On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains

Kamran, Muhammad; Athar, Muhammad; Imran, Muhammad

doi:10.1007/s11012-011-9467-4

Cited by 27 publications

(22 citation statements)

References 23 publications

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“…Similar solutions for the flow due to an infinite plate that applies a constant/time-dependent shear to a non-Newtonian fluid, have been also obtained by Erdogan [19], Fetecau and Kannana [20], Awan et al [21] and Kamran et al [22]. The computer techniques make the complete integration of the momentum equation feasible, the accuracy of the numerical results can be established by comparison with an exact solution.…”

Section: Introductionsupporting

confidence: 57%

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation

Imran¹

2015

AJAM

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Abstract:In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0 + , is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.

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Section: Introductionsupporting

confidence: 57%

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation

Imran¹

2015

AJAM

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“…The first exact solution for the motion of second grade fluids due to a shear stress on the boundary has been determined by Bandelli and Rajagopal [4].He studied a number of unidirectional transient flows of a second grade fluid in a domain with one finite dimension. Recently, many papers regarding such motions have been published [5][6][7][8][9][10][11][12]. Fetecau [13] used constitutive relation as follows…”

Section: Introductionmentioning

confidence: 99%

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Mathur¹,

Khandelwal²

2014

IOSRJM

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“…Taking O = 0 in our solutions, the corresponding solutions obtained in Kamran et al 28 are recovered as special case of our general solutions for the rotational flow of Oldroyd-B fluid with fractional derivatives.…”

Section: Special Casementioning

confidence: 74%

“…28 The governing equations corresponding to an Oldroyd-B fluid with fractional derivatives under the same motion are attained from equations (3) and (4) …”

Section: Governing Equationsmentioning

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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On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains

Cited by 27 publications

References 23 publications

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

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

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