Geodesic
On laminar flows of planar free convection
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 651-657

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

New exact steady-state solutions of the Oberbeck–Boussinesq system which describe laminar flows of the Benard–Marangoni convection are constructed. We consider two types of boundary conditions: those specifying a temperature gradient on one of the boundaries and those specifying it on both boundaries simultaneously. It is shown that when the temperature gradient is specified the problem is essentially two-dimensional: there is no linear transformation allowing the flows to be transformed into one-dimensional ones. The resulting solutions are physically interpreted and dimensions of the layers are found for which there is no friction on the solid surface and a change occurs in the direction of velocity on the free surface.
Keywords: laminar flow, analytical solution, decrease in dimension
Mots-clés : polynomial solution, Benard–Marangoni convection. 
@article{ND_2013_9_4_a3,
     author = {S. N. Aristov and E. Yu. Prosviryakov},
     title = {On laminar flows of planar free convection},
     journal = {Russian journal of nonlinear dynamics},
     pages = {651--657},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_4_a3/}
}
TY  - JOUR
AU  - S. N. Aristov
AU  - E. Yu. Prosviryakov
TI  - On laminar flows of planar free convection
JO  - Russian journal of nonlinear dynamics
PY  - 2013
SP  - 651
EP  - 657
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2013_9_4_a3/
LA  - ru
ID  - ND_2013_9_4_a3
ER  - 
%0 Journal Article
%A S. N. Aristov
%A E. Yu. Prosviryakov
%T On laminar flows of planar free convection
%J Russian journal of nonlinear dynamics
%D 2013
%P 651-657
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2013_9_4_a3/
%G ru
%F ND_2013_9_4_a3
S. N. Aristov; E. Yu. Prosviryakov. On laminar flows of planar free convection. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 651-657. http://geodesic.mathdoc.fr/item/ND_2013_9_4_a3/