On unsteady unidirectional flows of a second grade fluid

Erdogˇan, M. Emin; İmrak, C. Erdem

doi:10.1016/j.ijnonlinmec.2005.05.004

Cited by 38 publications

(17 citation statements)

References 34 publications

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“…One of the most popular models for non-Newtonian fluids is the model corresponding to second-grade fluids [1]. Although there are some criticisms of the applications of this model [2][3][4], many papers on this have been published in the last few years [5][6][7][8][9][10][11][12][13][14][15]. Furthermore, it has been shown by Walters [16] that for many types of problems in which the flow is slow enough in the viscoelastic sense, the results given by Oldroyd's constitutive equations will be substantially similar to those from the second-grade or third-order Rivlin-Ericksen constitutive equations.…”

Section: Introductionmentioning

confidence: 99%

Energetic balance for the flow of a second-grade fluid due to a plate subject to a shear stress

Vieru

Siddique

Kamran

et al. 2008

Computers & Mathematics with Applications

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Exact and approximative expressions for dissipation, the power due to the shear stress at the wall and the boundary layer thickness corresponding to the unsteady motion of a second-grade fluid, induced by an infinite plate subject to a shear stress, are established. For α 1 −→ 0, similar results for Newtonian fluids performing the same motion are obtained. The results that have been obtained here are different to those corresponding to the Rayleigh-Stokes problem. A series solution for the velocity field is also determined. Its form, as was to be expected, is identical to that resulting from the general solution using asymptotic approximations.

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Section: Introductionmentioning

confidence: 99%

Energetic balance for the flow of a second-grade fluid due to a plate subject to a shear stress

Vieru

Siddique

Kamran

et al. 2008

Computers & Mathematics with Applications

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“…In order to exhibit certain characteristics of non-Newtonian fluids there is not at least single constitutive equation, this is due to complex behavior of fluid. The rheology of non-Newtonian fluids has distinct characteristics in fermentation, boiling, polymer processing, molten plastic foam processing, composite processing many others (Fetecau and Corina, 2005;Fetecau et al, 2007;Erdogan and Imrak, 2005;Chen et al, 2004;Hayat et al, 2004a;2004b;Abro and Shaikh, 2015). Nowadays, viscoelastic fluid (Maxwell model) is acknowledged by many scientists and engineers in several engineering and industrial processes.…”

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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“…Ramakrishna [11] took up the study of this flow taking dusty fluid as the fluid under consideration. The analogous problem for various fluids was studied in [12][13][14], of course, without labeling it as run up flow.…”

Section: Introductionmentioning

confidence: 99%

Run up flow of an incompressible micropolar fluid between parallel plates – A state space approach

Devakar

Iyengar

2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we study the run up flow of an incompressible micropolar fluid between two horizontal infinitely long parallel plates. Initially a flow of the fluid is induced by a constant pressure gradient until steady state is reached. After the steady state is reached, the pressure gradient is suddenly withdrawn while the two plates are impulsively started with different velocities in their own plane. Using the Laplace transform technique and adopting the state space approach, we obtain the velocity and microrotation components in Laplace transform domain. A standard numerical inversion procedure is used to find the velocity and microrotation in space-time domain for various values of time, distance, material parameters and pressure gradient. The variation of velocity and microrotation components is studied and the results are illustrated through graphs. It is observed that the micropolarity parameter has a decreasing effect on velocity component. It is also found that as the gyration parameter increases there is a decrease in microrotation component and an increase in velocity component.

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On unsteady unidirectional flows of a second grade fluid

Cited by 38 publications

References 34 publications

Energetic balance for the flow of a second-grade fluid due to a plate subject to a shear stress

Energetic balance for the flow of a second-grade fluid due to a plate subject to a shear stress

Helical flows of fractional viscoelastic fluid in a circular pipe

Run up flow of an incompressible micropolar fluid between parallel plates – A state space approach

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