Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

Deng-ke, Tong; Wang, Ruihe; Yang, Heshan

doi:10.1360/04yw0105

Cited by 78 publications

(55 citation statements)

References 15 publications

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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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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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“…Li and Jiang [12] employ the fractional calculus to examine the behavior of sesbania gum and Xanthan gum in their experiments and attain adequate results. Moreover, here we mention some more contributions which regards with the generalized viscoelastic type fluids [13]- [20].…”

Section: Introductionmentioning

confidence: 99%

Some Exact Solutions of Generalized Jeffrey Fluid Using N-Transform

Khan¹,

Zaman²,

Ahmad³

et al. 2017

AJCM

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In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.

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“…Rotational motion within annulus of an Oldroyd-B fluid is discussed by Imran et al (2015). Some important attempts to get exact solutions of fractional non-Newtonian fluid models are listed here ), Tong et al (2005, Sultan and Nazar (2016)). …”

Section: Introductionmentioning

confidence: 99%

Oscillating Motion of an Oldroyd-B Fluid with Fractional Derivatives in a Circular Cylinder

Raza¹,

Haq²,

Rashidi³

et al. 2017

JAFM

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The velocity field and tangential shear stress for unsteady flow of an Oldroyd-B fluid with Caputo fractional derivatives through an infinite long cylinder are evaluated. The fluid in the infinitely long cylinder is initially at rest and at t = 0+, due to shear, the fluid starts to oscillate longitudinally. We have solved the fractional model with the tool of Laplace and finite Hankel transformations. The solutions are in series form and are written in generalized G-function to avoid the entanglement. In limiting cases, the solutions of ordinary Oldroyd-B fluid, Maxwell fluid with fractional as well as ordinary and Newtonian fluid are derived. Finally, behavior of different physical parameters on fluid is illustrated by graphs.

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Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

Cited by 78 publications

References 15 publications

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

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

Some Exact Solutions of Generalized Jeffrey Fluid Using N-Transform

Oscillating Motion of an Oldroyd-B Fluid with Fractional Derivatives in a Circular Cylinder

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