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Eugenii Yurevich Prosviryakov - One of the best experts on this subject based on the ideXlab platform.
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on marangoni shear convective flows of inhomogeneous viscous incompressible fluids in view of the soret effect
Journal of King Saud University - Science, 2020Co-Authors: N V Burmasheva, Eugenii Yurevich ProsviryakovAbstract:Abstract A new exact solution is obtained for the Oberbeck-Boussinesq equations describing the steady-state layered (shear) Marangoni convection of a binary viscous incompressible fluid with the Soret effect. When layered (shear) flows are considered, the Oberbeck-Boussinesq system is overdetermined. For it to be solvable, a class of exact solutions is constructed, which allows one to satisfy identically the “superfluous” equation (the incompressibility equation). The found exact solution allows the Oberbeck-Boussinesq system of equations to be reduced to a system of ordinary differential equations by the generalized method of separation of variables. The resulting system of ordinary differential equations has an analytical solution, which is polynomial. The polynomial velocity field describes counterflows in the case of a convective fluid flow. It is demonstrated that the components of the velocity vector can have one stagnant (zero) point inside the region under study. In this case, the corresponding component of the velocity vector can be stratified into two zones, in which the fluid flows in opposite directions. The exact solution describing the velocity field for the Marangoni convection of a binary fluid has non-zero helicity, the flow itself being almost everywhere vortex.
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convective layered flows of a vertically whirling viscous incompressible fluid velocity field investigation
Вестник Самарского государственного технического университета. Серия «Физико-математические науки», 2019Co-Authors: N V Burmasheva, бурмашева наталья владимировна, Eugenii Yurevich Prosviryakov, просвиряков евгений юрьевичAbstract: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 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.
N V Burmasheva - One of the best experts on this subject based on the ideXlab platform.
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on marangoni shear convective flows of inhomogeneous viscous incompressible fluids in view of the soret effect
Journal of King Saud University - Science, 2020Co-Authors: N V Burmasheva, Eugenii Yurevich ProsviryakovAbstract:Abstract A new exact solution is obtained for the Oberbeck-Boussinesq equations describing the steady-state layered (shear) Marangoni convection of a binary viscous incompressible fluid with the Soret effect. When layered (shear) flows are considered, the Oberbeck-Boussinesq system is overdetermined. For it to be solvable, a class of exact solutions is constructed, which allows one to satisfy identically the “superfluous” equation (the incompressibility equation). The found exact solution allows the Oberbeck-Boussinesq system of equations to be reduced to a system of ordinary differential equations by the generalized method of separation of variables. The resulting system of ordinary differential equations has an analytical solution, which is polynomial. The polynomial velocity field describes counterflows in the case of a convective fluid flow. It is demonstrated that the components of the velocity vector can have one stagnant (zero) point inside the region under study. In this case, the corresponding component of the velocity vector can be stratified into two zones, in which the fluid flows in opposite directions. The exact solution describing the velocity field for the Marangoni convection of a binary fluid has non-zero helicity, the flow itself being almost everywhere vortex.
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convective layered flows of a vertically whirling viscous incompressible fluid velocity field investigation
Вестник Самарского государственного технического университета. Серия «Физико-математические науки», 2019Co-Authors: N V Burmasheva, бурмашева наталья владимировна, Eugenii Yurevich Prosviryakov, просвиряков евгений юрьевичAbstract: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 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.
Essam M. Abulwafa - One of the best experts on this subject based on the ideXlab platform.
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formulation and solution of space time fractional Boussinesq equation
Nonlinear Dynamics, 2015Co-Authors: S A Elwakil, Essam M. AbulwafaAbstract:The fractional variational principles beside the semi-inverse technique are applied to derive the space–time fractional Boussinesq equation. The semi-inverse method is used to find the Lagrangian of the Boussinesq equation. The classical derivatives in the Lagrangian are replaced by the fractional derivatives. Then, the fractional variational principles are devoted to lead to the fractional Euler–Lagrange equation, which gives the fractional Boussinesq equation. The modified Riemann–Liouville fractional derivative is used to obtain the space–time fractional Boussinesq equation. The fractional sub-equation method is employed to solve the derived space-time fractional Boussinesq equation. The solutions are obtained in terms of fractional hyper-geometric functions, fractional triangle functions and a rational function. These solutions show that the fractional Boussinesq equation can describe periodic, soliton and explosive waves. This study indicates that the fractional order modulates the waves described by Boussinesq equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting waves are added by considering the fractional order derivatives beside the nonlinearity.
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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exact traveling wave solution for local fractional Boussinesq equation in fractal domain
Fractals, 2017Co-Authors: Xiaojun Yang, J Tenreiro A Machado, Dumitru BaleanuAbstract:The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
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two analytical methods for time fractional nonlinear coupled Boussinesq burger s equations arise in propagation of shallow water waves
Nonlinear Dynamics, 2016Co-Authors: Sunil Kumar, Amit Kumar, Dumitru BaleanuAbstract:In this paper, an analytical method based on the generalized Taylors series formula together with residual error function, namely residual power series method (RPSM), is proposed for finding the numerical solution of the coupled system of time–fractional nonlinear Boussinesq–Burger’s equations. The Boussinesq–Burger’s equations arise in studying the fluid flow in a dynamic system and describe the propagation of the shallow water waves. Subsequently, the approximate solutions of time-fractional nonlinear coupled Boussinesq–Burger’s equations obtained by RPSM are compared with the exact solutions as well as the solutions obtained by modified homotopy analysis transform method. Then, we provide a rigorous convergence analysis and error estimate of RPSM. Numerical simulations of the results are depicted through different graphical representations and tables showing that present scheme is reliable and powerful in finding the numerical solutions of coupled system of fractional nonlinear differential equations like Boussinesq–Burger’s equations.
Daniel Lear - One of the best experts on this subject based on the ideXlab platform.
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on the asymptotic stability of stratified solutions for the 2d Boussinesq equations with a velocity damping term
Mathematical Models and Methods in Applied Sciences, 2019Co-Authors: Angel Castro, Diego Cordoba, Daniel LearAbstract:We consider the 2D Boussinesq equations with a velocity damping term in a strip domain, with impermeable walls. In this physical scenario, where the Boussinesq approximation is accurate when densit...
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on the asymptotic stability of stratified solutions for the 2d Boussinesq equations with a velocity damping term
arXiv: Analysis of PDEs, 2018Co-Authors: Angel Castro, Diego Cordoba, Daniel LearAbstract:We consider the 2D Boussinesq equations with a velocity damping term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical scenario, where the \textit{Boussinesq approximation} is accurate when density/temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution. To prove this result, we use a suitably weighted energy space combined with linear decay, Duhamel's formula and "bootstrap" arguments.
