A new class of exact solutions for three-dimensional thermal diffusion equations

Aristov, S. N.; Prosviryakov, E. Yu.

doi:10.1134/s0040579516030027

Cited by 73 publications

(59 citation statements)

References 23 publications

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“…The paper studies the analytical solution describing complex stationary convection in view of the thermocapillary Marangoni effect [1][2][3][4][5], with heat transfer at the boundaries of the flow obeying the NewtonRichman law [6,7]. The analysis of the solution is made.…”

Section: Introductionmentioning

confidence: 99%

“…is the coefficient of fluid volume expansion; g is free fall acceleration; ( 2 ) are met at the lower (non-deformable) surface for velocity. On the free surface defined by the equation h z , the conditions of thermocapillary convection [6,7] are set as…”

Section: Introductionmentioning

confidence: 99%

“…It is assumed that the buoyant force 0 g T for convection is balanced by the pressure gradient in the vertical direction. The general system of differential equations describing layered stationary convection in an incompressible fluid in the OberbeckBoussinesq approximation, with 0 z V , has the form [1][2][3][4][5][6][7][8][9][10][11][12] ,…”

Section: Introductionmentioning

confidence: 99%

“…On the free surface defined by the equation h z , the conditions of thermocapillary convection [6,7] are set as…”

Section: Introductionmentioning

confidence: 99%

“…The selected conditions correspond to the theoretical and experimental studies on hydrodynamics [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton’s law

Gorshkov

Prosviryakov

2017

AIP Conference Proceedings

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Abstract. The paper considers the construction of analytical solutions to the Oberbeck-Boussinesq system. This system describes layered Bénard-Marangoni convective flows of an incompressible viscous fluid. The third-kind boundary condition, i. e. Newton's heat transfer law, is used on the boundaries of a fluid layer. The obtained solution is analyzed. It is demonstrated that there is a fluid layer thickness with tangential stresses vanishing simultaneously, this being equivalent to the existence of tensile and compressive stresses.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…On the free surface defined by the equation h z , the conditions of thermocapillary convection [6,7] are set as…”

Section: Introductionmentioning

confidence: 99%

“…The selected conditions correspond to the theoretical and experimental studies on hydrodynamics [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton’s law

Gorshkov

Prosviryakov

2017

AIP Conference Proceedings

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Computational study on the effects of variable viscosity of micropolar liquids on heat transfer in a channel

Rafiq

Abbas

Nawaz

et al. 2020

J Therm Anal Calorim

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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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A new class of exact solutions for three-dimensional thermal diffusion equations

Cited by 73 publications

References 23 publications

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton’s law

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton’s law

Computational study on the effects of variable viscosity of micropolar liquids on heat transfer in a channel

Layered Marangoni convection with the Navier slip condition

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