Skip to main content

Some recent results on swirling flows of Newtonian and non-Newtonian fluids

  • Conference paper
  • First Online:
Mathematical Aspects of Fluid and Plasma Dynamics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1460))

  • 533 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. T. von Karman, Uber laminare und turbulente Reibung, Z. Angen. Math. Mech. 1, 232–252 (1921).

    Article  MATH  Google Scholar 

  2. R. Berker, A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis, Archiwum Mechaniki Stosowanej, 31, 265–280 (1979).

    ADS  MathSciNet  MATH  Google Scholar 

  3. S.V. Parter and K.R. Rajagopal, Swirling flow between rotating plates, Arch. Ratl. Mech. Anal., 86, 305–315 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  4. C.Y. Lai, K.R. Rajagopal and A.Z. Szeri, Asymmetric flow between parallel rotating disks, J. Fluid Mech., 146, 203–225 (1984).

    Article  ADS  MATH  Google Scholar 

  5. K.R. Rajagopal and A.S. Gupta, Flow and stability of second grade fluids between two parallel rotating plates, Archiwum Mechaniki Stosowanej, 33, 663–674 (1981).

    MathSciNet  MATH  Google Scholar 

  6. K.R. Rajagopal and A.S. Gupta, Flow and stability of a second grade fluid between two parallel rotating plates about noncoincident axes, Intl. J. Eng. Science, 19, 1401–1409 (1985).

    Article  MATH  Google Scholar 

  7. K.R. Rajagopal and A.S. Wineman, A class of exact solutions for the flow of a viscoelastic fluid, Archiwum Mechaniki Stosowanej, 35 747–752 (1983).

    ADS  MathSciNet  MATH  Google Scholar 

  8. R.R. Huilgol and K.R. Rajagopal, Non-Axisymmetric flow of a viscoelastic fluid between rotating disks, submitted for publication.

    Google Scholar 

  9. B. Maxwell and R.P. Chartoff, Studies of a polymer melt in an orthogonal rheometer, Trans. Soc. Rheology, 9, 51–52 (1965).

    Article  ADS  Google Scholar 

  10. R.R. Huilgol, On the properties of the motion with constant stretch history occuring in the Maxwell Rheometers, Trans. Soc. Rheol., 13, 513–526 (1969).

    Article  Google Scholar 

  11. K.R. Rajagopal, On the flow of a simple fluid in an orthogonal rheometer, Arch. Ratl. Mech. Anal., 79, 29–47 (1982).

    Article  MathSciNet  Google Scholar 

  12. M. Bower, K.R. Rajagopal and A.S. Wineman, A numerical study of the inertial effects of the flow of a shear thinning K-BKZ fluid between rotating parallel plates, submitted for publication.

    Google Scholar 

  13. K.R. Rajagopal, M. Renardy, Y. Renardy and A.S. Wineman, Flow of viscoelastic fluids between plates rotating about distinct axes, In Press, Rheologica Acta.

    Google Scholar 

  14. G.K. Batchelor, Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow, Quart. J. Mech. Appl. Math., 4, 29–41 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  15. K. Stewartson, On the flow between two rotating co-axial disks, Proc. Cambridge Philos. Soc., 49, 333–341 (1953).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. S.P. Hastings, On existence theorems for some problems from boundary layer theory, Arch. Ratl. Mech. Anal., 38, 308–316.

    Google Scholar 

  17. A.R. Elcrat, On the swirling flow between rotating co-axial disks, J. Differential Equations, 18, 423–430 (1975).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. J.B. McLeod and S.V. Parter, On the flow between two counter-rotating infinite plane disks, Arch. Ratl. Mech. Anal., 54, 301–327 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  19. H.O. Kreiss and S.V. Parter, On the swirling flow between rotating co-axial disks: existence and non-uniqueness, Comm. Pure and Applied Math., 36, 35–84 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  20. G.L. Mellor, P.J. Chapple and V.K. Stokes, On the flow between a rotating and a stationary disk, J. Fluid Mech., 31, 95–112 (1968).

    Article  ADS  MATH  Google Scholar 

  21. D. Dijkstra and G.J.F. van Heijst, The flow between finite rotating disks enclosed by a cylinder, J. Fluid Mech., 128, 123–154 (1983).

    Article  ADS  MATH  Google Scholar 

  22. A.Z. Szeri, S.J. Schneider, F. Labbe and H.N. Kaufmann, Flow between rotating disks. part 1. Basic flow, J. Fluid Mech., 134, 103–131 (1983).

    Article  ADS  Google Scholar 

  23. N. Phan-Thien, Co-axial disk flow and flow about a rotating disk of a Maxwellian fluid, J. Fluid Mech., 128, 427–442.

    Google Scholar 

  24. N. Phan-Thien, Co-axial disk flow of an Oldroyd B-Fluid: Exact solution and stability, J. Non-Newt. Fluid Mech., 13, 325–340 (1983).

    Article  MATH  Google Scholar 

  25. R.R. Huilgol and J.B. Keller, Flow of viscoelastic fluids between rotating disks: Part 1, J. Non-Newt. Fluid Mech., 18, 110 (1975).

    MATH  Google Scholar 

  26. R. Drouot, Sur un cas d'integration des dquations du mouvement d'un fluide incompressible du deuxieme ordre, C.R. Acad. Sc. Paris, 265 A, 300–304 (1967).

    MATH  Google Scholar 

  27. T.N.G. Abbot and K. Walters, Rheometrical flow systems, Part 2, Theory for the orthogonal rheometer, including an exact solution fo the Navier-Stokes equations, J. Fluid Mech., 40, 205–213 (1970).

    Article  ADS  Google Scholar 

  28. R. Berker, An exact solution of the Navier-Stokes equation, the vortex with curvilinear axis, Intl. J. Eng. Science, 20, 217–230 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Berker, Integration des equations du mouvement d'un fluide visquex, incompressible, Hanbuch der Physik, VIII/2, Berlin-Gottingen-Heidelberg, Springer (1963).

    Google Scholar 

  30. R. Berker, Sur quelques cas d'integration des equations du mouvement d'un fluide incompressible, Lille, Paris (1936).

    Google Scholar 

  31. W. Noll, Motions with constant stretch history, Arch. Rational Mech., Anal., 11, 97–105 (1962).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. A. Kaye, Note No. 134, College of Aeronautics Cranfield Institute of Technology (1962).

    Google Scholar 

  33. B. Bernstein, E.A. Kearsley and L.J. Zapas, A study of stress relaxation with finite strain, Trans. Soc. Rheol., 7, 391–410 (1963).

    Article  MATH  Google Scholar 

  34. K.R. Rajagopal and A.S. Wineman, Flow of a BKZ fluid in an orthogonal rheometer, Journal of Rheology, 27, 509–516 (1983).

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Giuseppe Toscani Vinicio Boffi Salvatore Rionero

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Rajagopal, K.R. (1991). Some recent results on swirling flows of Newtonian and non-Newtonian fluids. In: Toscani, G., Boffi, V., Rionero, S. (eds) Mathematical Aspects of Fluid and Plasma Dynamics. Lecture Notes in Mathematics, vol 1460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091367

Download citation

  • DOI: https://doi.org/10.1007/BFb0091367

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53545-4

  • Online ISBN: 978-3-540-46779-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics