Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model

Mahmood, Ahsan; Parveen, Saima; Ara, Asmat; Khan, Nasir

doi:10.1016/j.cnsns.2009.01.017

Cited by 79 publications

(35 citation statements)

References 30 publications

(27 reference statements)

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“…These solutions have been already extended to Oldroyd-B fluids by Rajagopal et al [18]. Other interesting results have been recently obtained by Khan et al [19] and Fetecau et al [20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 64%

“…On the other hand, the exact solutions corresponding to the flow of these fluids between two cylinders, when both of them are oscillating along or around their common axis simultaneously, are very rare in literature. Recently, Mahmood et al [21] have studied the flow of fractional Maxwell fluid between two cylinders, when both of them are oscillating around their common axis. In this paper, we are interested into the longitudinal oscillatory motion of a generalized second grade fluid between two infinite coaxial circular cylinders when both of them are oscillating along their common axis with given constant angular frequencies 1 and 2 .…”

Section: Introductionmentioning

confidence: 99%

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Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

et al. 2010

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The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0 + both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies 1 and 2 . The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and A. Mahmood (B) · M. Jamil

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Section: Introductionmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

et al. 2010

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“…The most general solution corresponding to the helical flow of a second grade fluid seem to be those of Fetecau and Cornia Fetecau [10], in which the cylinder is rotating around its axis and sliding along the same axis with time-dependent velocities. There is a vast literature dealing with such fluids, but we shall recall here only a few of the most recent papers [12][13][14][15][16]. Most existing solutions in the literature correspond to problems with boundary conditions on the velocity.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for the Flow of a Generalized Oldroyd-B Fluid in a Circular Cylinder

Hai-tao¹,

Fatima²,

Waqas³

et al. 2017

Open J. Math. Sci.

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Abstract. The tangential stress and velocity field corresponding to the flow of a generalized Oldroyd-B fluid in an infinite circular cylinder will be determined by mean of Laplace and finite Hankel transform. The motion is produced by the cylinder, that after t = 0 + , begins to rotate about its axis, under the action of oscillating shear stress ΩR sin(ωt) given on boundary. The solutions are based on an important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions. The obtained solution will be presented under series form in term of generalized G-function. The similar solutions for the ordinary Oldroyd-B fluid, Maxwell, ordinary Maxwell and Newtonian fluids performing the same motion will be obtained as special cases of our general solutions.

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“…Qi et al [11,12] studied the unsteady flow of a viscoelastic fluid with fractional Maxwell model. Recently, Fetecau et al [13] and Mahmood et al [14] also studied the flow of fractional Maxwell fluid between coaxial cylinders. There is a vast literature dealing with such fluids, but we shall recall here only a few of the recent papers [15,16,17,18,19,20,21,22,23,24,25,26] in cylindrical domains.…”

Section: Introductionmentioning

confidence: 99%

On Unsteady Flow of a Viscoelastic Fluid Through Rotating Cylinders

Tahir¹,

Safdar²,

Vieru³

et al. 2017

Open J. Math. Sci.

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Abstract. The fractional calculus approach is used in the constitutive relationship model of fractional Maxwell fluid. Exact solutions for the velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are obtained by using the Laplace transform and finite Hankel transform for fractional calculus. The solutions that have been obtained are presented in terms of generalized G b,c,d (·, t) and R b,c (·, t) functions. In the limiting cases, the corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained from our general solutions. Furthermore, the solutions for the motion between the cylinders, when one of them is at rest, are also obtained as special cases from our results. Finally, the influence of the material parameters on the fluid motion is underlined by graphical illustrations.

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Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model

Cited by 79 publications

References 30 publications

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

Analytical Solution for the Flow of a Generalized Oldroyd-B Fluid in a Circular Cylinder

On Unsteady Flow of a Viscoelastic Fluid Through Rotating Cylinders

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