Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T03:02:19.761Z Has data issue: false hasContentIssue false
  • English
  • Français

A theoretical investigation of disturbance amplification in external laminar natural convection

Published online by Cambridge University Press:  28 March 2006

R. P. Dring  and
B. Gebhart
R. P. Dring
Affiliation:
N.S.F. Trainee, Cornell University
B. Gebhart
Affiliation:
Professor of Mechanical Engineering Cornell University
Get access Rights & Permissions [Opens in a new window]

Abstract

The nature of instability and disturbance amplification in the laminar natural convection boundary layer over a vertical flat surface with uniform heat flux has been theoretically investigated. The coupled Orr-Sommerfeld equation has been numerically integrated for a Prandtl number of 6·7, with the boundary condition that the disturbance heat flux be zero at the surface. The spatial amplification characteristics of disturbances convected downstream were analyzed, and constant amplification rate contours were determined. The relative amplification has been calculated from these contours and is presented in the form of amplitude ratio contours. An important feature of these results is that the low frequency disturbances, which become unstable first, amplify very slowly and also have wavelengths which are much longer than the distance to the leading edge. The higher frequency, shorter wavelength, disturbances amplify much faster and are, therefore, presumed to be the dominant ones in stability considerations. The nature of the velocity and temperature amplitudes and phase profiles across the boundary layer has also been examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 34 , Issue 3 , 2 December 1968 , pp. 551 - 564
Copyright
© 1968 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kaplan, R. E. 1964 M.I.T., ASRL TR 116-1.
Knowles, C. P. 1967 Ph.D. Thesis, Cornell University.
Knowles, C. P. & Gebhart, B. 1968 Submitted to J. Fluid Mech.
Nachtsheim, P. R. 1963 NASA TN-D-2089.
Plapp, J. E. 1957 Ph.D. Thesis, Cal. Inst. of Tech.
Polymeropoulos, C. E. & Gebhart, B. 1966 AIAA J. 4, 2066.
Polymeropoulos, C. E. & Gebhart, B. 1967 J. Fluid Mech. 30, 225.
Smith, A. M. O. 1956 9th Int. Cong. of Appl. Mech. 4, 234.
Sparrow, E. M. & Gregg, J. L. 1956 ASME Trans. 78, 435.