Geodesic
On thermodiffusion of binary mixture in a horizontal channel at inhomogeneous heating the walls
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 6, pp. 776-784.

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

The influence of the thermal load distributed unevenly at the walls of a long horizontal channel filled with a binary mixture on the convective flow is studied based on the constructed exact solution of the boundary value problem for the Oberbeck-Boussinesque equations. It is established that the obtained solution reflects the effect of thermal diffusion correctly, demonstrating the accumulation of a light component near a more heated wall. It is shown that an increase in the horizontal and vertical temperature gradient on the walls leads to the appearance of inhomogeneities in the temperature and concentration fields inside the layer.
Keywords: binary mixture
Mots-clés : Oberbeck-Boussinesque equations, exact solution, convection, thermal diffusion separation. 
@article{JSFU_2022_15_6_a10,
     author = {Irina V. Stepanova},
     title = {On thermodiffusion of binary mixture in a horizontal channel at inhomogeneous heating the walls},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {776--784},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_6_a10/}
}
TY  - JOUR
AU  - Irina V. Stepanova
TI  - On thermodiffusion of binary mixture in a horizontal channel at inhomogeneous heating the walls
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 776
EP  - 784
VL  - 15
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_6_a10/
LA  - en
ID  - JSFU_2022_15_6_a10
ER  - 
%0 Journal Article
%A Irina V. Stepanova
%T On thermodiffusion of binary mixture in a horizontal channel at inhomogeneous heating the walls
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 776-784
%V 15
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_6_a10/
%G en
%F JSFU_2022_15_6_a10
Irina V. Stepanova. On thermodiffusion of binary mixture in a horizontal channel at inhomogeneous heating the walls. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 6, pp. 776-784. http://geodesic.mathdoc.fr/item/JSFU_2022_15_6_a10/

[1] G.A. Ostroumov, Free Convection under the Conditions of an Internal Problem, Gostekhizdat Press, M.-L., 1952 (in Russian)

[2] R.V. Birikh, “Thermocapillary convection in a horizontal layer of liquid”, J. Appl. Mech. Tech. Phys., 3 (1966), 35–45

[3] V.K. Andreev, Birikh solutions for convection equations and thier generalizations, ICM SB RAS, Krasnoyarsk, 2010 (in Russian)

[4] V.V. Pukhnachev, “Non-stationary analogs of Birikh solutions”, Izvestiya of Altai State University, 69:1-2 (2011), 62–69 (in Russian)

[5] V.B. Bekezhanova, O.N. Goncharova, I.A. Shefer, “Analysis of an exact solution of problem of the evaporative convection (review). Part I. Plane case”, J. Sib. Fed. Univ. Math. Phys., 11:2 (2018), 178–190 | DOI

[6] L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, v. 6, Fluid Mechanics, 2nd ed., Butterworth-Heinemahh, Oxford, 1987

[7] S.R. De Groot, P. Mazur, Non-equilibrium Thermodynamic, Dover, London, 1984

[8] V.K. Andreev, I.V. Stepanova, “Inverse problem for source function in parabolic equation at Neumann boundary conditions”, J. Sib. Fed. Univ. Math. Phys., 14:4 (2021), 445–451 | DOI

[9] V.K. Andreev, Yu.A. Gaponenko, O.N. Goncharova, V.V. Pukhnachev, Mathematical Models of Convection, 2nd Edition, De Gryuter Publ, 2020

[10] I.I. Ryzhkov, Thermal diffusion in mixtures: equations, symmetry, solutions and their stability, SB RAS, Novosibirsk, 2013 (in Russian)

[11] I.V. Stepanova, “Study of convection of binary mixture in a horizontal channel based on exact solution of heat and mass transfer equations”, Int. J. Appl. Comput. Math. (to appear)

[12] V.K. Andreev, I.V. Stepanova, “Non-stationary Unidirectional Motion of Binary Mixture in Long Flat Layer”, Int. J. Appl. Comput. Math., 6:6 (2020) | DOI