Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-22T01:17:15.660Z Has data issue: false hasContentIssue false
  • English
  • Français

On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

Published online by Cambridge University Press:  14 August 2007

P. G. DANIELS
P. G. DANIELS*
Affiliation:
Centre for Mathematical Science, City University, Northampton Square, London EC1V 0HB, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers two-dimensional flow generated in a stably stratified porous medium by monotonic differential heating of the upper surface. For a rectangular cavity with thermally insulated sides and a constant-temperature base, the flow near the upper surface in the high-Darcy–Rayleigh-number limit is shown to consist of a double horizontal boundary layer structure with descending motion confined to the vicinity of the colder sidewall. Here there is a vertical boundary layer structure that terminates at a finite depth on the scale of the outer horizontal layer. Below the horizontal boundary layers the motion consists of a series of weak, uniformly stratified counter-rotating convection cells. Asymptotic results are compared with numerical solutions for the cavity flow at finite values of the Darcy–Rayleigh number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 347 - 370
Copyright
Copyright © Cambridge University Press 2007

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

Chang, I. D. & Cheng, P. 1983 Matched asymptotic expansions for free convection about an impermeable horizontal surface in a porous medium. Intl J. Heat Mass Transfer 26, 163–173.CrossRefGoogle Scholar
Cheng, P. & Chang, I. D. 1976 On buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces. Intl J. Heat Mass Transfer 19, 1267–1272.Google Scholar
Daniels, P. G. 2006 Shallow cavity flow in a porous medium driven by differential heating. J. Fluid Mech. 565, 441–459.CrossRefGoogle Scholar
Daniels, P. G., Blythe, P. A. & Simpkins, P. G. 1982 Thermally driven cavity flows in porous media. Part II. The horizontal boundary-layer structure. Proc. R. Soc. Lond. A 382, 135–154.Google Scholar
Daniels, P. G. & Punpocha, M. 2004 Cavity flow in a porous medium driven by differential heating. Intl J. Heat Mass Transfer 47, 3017–3030.CrossRefGoogle Scholar
Daniels, P. G. & Punpocha, M. 2005 On the boundary-layer structure of cavity flow in a porous medium driven by differential heating. J. Fluid Mech. 532, 321–344.CrossRefGoogle Scholar
Tayler, A. B. 1986 Mathematical Models in Applied Mechanics. Clarendon.Google Scholar
Weber, J. E. 1975 The boundary-layer regime for convection in a vertical porous layer. Intl J. Heat Mass Transfer 18, 569–573.CrossRefGoogle Scholar