Abstract:
The solution to the linear problem of axisymmetric thermocapillary motion of two non-miscible viscous fluids in a cylindrical tube is presented. Their common interface is fixed and undeformable. This problem is an inverse problem because pressure gradients are unknown functions. The solution of the non-stationary problem is presented in the form of analytical expressions. They are obtained with the use of the method of Laplace transformation. If the wall temperature is stabilized then the general solution tends to the stationary solution as time increases. Numerical calculations confirm the theoretical results.
Received: 21.04.2015 Received in revised form: 05.05.2015 Accepted: 20.06.2015
Document Type:
Article
UDC:
517.532
Language: English
Citation:
Evgeniy P. Magdenko, “Axisymmetric thermocapillary motion in a cylinder at small Marangoni number”, J. Sib. Fed. Univ. Math. Phys., 8:3 (2015), 303–311
\Bibitem{Mag15}
\by Evgeniy~P.~Magdenko
\paper Axisymmetric thermocapillary motion in a cylinder at small Marangoni number
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2015
\vol 8
\issue 3
\pages 303--311
\mathnet{http://mi.mathnet.ru/jsfu432}
\crossref{https://doi.org/10.17516/1997-1397-2015-8-3-303-311}
Linking options:
https://www.mathnet.ru/eng/jsfu432
https://www.mathnet.ru/eng/jsfu/v8/i3/p303
This publication is cited in the following 1 articles:
V. K. Andreev, M. V. Efimova, “The structure of a two-layer flow in a channel with radial heating of the lower substrate for small Marangoni numbers”, J. Appl. Industr. Math., 18:2 (2024), 179–191
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