[Текст] : статья / E. N. Lemeshkhova // Journal of Siberian Federal University. Mathematics & Physics = Журнал Сибирского федерального университета. Математика и физика. - 2013. - Т. 6, № 2. - С. 211-219
Перевод заглавия: Комбинированное движение трёх вязких теплопроводных жидкостей в плоском слое
Аннотация: Thejoint unidirectional motion of three viscousliquids undertheinfluence of thermocapillarityforces and pressure difference has been researched. An exact stationary solution of the problem has been found. The solution of the non — stationary problem has been obtained in the form of final analytical formulas in the image using the method of Laplace transformation. By the numerical inversion of Laplace transformation the evolution of the velocity fields and of the temperature perturbation to the stationary regime for specific liquids has been obtained.
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Лемешкова, Елена Николаевна
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Onset of convection in a two-phase binary mixture with the Soret effect in weightlessness
/ I. I. Ryzhkov, S. P. Tsarev // Phys. Fluids. - 2015. - Vol. 27, Is. 7. - Ст. 072103, DOI 10.1063/1.4926891
. - ISSN 1070-6631
Кл.слова (ненормированные):
Binary mixtures -- Temperature -- Weightlessness -- Concentration gradients -- Conservation of mass -- Critical temperature difference -- Interfacial concentrations -- Latent heat release -- Mechanical equilibrium -- Onset of convection -- Temperature differences -- Mixtures
Аннотация: The linear stability of mechanical equilibrium in a two-layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane-methanol binary mixture, which has a liquid-liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long-wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers. © 2015 AIP Publishing LLC.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Institute of Space and Information Technologies, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tsarev, S.P.; Рыжков, Илья Игоревич
Кл.слова (ненормированные):
Binary mixtures -- Temperature -- Weightlessness -- Concentration gradients -- Conservation of mass -- Critical temperature difference -- Interfacial concentrations -- Latent heat release -- Mechanical equilibrium -- Onset of convection -- Temperature differences -- Mixtures
Аннотация: The linear stability of mechanical equilibrium in a two-layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane-methanol binary mixture, which has a liquid-liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long-wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers. © 2015 AIP Publishing LLC.
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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Institute of Space and Information Technologies, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tsarev, S.P.; Рыжков, Илья Игоревич
The joint creeping motion of three viscid liquids in a plane layer: A priori estimates and convergence to steady flow
/ V. K. Andreev, N. Cheremnykh // J. Appl. Ind. Math. - 2016. - Vol. 10, Is. 1. - P7-20, DOI 10.1134/S1990478916010026
. - ISSN 1990-4789
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate initial-boundary value problem -- thermocapillarity -- Boundary value problems -- Estimation -- Heat conduction -- Initial value problems -- Liquids -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviors -- Conducting liquid -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Non-linear inverse problem -- Thermocapillarity -- Inverse problems
Аннотация: We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes. © 2016, Pleiades Publishing, Ltd.
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Держатели документа:
Institute of Computational Modelling, Akademgorodok 50, bld. 44, Krasnoyarsk, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, N.
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate initial-boundary value problem -- thermocapillarity -- Boundary value problems -- Estimation -- Heat conduction -- Initial value problems -- Liquids -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviors -- Conducting liquid -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Non-linear inverse problem -- Thermocapillarity -- Inverse problems
Аннотация: We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes. © 2016, Pleiades Publishing, Ltd.
Scopus
Держатели документа:
Institute of Computational Modelling, Akademgorodok 50, bld. 44, Krasnoyarsk, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, N.
