Exact solutions for the unsteady rotational flow of an Oldroyd-B fluid with fractional derivatives induced by a circular cylinder

Kamran, Muhammad; Imran, Muhammad; Athar, Muhammad

doi:10.1007/s11012-012-9662-y

Cited by 13 publications

(8 citation statements)

References 25 publications

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“…The first exact solution for the motion of second grade fluids due to a shear stress on the boundary has been determined by Bandelli and Rajagopal [4].He studied a number of unidirectional transient flows of a second grade fluid in a domain with one finite dimension. Recently, many papers regarding such motions have been published [5][6][7][8][9][10][11][12]. Fetecau [13] used constitutive relation as follows…”

Section: Introductionmentioning

confidence: 99%

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Mathur¹,

Khandelwal²

2014

IOSRJM

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Section: Introductionmentioning

confidence: 99%

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Mathur¹,

Khandelwal²

2014

IOSRJM

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“…Here, the formulation of velocity V and the extra-stress S for the fluid under consideration are as [28]…”

Section: Governing Equationsmentioning

confidence: 99%

“…where e θ is the unit vector of the cylindrical coordinates system and F(r, t) is the component of velocity along e θ . The initial conditions for the fluid at rest position are, as in [28];…”

Section: Governing Equationsmentioning

confidence: 99%

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

et al. 2019

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The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations.

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“…The academic workers and engineers are very much interested in the geometry of such types of flows [6,17]. The literature about motion under translating or rotating cylinders for non-Newtonian fluids is not so well organized, but some interesting studies of such types of fluid flows are given by Jamil et al [8,9], Kamran et al [10,11], and Mahmood et al [14,15].…”

Section: Introductionmentioning

confidence: 99%

Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders

Ullah¹,

Tanveer²,

Bajwa³

2019

Hacettepe Journal of Mathematics and Statistics

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This investigation deals with the study of unsteady flow of incompressible Oldroyd-B fluid between two rotating circular cylinders, both cylinders are rotating around their common axis (r = 0). The governing differential equations are formulated with appropriate boundary conditions and then solved by means of Laplace and Hankel transforms to obtain velocity and shear stress for unsteady flow of Oldroyd-B fluid between two infinite concentric rotating circular cylinders. The obtained solutions can easily be reduced to equivalent solutions for Maxwell and classical Newtonian fluids. Finally, the influence of different physical parameters on the fluid velocity and shear stress is graphically underlined and discussed.

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Exact solutions for the unsteady rotational flow of an Oldroyd-B fluid with fractional derivatives induced by a circular cylinder

Cited by 13 publications

References 25 publications

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

Exact solution for the flow of Oldroyd-B fluid due to constant shear and time dependent velocity

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

Study of velocity and shear stress for unsteady flow of incompressible Oldroyd-B fluid between two concentric rotating circular cylinders

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