Abstract
This paper reviews some aspects of our recent work pertinent to the character and stability of two dimensional and three dimensional thermocapillary and buoyant thermocapillary flows in a fixed rectangular cavity. For two dimensional calculations, the flow is assumed isothermal at the two vertical boundaries and adiabatic at the others. Three dimensional calculations include an assumed periodicity in the axial direction with planes of symmetry separating respective calculation regions. In all cases, thermocapillarity influences flow through a tangential shear boundary condition at the free surface. The limit of small Capillary number (Ca→0) is assumed and thus the free-surface is nondeformable to leading order.
Terrestrial calculations of bouyant convection, with no thermocapillary effects, exhibit a Hopf bifurcation at some predictable, critical Grashof number. However, numerical calculations which incorporated thermocapillarity in microgravity rectangular systems with imposed flat free surfaces have been generally steady. Three dimensional calculations were utilized to show a spatial bifurcation in the combined leading order problem while two dimensional calculations were utilized to investigate the influence of increasing thermocapillarity on the Hopf bifurcation in the combined leading order problem.
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Abbreviations
- A :
-
aspect ratio
- Ca :
-
Capillary number
- G :
-
Bond number
- Gr :
-
Grashof number
- Ma :
-
Marangoni number
- Pr :
-
Prandtl number
- Ra :
-
Rayleigh number
- Re :
-
Reynolds number
- g :
-
acceleration due to gravity
- α:
-
thermal diffusivity
- β:
-
coefficient of thermal expansion
- γ:
-
coefficient of thermocapillarity
- μ:
-
dynamic viscosity
- ν:
-
kinematic viscosity
- σ:
-
surface tension
- *:
-
dimensional quantity
- cr :
-
critical value
- r :
-
reference value
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Communicated by Y. Jaluria, 28 February 1994
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Mundrane, M., Zebib, A. Steady and oscillatory buoyant thermocapillary convection. Computational Mechanics 14, 411–419 (1994). https://doi.org/10.1007/BF00377595
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DOI: https://doi.org/10.1007/BF00377595