Self-similar solutions describing unsteady thermocapillary fluid flows

Unsteady thermocapillary flows in thin layers and layers of infinite thickness with non-uniform heating of the free boundary are investigated at high Marangoni numbers. In the plane and axially symmetric cases, self-similar solutions of the non-linear boundary-layer equations are constructed and asy...

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Bibliographic Details
Published in:Journal of applied mathematics and mechanics 1995, Vol.59 (6), p.957-963
Main Author: Batishchev, V.A
Format: Article
Language:English
Online Access:Get full text
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Summary:Unsteady thermocapillary flows in thin layers and layers of infinite thickness with non-uniform heating of the free boundary are investigated at high Marangoni numbers. In the plane and axially symmetric cases, self-similar solutions of the non-linear boundary-layer equations are constructed and asymptotic formulae are presented. It is shown that the self-similar solutions may be non-unique for certain values of the parameters of the problem. The branching points are calculated numerically and the branched solutions are investigated.
ISSN:0021-8928
0021-8928
DOI:10.1016/0021-8928(95)00129-8