Investigation of a velocity field for the Marangoni shear convection of a vertically swirling viscous incompressible fluid

Burmasheva, N. V.; Prosviryakov, E. Yu.

doi:10.1063/1.5084449

Cited by 7 publications

(15 citation statements)

References 21 publications

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“…The resulting system consists of five scalar equations with respect to five unknowns, namely the components , , of the velocity vector V, pressure , and temperature . When considering a number of practically important flows belonging to the class of layered and shear (unidirectional and non-one-dimensional) flows, a problem arises related to the overdetermination of the Oberbeck-Boussinesq system since ≡ 0 for these flows [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. One can resolve such an overdetermined system if, for example, one selects the projections of the velocity vector from a certain generalized class of exact solutions which allows one to satisfy the "unnecessary" equations [12-14, 16-19, 26, 27].…”

Section: Introductionmentioning

confidence: 99%

“…One can resolve such an overdetermined system if, for example, one selects the projections of the velocity vector from a certain generalized class of exact solutions which allows one to satisfy the "unnecessary" equations [12-14, 16-19, 26, 27]. The families of such classes differ, among other things, in that some of them can describe only flows of vertically unvortexed fluids, while others are suitable for modeling flows of fluids with nonzero vertical swirl [12][13][14][15][16][17][18][19][28][29][30][31][32][33][34][35][36][37]. Moreover, taking into account the vertical twist is certain to complicate the structure of the solution to the boundary value problem under study.…”

Section: Introductionmentioning

confidence: 99%

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Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

Burmasheva

Prosviryakov

2020

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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Приведен класс точных решений уравнений Обербека-Буссинеска, подходящих для описания трехмерных нелинейных слоистых течений вертикально завихренной вязкой несжимаемой жидкости. Неоднородное распределение поля скорости (имеет место зависимость компонент поля от горизонтальных координат) генерирует вертикальную закрутку в жидкости без внешнего вращения (без учета Кориолисова ускорения). Задание на границах области течения линейно распределенных теплового поля и поля касательных напряжений является одной из причин, индуцирующих конвекцию в вязкой несжимаемой жидкости. Основное внимание уделено исследованию свойств температурного поля. Изучено влияние вертикальной закрутки на распределение изолиний этого поля. Показано, что однородная составляющая температурного поля может стратифицироваться на несколько зон относительно отсчетного значения, причем число таких зон не превосходит девяти. Учет неоднородных составляющих поля температуры может приводить только к уменьшению этого числа. Также показано, что представленный в статье класс позволяет обобщить ранее полученные результаты по моделированию конвективных течений вязких несжимаемых жидкостей.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

Burmasheva

Prosviryakov

2020

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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“…A family of exact solutions for a vectorial velocity field generating no vertical twist was discussed in [30][31][32][33][34]. Taking into account vertical twist [35][36][37][38][39][40][41][42][43] changes the form of the particular solution of the boundary value problem and complicates its structure.…”

mentioning

confidence: 99%

“…An exact solution to the Oberbeck-Boussinesq system. The following system of equations of thermal shear convection in the Boussinesq approximation is considered [30,31,35,36,44,45]:…”

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confidence: 99%

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Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

Burmasheva

Prosviryakov

2019

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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This article discusses the solvability of an overdetermined system of heat convection equations in the Boussinesq approximation. The Oberbeck-Boussinesq system of equations, supplemented by an incompressibility equation, is overdetermined. The number of equations exceeds the number of unknown functions, since non-uniform layered flows of a viscous incompressible fluid are studied (one of the components of the velocity vector is identically zero). The solvability of the non-linear system of Oberbeck-Boussinesq equations is investigated. The solvability of the overdetermined system of non-linear Oberbeck-Boussinesq equations in partial derivatives is studied by constructing several particular exact solutions. A new class of exact solutions for describing three-dimensional non-linear layered flows of a vertical swirling viscous incompressible fluid is presented. The vertical component of vorticity in a non-rotating fluid is generated by a non-uniform velocity field at the lower boundary of an infinite horizontal fluid layer. Convection in a viscous incompressible fluid is induced by linear heat sources. The main attention is paid to the study of the properties of the flow velocity field. The dependence of the structure of this field on the magnitude of vertical twist Research Article c b The content is published under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/) Please cite this article in press as: B u r m a s h e v a N. V., P r o s v i r y a k o v E. Yu. Convective layered flows of a vertically whirling viscous incompressible fluid. B u r m a s h e v a N. V., P r o s v i r y a k o v E. Yu.is investigated. It is shown that, with nonzero vertical twist, one of the components of the velocity vector allows stratification into five zones through the thickness of the layer under study (four stagnant points). The analysis of the velocity field has shown that the kinetic energy of the fluid can twice take the zero value through the layer thickness.

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Layered Marangoni convection with the Navier slip condition

2021

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A new exact solution to the problem of Marangoni layered convection is obtained. This solution describes a layered steady-state flow of a viscous incompressible fluid at varying gradients of temperature and pressure. The velocity components depend only on the transverse coordinate; the temperature and pressure fields are three-dimensional. The Marangoni effect is observed on the upper free surface of the fluid layer. On the lower solid surface of the fluid layer, three different cases of defining boundary conditions are considered: the no-slip condition, the perfect slip condition and the Navier slip condition. The obtained exact solution is determined by the interaction of three flows: a flow caused by pressure drop (the Poiseuille flow), a flow caused by heating/cooling and the effect of the gravity force (the thermogravitational flow), and a flow caused by heating/cooling and the fluid surface tension effect (the thermocapillary flow). The obtained exact solutions in the case of each of the three types of boundary conditions specified on the lower surface are analyzed in detail. It has been proved that, when certain ratios of the boundary value problem parameters are fulfilled, the velocity components may acquire stagnation points, this being indicative of the presence of counterflow areas in the fluid layer under consideration. In particular, the presence of up to two stagnation points in each of the two longitudinal velocity components may cause a stratification of the velocity field in more than two regions. The obtained exact solution of the Marangoni layered convection problem can describe flows in thin films through the variation of the geometric anisotropy factor.

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Investigation of a velocity field for the Marangoni shear convection of a vertically swirling viscous incompressible fluid

Cited by 7 publications

References 21 publications

Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

Layered Marangoni convection with the Navier slip condition

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