Geodesic
Two-dimensional plane thermocapillary flow of two immiscible liquids
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 310-316

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of two-dimensional stationary flow of two immiscible liquids in a plane channel with rigid walls is considered. A temperature distribution is specified on one of the walls and another wall is heat-insulated. The interfacial energy change is taken into account on the common interface. The temperature in liquids is distributed according to a quadratic law. It agrees with velocities field of the Hiemenz type. The corresponding conjugate boundary value problem is nonlinear and inverse with respect to pressure gradients along the channel. The Tau method is used for the solution of the problem. Three different solutions are obtained. It is established numerically that obtained solutions converge to the solutions of the slow flow problem with decreasing the Marangoni number. For each of the solutions the characteristic flow structures are constructed.
Keywords: thermocapillary, inverse problem, Tau method.
Mots-clés : interface 
@article{JSFU_2019_12_3_a4,
     author = {Elena N. Lemeshkova},
     title = {Two-dimensional plane thermocapillary flow of two immiscible liquids},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {310--316},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a4/}
}
TY  - JOUR
AU  - Elena N. Lemeshkova
TI  - Two-dimensional plane thermocapillary flow of two immiscible liquids
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 310
EP  - 316
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a4/
LA  - en
ID  - JSFU_2019_12_3_a4
ER  - 
%0 Journal Article
%A Elena N. Lemeshkova
%T Two-dimensional plane thermocapillary flow of two immiscible liquids
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 310-316
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a4/
%G en
%F JSFU_2019_12_3_a4
Elena N. Lemeshkova. Two-dimensional plane thermocapillary flow of two immiscible liquids. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 310-316. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a4/