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Heat transport in an infinitely long Non-Newtonian liquid bridge due to marangoni convection

Wärmetransport in einer unendlich langen nicht-newtonischen Flüssigkeitsbrücke bezüglich Marangoni-Konvektion

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Abstract

An infinitely long liquid bridge, observing a Non-Newtonian flow law (Ostwald-de-Waal and Bingham), is subjected under weightless condition to a linear temperature field, which yields due to the local change of the surface tension a Marangoni convection. The velocity- and temperature distribution inside the liquid bridge is determined analytically.

Zusammenfassung

Eine unendlich lange Flüssigkeitsbrücke, die einem Nicht-Newtonischen Fließgesetz (Ostwald-de-Waal und Bingham) folgt, ist im schwerelosen Raum einem linearen Temperaturfeld ausgesetzt, das in der Flüssigkeitssäule eine Marangoni-Konvektion hervorruft. Es wird die Geschwindigkeits- und Temperaturverteilung in der Flüssigkeitsbrücke analytisch bestimmt.

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Abbreviations

a :

radius of liquid column

k :

thermal conductivity

K :

material constant of Ostwald-de-Waal liquid

n :

material constant of Ostwald-de-Waal liquid

p :

liquid pressure

r :

radial coordinate

T :

temperature

¯T1 :

temperature gradient along z-axis

w :

velocity distribution of liquid in axial direction

z :

axial coordinate

x :

diffusivity

σ :

liquid surface tension

τ:

tangential stress

τ0 :

flow shear stress for Bingham plastic

η :

dynamic viscosity of Newtonian liquid(k=η, n=1)

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  1. Fachbereich Luft- und Raumfahrttechnik Hochschule der Bundeswehr München, Werner-Heisenberg-Weg 39, 8014, Neubiberg

    F. Bauer

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Bauer, F. Heat transport in an infinitely long Non-Newtonian liquid bridge due to marangoni convection. Wärme- und Stoffübertragung 16, 229–235 (1982). https://doi.org/10.1007/BF01375647

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