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Marangoni convection in a rectangular container

Marangonikonvektion im Rechteckbehälter

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Abstract

If the free liquid-gas interface of a liquid in a rectangular Container is subjected to a temperature gra-dient the shear stress on the free liquid surface being temperature dependent transmits by viscous traction a thermo-capillary convection into the bulk of the liquid. For constant temperature T 1 at one wall and T 2 at the other a steady Marangoni convection takes place while for time-oscillatory temperatures of the walls a time-dependent thermo-capillary convection appears, which will create wave patterns on the free liquid surface. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution, the response magnitude inside the Container, the forced free surface displacement and the influence of the Prandtl number have been investigated.

Zusammenfassung

Wird die freie Flüssigkeitsoberfläche in einem Rechteckbehälter einem Temperaturgradienten unterworfen, so ergibt sich aufgrund der temperaturabhängigen Oberflächenspannung eine thermokapillare Konvektion. Diese wird von der Schubspannung auf der Oberfläche durch die Viskosität der Flüssigkeit in das Innere des Behälters übertragen. Für konstante Temperaturen T 1 und T 2 der Seitenwände entsteht eine stationäre Marangonikonvektionsströmung in der Flüssigkeit. Sind die Temperaturen zeitlich oszillierend, so ergeben sich auf der freien Flüssigkeitsoberfläche Oberflächenwellen, deren Vergrößerungsfunktionen bestimmt werden. Dabei wird auch der Einfluß der Prandtl-Zahl angegeben.

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Abbreviations

g :

gravity constant

h :

liquid height

l :

width of container

p :

liquid pressure

Pr=v/k :

Prandtl number

t :

time

T :

temperature

u, w :

velocity distribution of liquid

\(\vec \upsilon \) :

liquid velocity vector

x, z :

Cartesian coordinates

k :

diffusivity of liquid

Ψ:

stream function

η :

dynamic viscosity

v=η/gr :

kinematic viscosity

ρ :

liquid density

ζ :

free liquid surface displacement

τ xz :

shear stress

gs :

liquid surface tension

Ω:

forcing frequency of temperature fluctuation

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Author notes

  1. H. F. Bauer

    Present address: , 17251 Bermuda Village Dr., 33487, Boca Raton, FL, USA

Authors and Affiliations

  1. Institut für Raumfahrttechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany

    H. F. Bauer

  2. Giesserei-Institut RWTH Aachen, Intzestr. 5, 52056, Aachen

    A. Buchholz

Authors
  1. H. F. Bauer
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  2. A. Buchholz
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Bauer, H.F., Buchholz, A. Marangoni convection in a rectangular container. Forsch Ing-Wes 63, 339–348 (1998). https://doi.org/10.1007/PL00010754

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  • DOI: https://doi.org/10.1007/PL00010754

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