Exact solutions for some oscillating motions of a fractional Burgers’ fluid

Khan, Masood; Anjum, Aisha; Fetecău, Constantin; Qi, Haitao

doi:10.1016/j.mcm.2009.10.040

Cited by 61 publications

(30 citation statements)

References 46 publications

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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%

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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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Section: Development Of the Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Helical flows of fractionalized Burgers' fluids

Jamil

Khan

2012

AIP Advances

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“…Z et.al [11], discussed the MHD flow of a generalized Burgers' fluid due to an exponential accelerating plate, khan. M, et al [12], discussed the exact solutions for the oscillating motions of a fractional Burgers' fluid due to cosine and sine oscillations of an infinite flat plate. In Dhiman.B and Uma [13], studied the unsteady incompressible flow of a generalized Oldroyd-B fluid between two oscillating parallel plates in the presence of a transverse magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Effect of Unsteady Magnetic Hydrodynamic on Oscillating Flow for Fractional Burgers’ Model

Nassief¹

2017

JNUS

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The purpose of this paper is studying the effect of magnetic hydrodynamic (MHD) of unsteady flow with fractional Burger's model between two oscillating parallel plates. The fractional order derivative in described in the Riemann-Liouville sense. The solutions which we obtained of the velocity field and the shear stress by using Laplace transform and Fourier transform in the expression of Mittage-Lefller function. Furthermore, the influence of the parameters on the velocity field spotlighted by means of the several graphs.

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“…Later Ahmad et al 6 proposed an efficient algorithm for solving of linear and nonlinear fractional two-point boundary value problems. In paper, 7 the analytical solutions of a fractional Burgers' fluid over an infinite flat plate were presented. Hameed et al 8 studied the heat transfer of second grade fractional fluid in a cylindrical tube, the effects of magnetic field are analyzed.…”

Section: Introductionmentioning

confidence: 99%

Fractional boundary layer flow and radiation heat transfer of MHD viscoelastic fluid over an unsteady stretching surface

2015

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This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.

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Exact solutions for some oscillating motions of a fractional Burgers’ fluid

Cited by 61 publications

References 46 publications

Helical flows of fractionalized Burgers' fluids

Helical flows of fractionalized Burgers' fluids

Effect of Unsteady Magnetic Hydrodynamic on Oscillating Flow for Fractional Burgers’ Model

Fractional boundary layer flow and radiation heat transfer of MHD viscoelastic fluid over an unsteady stretching surface

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