A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress

Nazar, Mudassar; Fetecău, Constantin; Awan, Aziz Ullah

doi:10.1016/j.nonrwa.2009.06.010

Cited by 41 publications

(11 citation statements)

References 19 publications

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“…The list of their applications is quite long, it including fractal media, fractional wave diffusion, fractional Hamiltonian dynamics as well as many other topics in physics [8]. In the last time, a lot of papers regarding these fluids have been published but we remember here only a part of those concerning generalized second grade fluids [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

Imran

Kamran

Athar

et al. 2011

NAMC

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Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

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Section: Introductionmentioning

confidence: 99%

Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

Imran

Kamran

Athar

et al. 2011

NAMC

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“…They obtained numerical solutions by employing Runge-Kutta Felhberg technique. Of course the list of study on circular cylinder for viscoelastic fluid can be continuous but we end it with some recent references (Shah and Qi, 2010;Wang and Xu, 2009;Nazar et al, 2010;Fetecau et al, 2010;Malekzadeh et al, 2011;Abro and Solangi, 2017;Muhammad et al, 2015;Abro, 2016;Rostami et al, 2014;Rashidi et al, 2014;Rashidi et al, 2012;Rashidi et al, 2015 …”

Section: Introductionmentioning

confidence: 99%

Helical flows of fractional viscoelastic fluid in a circular pipe

Laghari

2017

Int. j. adv. appl. sci.

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The exploration of this study is devoted to investigate the helical effects for the flow of fractionalized viscoelastic fluid in helically moved cylinder. The cylinder starts to oscillate and rotate about its axis when = 0 + with velocities. By applying mathematical transforms (Hankel and discrete Laplace transforms) exact solutions are found out for velocities and shear stresses. The general solutions satisfy initial conditions 1 ( , 0) = 2 ( , 0) = 1 ( ,0) = 2 ( ,0) = 0, as well as boundary conditions

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“…of a generalized second grade fluid [12][13][14][15][16][17]. The flow of a generalized second grade fluid past a porous plate was analyzed with the homotopy analysis method by Hayat and Khan [18].…”

Section: Introductionmentioning

confidence: 99%

Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

Wang

2017

Can. J. Phys.

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This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

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A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress

Cited by 41 publications

References 19 publications

Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

Helical flows of fractional viscoelastic fluid in a circular pipe

Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

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