2D thermocapillary motion of three fluids in a flat channel
/ V. K. Andreev, E. N. Cheremnykh // J. Sib. Fed. Univ. Math. Phys. - 2016. - Vol. 9, Is. 4. - P404-415, DOI 10.17516/1997-1397-2016-9-4-404-415
. - ISSN 1997-1397
Кл.слова (ненормированные):
Interface -- Mathematical modeling -- Numerical experiments -- Thermocapillarity
Аннотация: Two-dimensional creeping motion of three immiscible, incompressible viscous fluids in a flat channel bounded by fixed solid walls, on which the temperature distribution is known, is investigated. The motion is induced only by the thermalcapillary forces beginning from the state of rest. Unsteady motion is described by finite analytic formulas obtained by Laplace transform in images. The evolution of the velocity fields to the stationary regime for specific liquids is obtained by the numerical inversion of Laplace transformation. © Siberian Federal University. All rights reserved.
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Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, Russian Federation
Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, E. N.
Кл.слова (ненормированные):
Interface -- Mathematical modeling -- Numerical experiments -- Thermocapillarity
Аннотация: Two-dimensional creeping motion of three immiscible, incompressible viscous fluids in a flat channel bounded by fixed solid walls, on which the temperature distribution is known, is investigated. The motion is induced only by the thermalcapillary forces beginning from the state of rest. Unsteady motion is described by finite analytic formulas obtained by Laplace transform in images. The evolution of the velocity fields to the stationary regime for specific liquids is obtained by the numerical inversion of Laplace transformation. © Siberian Federal University. All rights reserved.
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Держатели документа:
Institute of computational modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, Russian Federation
Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Cheremnykh, E. N.
2D Thermocapillary Motion of Three Fluids in a Flat Channel
: статья / Victor K. Andreev, Elena N. Cheremnykh // Журнал Сибирского федерального университета. Серия: Математика и физика. - 2016. - Т. 9, № 4. - P404-415, DOI 10.17516/1997-1397-2016-9-4-404-415
. - ISSN 1997-1397
Перевод заглавия: Двумерное термокапиллярное движение трех жидкостей в плоском канале
Кл.слова (ненормированные):
thermocapillarity -- interface -- mathematical modeling -- numerical experiments -- термокапиллярность -- поверхность раздела -- математическое моделирование -- численные эксперименты
Аннотация: Two-dimensional creeping motion of three immiscible, incompressible viscous ?uids in a ?at channel bounded by ?xed solid walls, on which the temperature distribution is known, is investigated. The motion is induced only by the thermalcapillary forces beginning from the state of rest. Unsteady motion is described by ?nite analytic formulas obtained by Laplace transform in images. The evolution of the velocity ?eldstothe stationaryregimeforspeci?c liquidsis obtainedbythe numerical inversionofLaplace transformation.
Исследовано двумерное ползущее движение трех несмешивающихся несжимаемых вязких теплопроводных жидкостей в плоском канале, ограниченном твердыми неподвижными стенками, на которых известнораспределение температур.Вобразах по Лапласу построено точное нестационарное решение в виде квадратур и приведены некоторые численные результаты поведения полей скоростей и температур в слоях.
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Держатели документа:
Institute of computational modelling SB RAS
Institute of Mathematics and Computer Science Siberian Federal University
Доп.точки доступа:
Cheremnykh, E. N.; Черемных, Елена Николаевна; Андреев, Виктор Константинович
Перевод заглавия: Двумерное термокапиллярное движение трех жидкостей в плоском канале
| УДК |
Кл.слова (ненормированные):
thermocapillarity -- interface -- mathematical modeling -- numerical experiments -- термокапиллярность -- поверхность раздела -- математическое моделирование -- численные эксперименты
Аннотация: Two-dimensional creeping motion of three immiscible, incompressible viscous ?uids in a ?at channel bounded by ?xed solid walls, on which the temperature distribution is known, is investigated. The motion is induced only by the thermalcapillary forces beginning from the state of rest. Unsteady motion is described by ?nite analytic formulas obtained by Laplace transform in images. The evolution of the velocity ?eldstothe stationaryregimeforspeci?c liquidsis obtainedbythe numerical inversionofLaplace transformation.
