Skip to main content
SpringerLink
Log in

Zur Stabilität der Strömung in einem horizontalen Rohr bei ungleichmässig erwärmter Wand

  • Kurze Mitteilungen
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

The linear fluid motion in a horizontal pipe heated from below is considered, when the temperature field outside the pipe is linear. By the method of small perturbations it is shown that the fluid motion becomes unstable for a critical value of the Rayleigh number, i.e., there is an additional convective motion, the streamlines of which are concentric curves in the plane of a cross-section of the pipe.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literaturverzeichnis

  1. W. R. Dean,Note on the Motion of Fluid in a Curved Pipe. Phil. Mag.4, 208–223 (1957).

    Google Scholar 

  2. W. R. Dean,The Stream-Line Motion of Fluid in a Curved Pipe, Phil. Mag.5, 673–695 (1928).

    Google Scholar 

  3. W. Jeffreys,The Stability of a Layer of Fluid Heated Below. Phil. Mag.2, 833–844 (1926). —Some Cases of Instability of Fluid Motions. Proc. Roy. Soc. (London) Ser. A118, 195–208 (1928).

    Google Scholar 

  4. B. R. Morton,Laminar Convection in Uniformely Heated Horizontal Pipes at Low Rayleigh Numbers. Quart. J. Mech. App. Math.12, 410–420 (1959).

    Google Scholar 

  5. G. A. Ostroumov,Free Convection Under the Conditions of the Internal Problem. NACA TM 1407, April 1958. Translation of:Svobodnaya convectzia v ousloviakh vnoutrennei zadachi, Moscow-Leningrad 1952.

  6. A. Pellew andR. V. Southwell,On Maintained Convective Motion in a Fluid Heated from Below. Proc. Roy. Soc. London, Ser. A176, 312–343 (1940).

    Google Scholar 

  7. Lord Rayleigh,On Convection Currents in a Horizontal Layer of Fluid. Phil. Mag.32, 529–546 (1916) (collected papers6, 432–436).

    Google Scholar 

  8. R. Courant undD. Hilbert,Methoden der Mathematischen Physik, 2. Aufl. Bd. II (Springer, Berlin 1931).

    Google Scholar 

  9. K. Friedrichs,Die Randwert- und Eigenwertprobleme aus der Theorie der elastischen Platten. Math. Ann.98, 206–247 (1928).

    Google Scholar 

  10. L. Nirenberg,Remarks on Strongly Elliptic Partial Differential Equations. Comm. Pure Appl. Math.8, 648–674 (1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für angewandte Mathematik und Mechanik der DVL, Universität Freiburg i. Br., Freiburg i. Br., Deutschland

    Waldemar Velte

Authors
  1. Waldemar Velte
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Die Untersuchung wurde vom Wirtschaftsministerium des Landes Baden-Württemberg gefördert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Velte, W. Zur Stabilität der Strömung in einem horizontalen Rohr bei ungleichmässig erwärmter Wand. Journal of Applied Mathematics and Physics (ZAMP) 13, 591–600 (1962). https://doi.org/10.1007/BF01595583

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01595583

Search

Navigation