makris, G.F. Dargush, M.C. Constantinou, J. Eng. Mech. 119, 1663 (1993)

    Article  Google Scholar 

  11. A. Hernández-Jiménez, J. Hernández-Santiago, A. Macias-García, J. Sánchez-González, Polym. Test. 21, 325 (2002)

    Article  Google Scholar 

  12. W.C. Tan, M.Y. Xu, Acta Mech. Sin. 18, 342 (2002)

    Article  MathSciNet  Google Scholar 

  13. W.C. Tan, W.X. Pan, M.Y. Xu, Int. J. Non-Linear Mech. 38, 645 (2003)

    Article  MATH  Google Scholar 

  14. T. Hayat, S. Nadeem, S. Asghar, Appl. Math. Comput. 151, 153 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. H.T. Qi, H. Jin, Acta Mech. Sin. 22, 301 (2006)

    Article  ADS  MATH  Google Scholar 

  16. H.T. Qi, M.Y. Xu, Mech. Res. Commun. 34, 210 (2007)

    Article  MATH  Google Scholar 

  17. S.W. Wang, M.Y. Xu, Nonlinear Anal. RWA 10, 1087 (2009)

    Article  MATH  Google Scholar 

  18. D. Vieru, Corina Fetecau, C. Fetecau, Appl. Math. Comput. 200, 459 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Vieru, Corina Fetecau, M. Athar, C. Fetecau, ZAMP 60, 334 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. D. Yang, K.Q. Zhu, Comput. Math. Appl. 60, 2231 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. M.E. Erdoǧan, C.E. .Imrak, Int. J. Non-Linear Mech. 39, 1379 (2004)

    Article  Google Scholar 

  22. M.E. Erdoǧan, C.E. .Imrak, Int. J. Non-Linear Mech. 40, 103 (2005)

    Article  ADS  Google Scholar 

  23. C. Fetecau, Corina Fetecau, Int. J. Non-Linear Mech. 40, 1214 (2005)

    Article  ADS  MATH  Google Scholar 

  24. S. Nadeem, S. Asghar, T. Hayat, M. Hussain, Meccanica 43, 495 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. C.F. Lorenzo, T.T. Hartley, NASA/TP–1999-209424/REV1 (1999)

  26. C. Fetecau, A. Mahmood, M. Jamil, Commun. Nonlinear Sci. Numer. Simul. 15, 3931 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. N.P. Cheremisinoff, Rheology and Non-Newtonian Flows, Vol. 7 (Gulf Publishing Co., Houston, 1986)

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University at Weihai, Weihai, 264209, PR China

    H.T. Qi & J.G. Liu

Authors
  1. H.T. Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.G. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to H.T. Qi or J.G. Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qi, H., Liu, J. Some duct flows of a fractional Maxwell fluid. Eur. Phys. J. Spec. Top. 193, 71–79 (2011). https://doi.org/10.1140/epjst/e2011-01382-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2011-01382-6

Keywords

Search

Navigation