Исследовано двумерное ползущее движение трех несмешивающихся несжимаемых вязких теплопроводных жидкостей в плоском канале, ограниченном твердыми неподвижными стенками, на которых известнораспределение температур.Вобразах по Лапласу построено точное нестационарное решение в виде квадратур и приведены некоторые численные результаты поведения полей скоростей и температур в слоях.
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Держатели документа:
Institute of computational modelling SB RAS
Institute of Mathematics and Computer Science Siberian Federal University
Доп.точки доступа:
Cheremnykh, E. N.; Черемных, Елена Николаевна; Андреев, Виктор Константинович
On the inverse problem of a creeping motion in thin layers
/ V. Andreev // CEUR Workshop Proceedings : CEUR-WS, 2017. - Vol. 1839: 2016 International Conference Mathematical and Information Technologies, MIT 2016 (28 August 2016 through 5 September 2016, ) Conference code: 127940. - P258-270
. -
Кл.слова (ненормированные):
A priori estimates -- Asymptotic behaviour -- Conjugate initial-boundary value problem -- Numerical simulation -- Thermocapillarity -- Boundary value problems -- Capillary flow -- Computer simulation -- Estimation -- Initial value problems -- Laplace transforms -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviour -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Numerical results -- Thermo-capillary forces -- Thermocapillarity -- Inverse problems
Аннотация: The new partially invariant solution of two-dimential motions of heated viscous liquid equations is considered. For factor-system arised the initial boundary value problem is formulated. This problem is inverse one and describing of common motion of two immiscible liquids in a plane channel under the action of thermocapillary forces. As Marangoni number is small (so-called creeping flow) the problem becomes the linear one. Some a priori estimates are obtained and input data conditions when solution tends to stationary one are found. In Laplace transforms the exact solution is obtained as quadratures and some numerical results of velocities behavior in layers are presented.
Scopus
Держатели документа:
Institute Computational Modelling SB RAS, Siberian Federal University, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V.
Кл.слова (ненормированные):
A priori estimates -- Asymptotic behaviour -- Conjugate initial-boundary value problem -- Numerical simulation -- Thermocapillarity -- Boundary value problems -- Capillary flow -- Computer simulation -- Estimation -- Initial value problems -- Laplace transforms -- Nonlinear equations -- A-priori estimates -- Asymptotic behaviour -- Immiscible liquids -- Initial-boundary value problems -- Invariant solutions -- Numerical results -- Thermo-capillary forces -- Thermocapillarity -- Inverse problems
Аннотация: The new partially invariant solution of two-dimential motions of heated viscous liquid equations is considered. For factor-system arised the initial boundary value problem is formulated. This problem is inverse one and describing of common motion of two immiscible liquids in a plane channel under the action of thermocapillary forces. As Marangoni number is small (so-called creeping flow) the problem becomes the linear one. Some a priori estimates are obtained and input data conditions when solution tends to stationary one are found. In Laplace transforms the exact solution is obtained as quadratures and some numerical results of velocities behavior in layers are presented.
Scopus
Держатели документа:
Institute Computational Modelling SB RAS, Siberian Federal University, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V.
Properties of Solutions for the Problem of a Joint Slow Motion of a Liquid and a Binary Mixture in a Two-Dimensional Channel
/ V. K. Andreev, M. V. Efimova // J. Appl. Ind. Math. - 2018. - Vol. 12, Is. 3. - P395-408, DOI 10.1134/S1990478918030018
. - ISSN 1990-4789
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate problem -- inverse problem -- surface tension -- thermocapillarity -- Binary mixtures -- Channel flow -- Heat conduction -- Nonlinear equations -- Surface tension -- A-priori estimates -- Asymptotic behaviors -- Conjugate problems -- Horizontal components -- Non-stationary problems -- Properties of solutions -- Thermocapillarity -- Two dimensional channels -- Inverse problems
Аннотация: Under study is a conjugate boundary value problemdescribing a joint motion of a binary mixture and a viscous heat-conducting liquid in a two-dimensional channel, where the horizontal component of the velocity vector depends linearly on one of the coordinates. The problemis nonlinear and inverse because the systems of equations contain the unknown time functions—the pressure gradients in the layers. In the case of small Marangoni numbers (the so-called creeping flow) the problem becomes linear. For its solutions the two different integral identities are valid which allow us to obtain a priori estimates of the solution in the uniform metric. It is proved that if the temperature on the channel walls stabilizes with time then, as time increases, the solution of the nonstationary problem tends to a stationary solution by an exponential law. © 2018, Pleiades Publishing, Ltd.
