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Comparison of buoyancy and surface tension in a square cavity

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Abstract

Laminar natural convection induced by free surface temperature gradient has been investigated numerically. Buoyancy effect and surface tension effect were made to oppose against each other. For fluid of unit Prandtl number and cavity of unit aspect ratio, the flow field was examined to determine the relative importance of surface tension force and buoyancy force. The flow patterns of each regime are: free surface-concentrated streamlines for surface tension flows, opposite direction circulation for buoyancy driven flows, and surface tension cell above with buoyancy driven cell below for mixed flows. The borderlines of each flow regime were obtained by interpolation and the flow regime map was obtained.

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Abbreviations

Cp :

Specific heat

g:

Gravitational constant

H :

Cavity height

k:

Thermal conductivity

L:

Cavity length

p:

Pressure

T:

Temperature

u:

Horizontal velocity

v:

Vertical velocity

x:

Horizontal coordinate

y:

Vertical coordinate

β:

Volumetric thermal expansion coefficient

M:

Dynamic viscosity

υ:

Kinematic viscosity

σ:

Density

γ:

Dimensionless temperature

Bo :

Bond number

Gr :

Grashof number

Ma :

Marangoni number

Pr:

Prandtl number

Re:

Reynolds number

References

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Song, T. Comparison of buoyancy and surface tension in a square cavity. KSME Journal 5, 10–15 (1991). https://doi.org/10.1007/BF02945145

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Key Words

  • Flow regime
  • Natural Convection
  • Surface Tension