Skip to main content
Log in

Exact flow/heat solutions for the non-axisymmetric flow over a rotating disk

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The present note is concerned with the exact non-axisymmetric solutions for the flow over a rotating disk. The governing non-axisymmetric flow equations of motion generate exact flow solutions from which analytic expressions for the vorticity, shear stresses, flow/thermal layer thicknesses and rate of heat transfer are obtained. The effects of Brinkman number, heat generation/absorption as well as thermal radiation on the temperature field can be better pursued from the extracted formulae.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kármán T.V.: Über laminare und turbulente Reibung. Zeitschrift für Angewandte Mathematik und Mechanik 1, 233–252 (1921)

    Article  MATH  Google Scholar 

  2. Cochran W.G.: The flow due to a rotating disk. Proc. Camb. Phil. Soc. 30, 365–375 (1934)

    Article  MATH  Google Scholar 

  3. Hall P.: An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating-disk. Proc. Roy. Soc. Lond. Ser. A 406, 93–106 (1986)

    Article  MATH  Google Scholar 

  4. Jarre S.L.G., Chauve M.P.: Experimental study of rotating-disk instability. I. Natural flow. Phys. Fluids 8, 496–508 (1996)

    Article  Google Scholar 

  5. Turkyilmazoglu, M.: Linear Absolute and Convective Instabilities of Some Two- and Three Dimensional Flows. PhD thesis, University of Manchester (1998)

  6. Shevchuk I.V.: Convective Heat and Mass Transfer in Rotating Disk Systems. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  7. Berker R.: A new solution of the Navier–Stokes equation for the motion of a fluid contained between two parallel plates rotating about the same axis. Arch Mech. 31, 265–280 (1979)

    MATH  MathSciNet  Google Scholar 

  8. Parter S.V., Rajagopal K.R.: Swirling flow between rotating plates. Arch. Rat. Mech. Anal. 86, 305–315 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Berker R.: An exact solution of the Navier–Stokes equation the vortex with curvilinear axis. Int. J. Eng. Sci. 20, 217–230 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rajagopal K.R.: A class of exact solutions to the Navier–Stokes equations. Int. J. Eng. Sci. 22, 451–455 (1984)

    Article  MATH  Google Scholar 

  11. Sherman R.S.: Viscous Flow. McGraw-Hill, New York (1990)

    MATH  Google Scholar 

  12. Sparrow E.M., Gregg J.L.: Heat transfer from a rotating disk to fluids of any Prandtl number. J. Heat Transf. 81, 249–251 (1959)

    Google Scholar 

  13. Riley N.: The heat transfer from a rotating-disk. Q. J. Mech. Appl. Math. 17, 331–349 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  14. Arnold J.C., Asir A.A., Somasundaram S., Christopher T.: Heat transfer in a viscoelastic boundary layer flow over a stretching sheet. Int. J. Heat Mass Transf. 53, 1112–1118 (2010)

    Article  MATH  Google Scholar 

  15. Khan Y.: The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. Comput. Math. Appl. 61, 3391–3399 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Turkyilmazoglu M.: Exact solutions for the incompressible viscous fluid of a rotating disk flow. Prog. Appl. Math. 1, 90–97 (2011)

    Google Scholar 

  17. Erdogan M.E.: Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane. Int. J. Non-linear Mech. 34, 1019–1030 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Turkyilmazoglu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Turkyilmazoglu, M. Exact flow/heat solutions for the non-axisymmetric flow over a rotating disk. Acta Mech 223, 161–166 (2012). https://doi.org/10.1007/s00707-011-0553-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-011-0553-4

Keywords

Navigation