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Держатели документа:
Institute of Computational Modeling, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Efimova, M. V.
Кл.слова (ненормированные):
a priori estimates -- asymptotic behavior -- conjugate problem -- inverse problem -- surface tension -- thermocapillarity -- Binary mixtures -- Channel flow -- Heat conduction -- Nonlinear equations -- Surface tension -- A-priori estimates -- Asymptotic behaviors -- Conjugate problems -- Horizontal components -- Non-stationary problems -- Properties of solutions -- Thermocapillarity -- Two dimensional channels -- Inverse problems
Аннотация: Under study is a conjugate boundary value problemdescribing a joint motion of a binary mixture and a viscous heat-conducting liquid in a two-dimensional channel, where the horizontal component of the velocity vector depends linearly on one of the coordinates. The problemis nonlinear and inverse because the systems of equations contain the unknown time functions—the pressure gradients in the layers. In the case of small Marangoni numbers (the so-called creeping flow) the problem becomes linear. For its solutions the two different integral identities are valid which allow us to obtain a priori estimates of the solution in the uniform metric. It is proved that if the temperature on the channel walls stabilizes with time then, as time increases, the solution of the nonstationary problem tends to a stationary solution by an exponential law. © 2018, Pleiades Publishing, Ltd.
Scopus,
Смотреть статью
Держатели документа:
Institute of Computational Modeling, Akademgorodok 50/44, Krasnoyarsk, 660036, Russian Federation
Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Andreev, V. K.; Efimova, M. V.
On the solution properties of boundary problem simulating thermocapillary flow
/ V. K. Andreev // Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Softw. - 2018. - Vol. 11, Is. 4. - С. 31-40, DOI 10.14529/mmpl80402
. - ISSN 2071-0216
Аннотация: An inverse initial boundary value problem that arises as a result of mathematical modelling of specific thermocapillary 2D motion near an extreme point on solid wall is investigated. One of the velocity field components considered motion linearly depends on the longitudinal coordinate. This is a good agrement with the quadratic dependence of temperature field on the same coordinate. For stationary flow in the case of small Marangoni numbers the solution can be found by exact formulae. Nonstationary solution is found in quadratures in Laplace transformation space. The calculation results of zero and first solution approximations of this inverse stationary problem are given. If temperature on the solid wall is stabilized with time, then the nonstationary solution will converge to steady regime. The calculations are performed for different values of the Prandtl number and Bio number. Numerical results well support the theoretical conclusions on the example of modelling process arising the thermocapillary motion from a state of rest in the transformer oil layer. It is shown that choosing a specific thermal regime on a solid wall it is possible to control the fluid motion inside a layer. © 2018 South Ural State University. All rights reserved.
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Держатели документа:
Institute Computational Modelling SBRAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.
Аннотация: An inverse initial boundary value problem that arises as a result of mathematical modelling of specific thermocapillary 2D motion near an extreme point on solid wall is investigated. One of the velocity field components considered motion linearly depends on the longitudinal coordinate. This is a good agrement with the quadratic dependence of temperature field on the same coordinate. For stationary flow in the case of small Marangoni numbers the solution can be found by exact formulae. Nonstationary solution is found in quadratures in Laplace transformation space. The calculation results of zero and first solution approximations of this inverse stationary problem are given. If temperature on the solid wall is stabilized with time, then the nonstationary solution will converge to steady regime. The calculations are performed for different values of the Prandtl number and Bio number. Numerical results well support the theoretical conclusions on the example of modelling process arising the thermocapillary motion from a state of rest in the transformer oil layer. It is shown that choosing a specific thermal regime on a solid wall it is possible to control the fluid motion inside a layer. © 2018 South Ural State University. All rights reserved.
