Acta Mechanica

, Volume 189, Issue 1–4, pp 53–63 | Cite as

On some helical flows of Oldroyd-B fluids

Article

Summary

In this study the velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in terms of Bessel functions. At time t = 0 the fluid is at rest and the motion is produced by the combined action of rotating and sliding cylinders. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For λr = 0, λ = 0 or λr = λ = 0 they reduce to the similar solutions for a Maxwell, second grade or Newtonian fluid, respectively. Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of t.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Taylor, G. I. 1923Stability of a viscous liquid contained between two rotating cylindersPhil. Trans. A223289298Google Scholar
  2. Batchelor, G. K. 1967An introduction to fluid dynamicsCambridge University PressCambridgeMATHGoogle Scholar
  3. Yih, C. S. 1969Fluid mechanicsMcGraw-HillNew YorkGoogle Scholar
  4. Waters, N. D., King, M. J. 1971The unsteady flow of an elasto-viscous liquid in a straight pipe of circular cross sectionJ. Phys. D: Appl. Phys.4204211CrossRefGoogle Scholar
  5. Rahaman, K. D., Ramkissoon, H. 1995Unsteady axial viscoelastic pipe flowsJ. Non-Newtonian Fluid Mech.572738CrossRefGoogle Scholar
  6. Wood, W. P. 2001Transient viscoelastic helical flows in pipes of circular and annular cross-sectionJ. Non-Newtonian Fluid Mech.100115126MATHCrossRefGoogle Scholar
  7. Hayat, T., Siddiqui, A. M., Asghar, S. 2001Some simple flows of an Oldroyd-B fluidInt. J. Engng. Sci.39135147CrossRefGoogle Scholar
  8. Fetecau, C. 2004Analytical solutions for non-Newtonian fluid flows in pipe-like domainsInt. J. Non-Linear Mech.39225231CrossRefMathSciNetGoogle Scholar
  9. Rajagopal, K. R.: Mechanics of non-Newtonian fluids. In: Recent developments in theoretical fluid mechanics, Pitman Research Notes in Mathematics, vol. 291, pp. 129–162. New York: Longman 1993.Google Scholar
  10. Rajagopal, K. R., Bhatnagar, R. K. 1995Exact solutions for some simple flows of an Oldroyd-B fluidActa Mech.113233239MATHCrossRefMathSciNetGoogle Scholar
  11. Bandelli, R., Rajagopal, K. R., Galdi, G. P. 1995On some unsteady motions of fluids of second gradeArch. Mech.47661676MATHMathSciNetGoogle Scholar
  12. Bandelli, R., Rajagopal, K. R. 1995Start-up flows of second grade fluids in domains with one finite dimensionInt. J. Non-Linear Mech.30817839MATHCrossRefMathSciNetGoogle Scholar
  13. Srivastava, P. N. 1966Non-steady helical flow of a visco-elastic liquidArch. Mech. Stos.18145150Google Scholar
  14. Tan, W., Masuoka, T. 2005Stokes' first problem for an Oldroyd-B fluid in a porous half spacePhysics of Fluids170231017CrossRefMathSciNetGoogle Scholar
  15. Truesdell, C., Noll, W. 1965The nonlinear field theories of mechanics. Encyclopedia of Physics, vol. III/3SpringerBerlin Heidelberg New YorkGoogle Scholar
  16. Sneddon, I. N.: Functional analysis. In: Encyclopedia of Physics, vol. II. Berlin Göttingen Heidelberg: Springer 1955.Google Scholar
  17. Fetecau, C., Fetecau, Corina 1985On the uniqueness of some helical flows of a second grade fluidActa Mech.57247252MATHCrossRefMathSciNetGoogle Scholar
  18. Fetecau, C., Prasad, Sharat C. 2005A note on the flow induced by a constantly accelerating edge in an Oldroyd-B fluidIJMMS1626772688CrossRefMathSciNetGoogle Scholar
  19. Fetecau, C., Prasad, Sharat C., Rajagopal, K. R.: A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. To appear in AMM (Applied Mathematical Modelling).Google Scholar

Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University “Gh. Asachi”Iasi
  2. 2.Department of Theoretical MechanicsTechnical University “Gh. Asachi”IasiRomania

Personalised recommendations