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.
Similar content being viewed by others
References
Kármán T.V.: Über laminare und turbulente Reibung. Zeitschrift für Angewandte Mathematik und Mechanik 1, 233–252 (1921)
Cochran W.G.: The flow due to a rotating disk. Proc. Camb. Phil. Soc. 30, 365–375 (1934)
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)
Jarre S.L.G., Chauve M.P.: Experimental study of rotating-disk instability. I. Natural flow. Phys. Fluids 8, 496–508 (1996)
Turkyilmazoglu, M.: Linear Absolute and Convective Instabilities of Some Two- and Three Dimensional Flows. PhD thesis, University of Manchester (1998)
Shevchuk I.V.: Convective Heat and Mass Transfer in Rotating Disk Systems. Springer, Berlin (2009)
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)
Parter S.V., Rajagopal K.R.: Swirling flow between rotating plates. Arch. Rat. Mech. Anal. 86, 305–315 (1984)
Berker R.: An exact solution of the Navier–Stokes equation the vortex with curvilinear axis. Int. J. Eng. Sci. 20, 217–230 (1982)
Rajagopal K.R.: A class of exact solutions to the Navier–Stokes equations. Int. J. Eng. Sci. 22, 451–455 (1984)
Sherman R.S.: Viscous Flow. McGraw-Hill, New York (1990)
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)
Riley N.: The heat transfer from a rotating-disk. Q. J. Mech. Appl. Math. 17, 331–349 (1964)
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)
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)
Turkyilmazoglu M.: Exact solutions for the incompressible viscous fluid of a rotating disk flow. Prog. Appl. Math. 1, 90–97 (2011)
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)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-011-0553-4