Solutions of the Jeffery-Hamel Problem Regularly Extendable in the Reynolds Number

Акуленко, Л. Д.; Георгиевский, Д. В.; Kumakshev, S. A.

doi:10.1023/b:flui.0000024807.80902.cb

Cited by 12 publications

(15 citation statements)

References 10 publications

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“…Solutions regularly continuable in the number Re < 0, i.e., in the parameter b < 0, exist if a = a * = arg D(a), i.e., β = β * ≡ 2.2467047 [10]. The critical angle of divergence 2β * 257 • is greater than the straight angle and less than the angle corresponding to a right angle between the outer sides of the divergent channel walls.…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The algorithm (2.4), (2.5) possesses the property of accelerated (quadratic) convergence [2,10,12] and makes it possible to carry out high-accuracy (with relative and absolute errors of the order of 10 −5 -10 −8 ) rapid mass calculations of the unknown parameters γ = γ(b) and λ = λ (b) for fixed values of β . After integration of the Cauchy problem (2.2), the obtained dependences of y and y , and γ and λ can be used to determine the kinematic and dynamic characteristics of viscous fluid flows in a plane divergent channel (see Section 5).…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The system has two dimensionless parameters: the angle of divergence 2β and the Reynolds number Re = ρQ/µ (Re < 0). It is well known that the problems own parameters are insufficient or the complete nondimensionalization of the equations of motion [4,5,9,10].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The stress vector components can be determined in terms of σ rr and σ rθ [10]. The components of the total force density vector F = (F r , F θ ) at a distance r are equal to…”

Section: Physical Characteristics Of Divergent Channel Flowsmentioning

confidence: 99%

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Bifurcation of a Main Steady-State Viscous Fluid Flow in a Plane Divergent Channel

Акуленко¹,

Kumakshev²

2005

Fluid Dyn

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The evolution of steady-state viscous incompressible fluid flows in a plane divergent channel is investigated. For the classical formulation of the Jeffery-Hamel problem a complete solution is given as a function of the determining parameters. For a fixed angle of divergence the behavior of the main unimodal flow is determined as a function of the Reynolds number. Critical values at which the flow pattern bifurcates and the steady-state unimodal flow ceases to exist are found. The mechanism of bifurcation is established and its diagram is constructed. This mechanism and the diagram were not previously known in the scientific literature in connection with the investigation of the Jeffery-Hamel problem. The critical Reynolds number at which bifurcation occurs is given as a function of the channel divergence angle. The results may be of interest for hydromechanical, technological, and geophysical applications. Keywords: divergent channel, viscous fluid, Jeffery-Hamel problem, steady-state flow, bifurcation. 0015-4628/05/4003-0359  2005 Springer Science+Business Media, Inc. z = y − 1, z(0) = 0; y(1) = z(1) = 0 (2.2)

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Section: Methods Of Solutionmentioning

confidence: 99%

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The stress vector components can be determined in terms of σ rr and σ rθ [10]. The components of the total force density vector F = (F r , F θ ) at a distance r are equal to…”

Section: Physical Characteristics Of Divergent Channel Flowsmentioning

confidence: 99%

See 2 more Smart Citations

Bifurcation of a Main Steady-State Viscous Fluid Flow in a Plane Divergent Channel

Акуленко¹,

Kumakshev²

2005

Fluid Dyn

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“…A stationary problem with a finite number of "outlets" to infinity in the form of infinite sectors is considered by Rivkind and Solonnikov [3]. The problem of steady viscous flow in a convergent channel is analyzed analytically and numerically for small, moderately large and asymptotically large Reynolds numbers over the entire range of allowed convergence angles by Akulenko, et al [4]. The MHD Jeffery-Hamel problem is solved by Makinde and Mhone [5] using a special type of Hermite-Padé approximation semi-numerical approach and by Esmaili et al [6] by applying the Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Marinca

Ene

2017

Open Physics

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Abstract:In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.

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The Influence of Controlled Vibration Effects on Fluid Flow in Technological and Engineering Processes

Fedyushkin

2024

Lecture Notes in Civil Engineering

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This article presents the results of studies demonstrating the influence of nonlinear effects of laminar flow under vibrational harmonic effects on fluid flow and heat transfer. The paper summarizes the results of research on the influence of vibrations in various fluid flow problems. The effect of periodic oscillations on the symmetrization of an asymmetric flow in a diffuser, on Rayleigh-Bernard convection and on the wide of boundary layers in various single crystal growth processes are shown.

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Solutions of the Jeffery-Hamel Problem Regularly Extendable in the Reynolds Number

Cited by 12 publications

References 10 publications

Bifurcation of a Main Steady-State Viscous Fluid Flow in a Plane Divergent Channel

Bifurcation of a Main Steady-State Viscous Fluid Flow in a Plane Divergent Channel

Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

The Influence of Controlled Vibration Effects on Fluid Flow in Technological and Engineering Processes

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