Geodesic
The influence of changes in the internal energy of the interface on a two-layer flow in a cylinder
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 213-221

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The exact solution of the equations of the creeping flow model with the Himentsa type velocity field is considered in this paper. The solution describes thermocapillary convection in layers. It is interpreted as the motion of viscous heat-conducting liquids in a cylinder with solid walls and combined movable non-deformable interface. At the same time there are no mass forces. From a mathematical point of view the resulting initial-boundary problem is inversible and nonlinear because the total energy condition at the interface is taken into account. It is established that there can be two such solutions.
Keywords: nonlinear inverse problem, Marangoni number, energy condition, creeping thermocapillary motion
Mots-clés : Himentsa solution. 
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     title = {The influence of changes in the internal energy of the interface on a two-layer flow in a cylinder},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2019},
     language = {en},
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Evgeniy P. Magdenko. The influence of changes in the internal energy of the interface on a two-layer flow in a cylinder. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 213-221. http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a7/