Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

Fetecău, Constantin

doi:10.1016/j.ijnonlinmec.2005.05.005

Cited by 68 publications

(26 citation statements)

References 14 publications

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“…The Reynolds number is the same in all cases Re G = 18.9, the elasticity number is El = 0.05 in both the Oldroyd-B and Giesekus fluids and α = 0.2 for the Giesekus fluid. Far away from the particle, the flow velocity (blue arrows) in the Oldroyd-B channel shows the same distribution as in the Newtonian Poiseuille flow in a square channel (Fetecau & Fetecau 2005). While in a Giesekus fluid, the velocity profile is flatter near the centre of the channel and a larger maximum velocity is achieved due to the shear-thinning effect.…”

Section: Resultsmentioning

confidence: 71%

“…For a square-shaped channel, k = ∞ n,odd 1 n 3 (1 − sech nπ 2 ) ≃ 0.571. In Newtonian and Oldroyd-B fluids, U 0 is equal to the steady centreline velocity of the channel U c (Fetecau & Fetecau 2005), whereas in shear-thinning fluids U c > U 0 . The particle is neutrally buoyant and has a spherical shape with diameter d. The blockage ratio is set to κ = d/H = 0.25, unless otherwise stated.…”

Section: Mathematical Model and Numerical Methodsmentioning

confidence: 99%

“…In the poiseuille flow of viscoelastic fluids, velocity oscillation can be observed during flow start-up (Fetecau & Fetecau 2005) because of the propagation of stress waves in the channel (Duarte et al 2008). Transient velocity oscillations also occur for a particle settling in viscoelastic fluids, often causing the particle to "rebound" during the first oscillation (Arigo & McKinley 1997;Goyal & Derksen 2012).…”

Section: Particle Migration During Flow Start-upmentioning

confidence: 99%

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Dynamics of particle migration in channel flow of viscoelastic fluids

2015

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The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertia effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle-focusing.

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Section: Resultsmentioning

confidence: 71%

Section: Mathematical Model and Numerical Methodsmentioning

confidence: 99%

Section: Particle Migration During Flow Start-upmentioning

confidence: 99%

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Dynamics of particle migration in channel flow of viscoelastic fluids

2015

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“…Gardner and Gardner [10] discussed magnetohydrodynamic (MHD) duct flow of two-dimensional bi-cubic B-spline finite element. Fetecau and Fetecau [11] investigated the flows of Oldroyd-B fluid in a channel of rectangular cross-section. Nazar et al [12] examined oscillating flow passing through rectangular duct for Maxwell fluid using integral transforms.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Magnetohydrodynamic Flow of Jeffrey Fluid through a Porous Oscillating Rectangular Duct

Khan¹,

Zaman²,

Algahtani³

2018

Porosity - Process, Technologies and Applications

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This chapter presents some new exact solutions corresponding to unsteady magnetohydrodynamic (MHD) flow of Jeffrey fluid in a long porous rectangular duct oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform (DFFST) and discrete Laplace transform (LT). The series solution of velocity field, associated shear stress and volume flow rate in terms of Fox Hfunctions, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameter.

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“…Many researchers are paying attention toward this model as it best describes the fluid with viscoelastic properties. Hayat et al considered the magnetohydrodynamics (MHD) flow of Oldroyd-B fluid with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, 8 velocity and shear stress for an Oldroyd-B fluid within two cylinders have been discussed by Kang et al, 9 withdrawal and drainage of thin film flow of a generalized Oldroyd-B fluid on non-isothermal cylindrical surfaces have been discussed by S Ullah et al, 10 Fetecau and Fetecau 11 investigated the unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section, and translational flows of an Oldroyd-B fluid with fractional derivatives have been discussed by Jamil et al 12 The motion of a fluid in a rotating or translating cylinder is of interest to both theoretical and practical domains. It is of crucial significance to study the mechanism of viscoelastic fluids flow within the circular cylinder domains as it has applications in many industrial fields, such as oil exploitation, chemical and food industry, and bio-engineering.…”

Section: Introductionmentioning

confidence: 99%

Some exact solutions for the rotational flow of Oldroyd-B fluid between two circular cylinders

Ullah

Khan

Bajwa

et al. 2017

Advances in Mechanical Engineering

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In this article, an effort has been made to compute and inspect the rotational flow of Oldroyd-B fluid between two co-axial circular cylinders. As novelty, the rotation of both cylinders produces motion of the fluid. The velocity field and tangential stress corresponding to the motion of an Oldroyd-B fluid with fractional derivatives have been obtained using Laplace and Hankel integral transforms. The velocity profiles of the respective model are graphically presented and deliberated for the pertinent parameters. Corresponding solutions are also obtained for ordinary Oldroyd-B fluid, ordinary and fractional Maxwell fluids, ordinary and fractional second-grade fluids, and Newtonian fluid as limiting cases of our general solutions.

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Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

Cited by 68 publications

References 14 publications

Dynamics of particle migration in channel flow of viscoelastic fluids

Dynamics of particle migration in channel flow of viscoelastic fluids

Unsteady Magnetohydrodynamic Flow of Jeffrey Fluid through a Porous Oscillating Rectangular Duct

Some exact solutions for the rotational flow of Oldroyd-B fluid between two circular cylinders

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