Temperature Field Investigation in Layered Flows of a Vertically Swirling Viscous Incompressible Fluid Under Two Thermocapillar Forces at a Free Boundary

Abstract

Burmasheva N. V., Prosviryakov E. Yu. Temperature field investigation in layered flows of a vertically swirling viscous incompressible fluid under two thermocapillar forces at a free boundary // Diagnostics, Resource and Mechanics of materials and structures.

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

“…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].…”

“…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.…”

“…The velocity field of convective flows of a vertically swirling fluid was studied in [13,18,19]. It was shown that the vertical vorticity component can exist when the fluid does not rotate.…”

An Exact Solution to the Description of a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid With the Navier Boundary Condition. Velocity Field Investigation

“…Изучение конвективных движений в жидкости основывается на анализе свойств точных решений уравнений тепловой конвекции [12]. В работах [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] построены обобщенные классы точных решений, в том числе и для конвективных термокапиллярных течений [25][26][27][28][29][30][31]. Предложенные точные решения описывают неодномерные течения жидкости.…”

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

“…We set the task to analyze how the consideration of vertical twist affects the behavior of the flow. For convenience and clarity, we choose a family of exact solutions [35,36,44,61]…”