Meccanica

, Volume 44, Issue 4, pp 427–431

Exact solutions for generalized Burgers’ fluid in an annular pipe

Article

Abstract

This paper deals with some unsteady unidirectional transient flows of generalized Burgers’ fluid in an annular pipe. Exact solutions of some unsteady flows of generalized Burgers’ fluid in an annular pipe are obtained by using Hankel transform and Laplace transform. The following two problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in a annulus. The well known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid, a second grade fluid and an Oldroyd-B fluid appear as limiting cases of our solutions.

Keywords

Generalized Burgers’ fluid Exact solutions Velocity fields 

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References

  1. 1.
    Dunn JE, Rajagopal KR (1995) Fluids of differential type:critical review and thermodynamic analysis. Int J Eng Sci 33(5):689–729 MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Rajagopal KR (1993) Mechanics of non-Newtonian fluids. In: Recent developments in theoretical fluids mechanics. Pirman research notes in mathematics, vol 291. Longman, New York, pp 129–162 Google Scholar
  3. 3.
    Han SF (2000) Constitutive equation and computational analytical theory of non-Newtonian fluids. Science, Beijing Google Scholar
  4. 4.
    Bandeli R, Rajagopal KR (1995) Start-up flows of second grade fluids in domains with one finite dimension. Int J Non-Linear Mech 30(6):818–839 Google Scholar
  5. 5.
    Liu CQ, Huang JQ (1989) Analytical solutions for equations of unsteady flow of non-Newtonian fluids in tube. Appl Math Mech 10(11):939–946 MathSciNetGoogle Scholar
  6. 6.
    Vieru D, Akhtar W, Fetecau C, Fetecau C (2008) Starting solutions for the oscillating motion of a Maxwell fluid in cylindrical domains. Meccanica. doi:10.1007/s11012-007-9081-7 Google Scholar
  7. 7.
    Fetecau C (2004) Analytical solutions for non-Newtonian fluid flow in pipe-like domains. Int J Non-Linear Mech 39:225–231 MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tong D, Wang R (2005) Exact solutions for the flow of non-Newtonian fluidwith fractional derivative in an annular pipe. Sci China (Ser G) 48(4):485–495 CrossRefGoogle Scholar
  9. 9.
    Hayat T, Fetecau, C, Asghar S (2006) Some simple flows of a Burgers’fluid. Int J Eng Sci 44(5):1423–1431 CrossRefMathSciNetGoogle Scholar
  10. 10.
    Ravindran P, Krishnan JM, Rajagopal KRA (2004) Note on the flow of a Burgers’fluid in an orthogonal rheometer. Int J Eng Sci 42:1973–1985 CrossRefMathSciNetGoogle Scholar
  11. 11.
    Quintanilla R, Rajagopal KR (2006) On Burgers fluids. Math Methods Appl Sci 29:2133–2147 MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Chen CI, Chen CK (2006) Exact solutions for the unsteady flow of a Burgers’fluid in a duct induced by time-dependent prescribed volume flow rate. Heat Mass Transf 43:85–90 CrossRefADSGoogle Scholar
  13. 13.
    Krishnan JM, Rajagopal KR (2004) Thermodynamic framework for the constitutive modeling of asphalt concrete: theory and applications. J Mater Civil Eng 16:155–166 CrossRefGoogle Scholar
  14. 14.
    Chopra PN (1997) High-temperature transient creep in olivine rocks. Tectonophysics 279:93–111 CrossRefADSGoogle Scholar
  15. 15.
    Tan WC, Xian F, Wei L (2002) Exact solution for the unsteady Couette flow of the generalized second grade fluid. Chin Sci Bull 47(16):1226–1228 MathSciNetGoogle Scholar
  16. 16.
    Rumpher G, Wolf D (1996) Viscoelastic relaxation of a Burgers half-space: implications for the interpretation of the Fennoscandian uolife. Geophys J Int 124:541–555 CrossRefADSGoogle Scholar
  17. 17.
    Fetecau C, Hayat T, Fetecau C (2006) Steady-state solutions for some simple flows of generalized Burgers fluids. Int J Non-Linear Mech 41(8):880–887 MATHCrossRefGoogle Scholar
  18. 18.
    Le Roux C, Patidar KC (2008) On the flow of a generalized Burgers fluid in an orthogonal rheometer. Nonlinear Anal Real World Appl. doi:10.1016/j.nonrwa.2007.06.012 Google Scholar
  19. 19.
    Xue C, Nie J (2008) Exact solutions of Stokes’ first problem for heated generalized Burgers’ fluid in a porous half-space. Nonlinear Anal Real World Appl. doi:10.1016/j.nonrwa.2007.04.007 MathSciNetGoogle Scholar
  20. 20.
    Hayat T, Khan SB, Khan M (2007) Exact solution for rotating flows of a generalized Burgers’ fluid in a porous space. Appl Math Model. doi:10.1016/j.apm.2007.02.011 Google Scholar
  21. 21.
    Xue C, Nie J (2008) An exact solution of start-up flow for the fractional generalized Burgers’ fluid in a porous half-space. Nonlinear Anal Real World Appl. doi:10.1016/j.nonrwa.2007.07.047 MathSciNetGoogle Scholar
  22. 22.
    Zhu WH, Liu CQ (1993) Analytical solution of flow of second-order non-Newtonian fluid through annular pipes. Appl Math Mech 14(3):195–201 Google Scholar
  23. 23.
    Zhu WH, Liu CQ (1992) Analytical solution for the unsteady flow of Maxwell fluids through annular pipes. Acta Mech Sin 24(1):116–121 Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.China University of Petroleum (at East of China)DongyiingChina

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