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Держатели документа:
Institute Computational Modelling SBRAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Andreev, V. K.
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О свойствах решений краевой задачи, моделирующей термокапиллярное течение
: статья / В. К. Андреев // Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование. - 2018. - Т. 11, № 4. - С. 31-40, DOI 10.14529/mmp180402
. - ISSN 2071-0216
Перевод заглавия: On the Solution Properties of Boundary Problem Simulating Thermocapillary Flow
Кл.слова (ненормированные):
обратная задача -- преобразование Лапласа -- термокапиллярность -- inverse problem -- Laplace transform -- thermocapillarity
Аннотация: Исследуется обратная начально-краевая задача, возникающая при математическом моделировании специальных термокапиллярных двумерных движений жидкости вблизи точки экстремума температуры на твердой стенке. Одна из компонент поля скоростей рассматриваемого движения линейно зависит от продольной координаты, что согласуется с квадратичной зависимостью поля температур от этой же координаты. При малых числах Марангони задача аппроксимируется линейной, решение которой находится в явном виде для стационарного течения. Приведены результаты вычисления нулевого и первого приближения решения обратной стационарной задачи. В нестационарном случае решение определяется в виде квадратур в пространстве изображений по Лапласу. Показано, что если температура на твердой стенке стабилизируется с ростом времени, то решение стремится к найденному стационарному режиму. Приведены численные результаты обращения преобразования Лапласа, подтверждающие теоретические выводы на примере моделирования процесса возникновения термокапиллярного движения из состояния покоя в слое трансформаторного масла. Показано, что, выбирая тот или иной тепловой режим на твердой стенке, можно управлять движением жидкости внутри слоя.
An inverse initial boundary value problem that arises as a result of mathematical modelling of specific thermocapillary 2D motion near an extreme point on solid wall is investigated. One of the velocity field components considered motion linearly depends on the longitudinal coordinate. This is a good agrement with the quadratic dependence of temperature field on the same coordinate. For stationary flow in the case of small Marangoni numbers the solution can be found by exact formulae. Nonstationary solution is found in quadratures in Laplace transformation space. The calculation results of zero and first solution approximations of this inverse stationary problem are given. If temperature on the solid wall is stabilized with time, then the nonstationary solution will converge to steady regime. The calculations are performed for different values of the Prandtl number and Bio number. Numerical results well support the theoretical conclusions on the example of modelling process arising the thermocapillary motion from a state of rest in the transformer oil layer. It is shown that choosing a specific thermal regime on a solid wall it is possible to control the fluid motion inside a layer.
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Держатели документа:
Институт вычислительного моделирования СО РАН - обособленное подразделение ФИЦ КНЦ СО РАН
Доп.точки доступа:
Андреев, Виктор Константинович; Andreev V.K.
Перевод заглавия: On the Solution Properties of Boundary Problem Simulating Thermocapillary Flow
| УДК |
Кл.слова (ненормированные):
обратная задача -- преобразование Лапласа -- термокапиллярность -- inverse problem -- Laplace transform -- thermocapillarity
Аннотация: Исследуется обратная начально-краевая задача, возникающая при математическом моделировании специальных термокапиллярных двумерных движений жидкости вблизи точки экстремума температуры на твердой стенке. Одна из компонент поля скоростей рассматриваемого движения линейно зависит от продольной координаты, что согласуется с квадратичной зависимостью поля температур от этой же координаты. При малых числах Марангони задача аппроксимируется линейной, решение которой находится в явном виде для стационарного течения. Приведены результаты вычисления нулевого и первого приближения решения обратной стационарной задачи. В нестационарном случае решение определяется в виде квадратур в пространстве изображений по Лапласу. Показано, что если температура на твердой стенке стабилизируется с ростом времени, то решение стремится к найденному стационарному режиму. Приведены численные результаты обращения преобразования Лапласа, подтверждающие теоретические выводы на примере моделирования процесса возникновения термокапиллярного движения из состояния покоя в слое трансформаторного масла. Показано, что, выбирая тот или иной тепловой режим на твердой стенке, можно управлять движением жидкости внутри слоя.
