Exact solutions of starting flows for a fractional Burgers’ fluid between coaxial cylinders

Khan, Masood; Ali, S. Hyder; Qi, Haitao

doi:10.1016/j.nonrwa.2008.02.015

Cited by 36 publications

(21 citation statements)

References 18 publications

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“…They showed that the classical Navier-Stokes and also Maxwell fluid and second grade fluid solutions may be extracted as special cases of the fractional viscoelastic model. Khan et al [22] have derived exact solutions for transient starting flow of fractional Burger's fluid in the gap between two infinitely long concentric circular cylinders, both for the case where the outer cylinder makes a simple harmonic oscillation and also when the outer cylinder suddenly begins rotating while the inner cylinder remains stationary. Further appraisals of fractional viscoelastic flows have been made by Bagley and Torvik [23], Song and Jiang [24], Hilfer [25], Qi and Xu [26] and also Qi and Jin [27].…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model

Maqbool¹,

Bég

Sohail

et al. 2016

Eur. Phys. J. Plus

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Section: Introductionmentioning

confidence: 99%

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model

Maqbool¹,

Bég

Sohail

et al. 2016

Eur. Phys. J. Plus

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“…In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method will be used. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] …”

Section: Development Of the Governing Equationsmentioning

confidence: 99%

“…In general, fractional model of viscoelastic fluids is derived from well known ordinary model by replacing the ordinary time derivatives to fractional order time derivatives and this plays an important role to study the valuable tool of viscoelastic properties. Some authors [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] have investigated unsteady flows of fractionalized viscoelastic second grade, Maxwell, Oldroyed-B, Burgers' and generalized Burgers' model through walls/channel/ annulus and solutions for velocity field and the associated shear stress are obtained by using discrete Laplace transform, Fourier transform, Weber transform and finite Hankel transforms.…”

Section: Introductionmentioning

confidence: 99%

Helical flows of fractionalized Burgers' fluids

Jamil

Khan

2012

AIP Advances

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The unsteady flows of Burgers’ fluid with fractional derivatives model, through a circular cylinder, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Ut. The solutions that have been obtained, presented in series form in terms of the generalized Ga,b,c(•, t) functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for fractionalized Oldroyd-B, Maxwell and second grade fluids appear as special cases of the present results. Furthermore, the solutions for ordinary Burgers’, Oldroyd-B, Maxwell, second grade and Newtonian performing the same motion, are also obtained as special cases of general solutions by substituting fractional parameters α = β = 1. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison among models, is shown by graphical illustrations

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“…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 solutions of starting flows for a fractional Burgers’ fluid between coaxial cylinders

Cited by 36 publications

References 18 publications

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model

Analytical solutions for wall slip effects on magnetohydrodynamic oscillatory rotating plate and channel flows in porous media using a fractional Burgers viscoelastic model

Helical flows of fractionalized Burgers' fluids

On Unsteady Flow of a Viscoelastic Fluid Through Rotating Cylinders

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