NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containersMultiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.
Document ID
19930030765
Document Type
Reprint (Version printed in journal)
Authors
Dijkstra, Henk A. (Cornell Univ. Ithaca, NY, United States)
Date Acquired
August 16, 2013
Publication Date
October 1, 1992
Publication Information
Publication: Journal of Fluid Mechanics
ISSN: 0022-1120
Subject Category
FLUID MECHANICS AND HEAT TRANSFER
Funding Number(s)
CONTRACT_GRANT: NAG3-801
Distribution Limits
Public
Copyright
Other