An inverse initial boundary value problem that arises as a result of mathematical modelling of specific thermocapillary 2D motion near an extreme point on solid wall is investigated. One of the velocity field components considered motion linearly depends on the longitudinal coordinate. This is a good agrement with the quadratic dependence of temperature field on the same coordinate. For stationary flow in the case of small Marangoni numbers the solution can be found by exact formulae. Nonstationary solution is found in quadratures in Laplace transformation space. The calculation results of zero and first solution approximations of this inverse stationary problem are given. If temperature on the solid wall is stabilized with time, then the nonstationary solution will converge to steady regime. The calculations are performed for different values of the Prandtl number and Bio number. Numerical results well support the theoretical conclusions on the example of modelling process arising the thermocapillary motion from a state of rest in the transformer oil layer. It is shown that choosing a specific thermal regime on a solid wall it is possible to control the fluid motion inside a layer.
РИНЦ,
WOS,
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Держатели документа:
Институт вычислительного моделирования СО РАН - обособленное подразделение ФИЦ КНЦ СО РАН
Доп.точки доступа:
Андреев, Виктор Константинович; Andreev V.K.
Two-Dimensional Plane Steady-State Thermocapillary Flow
/ E. N. Lemeshkova // Fluid Dyn. - 2019. - Vol. 54, Is. 1. - P33-41, DOI 10.1134/S0015462819010087. - Cited References:10. - The work was supported by the RFBR (project no. 17-01-00229).
. - ISSN 0015-4628. - ISSN 1573-8507
РУБ Mechanics + Physics, Fluids & Plasmas
Аннотация: The problem of a two-dimensional steady flow of a fluid in a flat channel with a free boundary when the surface tension coefficient depends linearly on the temperature is considered. On the channel bottom, a fixed temperature distribution is maintained. The temperature in the fluid is distributed in accordance with the quadratic law, which is consistent with the velocity field of the Xiemenz type. The arising boundary-value problem is strongly nonlinear and inverse with respect to the pressure gradient along the channel. The application of the tau-method shows that this problem has three different solutions. In the case of a thermally insulated free boundary, only one solution exists. Typical flow patterns are studied for each solution.
WOS,
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Scopus
Держатели документа:
RAS, Inst Computat Modeling SB, Krasnoyarsk, Russia.
Siberian Fed Univ, Inst Math & Fundamental Informat, Krasnoyarsk, Russia.
Доп.точки доступа:
Lemeshkova, E. N.; RFBR [17-01-00229]
Аннотация: The problem of a two-dimensional steady flow of a fluid in a flat channel with a free boundary when the surface tension coefficient depends linearly on the temperature is considered. On the channel bottom, a fixed temperature distribution is maintained. The temperature in the fluid is distributed in accordance with the quadratic law, which is consistent with the velocity field of the Xiemenz type. The arising boundary-value problem is strongly nonlinear and inverse with respect to the pressure gradient along the channel. The application of the tau-method shows that this problem has three different solutions. In the case of a thermally insulated free boundary, only one solution exists. Typical flow patterns are studied for each solution.
WOS,
Смотреть статью,
Scopus
Держатели документа:
RAS, Inst Computat Modeling SB, Krasnoyarsk, Russia.
Siberian Fed Univ, Inst Math & Fundamental Informat, Krasnoyarsk, Russia.
Доп.точки доступа:
Lemeshkova, E. N.; RFBR [17-01-00229]