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Nelin. Dinam., 2013, Volume 9, Number 4, Pages 651–657 (Mi nd412)  

This article is cited in 13 scientific papers (total in 13 papers)

On laminar flows of planar free convection

S. N. Aristova, E. Yu. Prosviryakovb

a Institute of Continuous Media Mechanics UB RAS, Ak. Koroleva str. 1, Perm, 614013, Russia
b Kazan National Research Technical University named after A. N. Tupolev, Karl Marx str. 10, Kazan, 420111, Russia

Abstract: 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, polynomial solution, decrease in dimension, Benard–Marangoni convection.

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UDC: 532.51
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Received: 09.07.2013
Revised: 05.09.2013

Citation: S. N. Aristov, E. Yu. Prosviryakov, “On laminar flows of planar free convection”, Nelin. Dinam., 9:4 (2013), 651–657

Citation in format AMSBIB
\by S.~N.~Aristov, E.~Yu.~Prosviryakov
\paper On laminar flows of planar free convection
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 4
\pages 651--657

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    This publication is cited in the following articles:
    1. S. N. Aristov, V. V. Privalova, E. Yu. Prosviryakov, “Statsionarnoe neizotermicheskoe techenie Kuetta. Kvadratichnyi nagrev verkhnei granitsy sloya zhidkosti”, Nelineinaya dinam., 12:2 (2016), 167–178  mathnet  elib
    2. S. Vakulenko, I. Sudakov, “Complex bifurcations in Bénard-Marangoni convection”, J. Phys. A-Math. Theor., 49:42 (2016), 424001  crossref  isi
    3. S. N. Aristov, E. Yu. Prosviryakov, “Nonuniform convective couette flow”, Fluid Dyn., 51:5 (2016), 581–587  crossref  isi
    4. S. N. Aristov, E. Yu. Prosviryakov, “A new class of exact solutions for three-dimensional thermal diffusion equations”, Theor. Found. Chem. Eng., 50:3 (2016), 286–293  crossref  isi
    5. V. K. Andreev, I. V. Stepanova, “Unidirectional flows of binary mixtures within the framework of the Oberbeck-Boussinesq model”, Fluid Dyn., 51:2 (2016), 136–147  crossref  isi
    6. S. N. Aristov, E. Yu. Prosviryakov, L. F. Spevak, “Unsteady-state Bénard-Marangoni convection in layered viscous incompressible flows”, Theor. Found. Chem. Eng., 50:2 (2016), 132–141  crossref  isi
    7. N. V. Burmasheva, E. Yu. Prosviryakov, “Krupnomasshtabnaya sloistaya statsionarnaya konvektsiya vyazkoi neszhimaemoi zhidkosti pod deistviem kasatelnykh napryazhenii na verkhnei granitse. Issledovanie polya skorostei”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 180–196  mathnet  crossref  elib
    8. E. V. Rezanova, I. A. Shefer, “Influence of the thermal load on the characteristics of a flow with evaporation”, J. Appl. Industr. Math., 11:2 (2017), 274–283  mathnet  crossref  crossref  elib
    9. N. V. Burmasheva, E. Yu. Prosviryakov, “Exact solutions for layered large-scale convection induced by tangential stresses specified on the free boundary of a fluid layer”, Winter school on continuous media mechanics, IOP Conference Series-Materials Science and Engineering, 208, IOP Publishing Ltd, 2017, UNSP 012010  crossref  isi  scopus
    10. E. Yu. Prosviryakov, L. F. Spevak, “Exact solutions for stationary and unsteady layered convection of a viscous incompressible fluid with the specified velocities at the bottom”, Winter school on continuous media mechanics, IOP Conference Series-Materials Science and Engineering, 208, IOP Publishing Ltd, 2017, UNSP 012035  crossref  isi  scopus
    11. N. V. Burmasheva, E. Yu. Prosviryakov, “Krupnomasshtabnaya sloistaya statsionarnaya konvektsiya vyazkoi neszhimaemoi zhidkosti pod deistviem kasatelnykh napryazhenii na verkhnei granitse. Issledovanie polei temperatury i davleniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:4 (2017), 736–751  mathnet  crossref  zmath  elib
    12. V. V. Privalova, E. Yu. Prosviryakov, “Statsionarnoe konvektivnoe techenie KuettaKhimentsa pri kvadratichnom nagreve nizhnei granitsy sloya zhidkosti”, Nelineinaya dinam., 14:1 (2018), 69–79  mathnet  crossref  elib
    13. A. V. Gorshkov, E. Yu. Prosviryakov, “Ekman convective layer flow of a viscous incompressible fluid”, Izv. Atmos. Ocean. Phys., 54:2 (2018), 189–195  crossref  mathscinet  isi  scopus
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