Start-up flows of second grade fluids in domains with one finite dimension

Bandelli, R.; Rajagopal, Κ. R.

doi:10.1016/0020-7462(95)00035-6

Cited by 180 publications

(97 citation statements)

References 9 publications

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“…2 Amongst different non-Newtonian fluids, the second and third grade fluids become much popular. 3,4 Important contributions to the topic include the works of Bandelli, 5 Hayat et al, 6,7 Sajid et al 8 and references therein. One of the key problems while obtaining the numerical solutions of the two-dimensional flows of viscoelastic fluids is the vanishing of coefficient of the leading order derivative term appearing in the governing equation with the viscoelastic parameter.…”

Section: Introductionmentioning

confidence: 99%

On numerical and approximate solutions for stagnation point flow involving third order fluid

et al. 2015

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This article addresses the two-dimensional boundary layer flow of third order fluid in the region of a stagnation point over a surface lubricated with a power law fluid. The lubricant is assumed to have a thin layer of variable thickness over the surface. The third order fluid experiences a partial slip due to this lubrication layer. Mathematical model of the flow problem is represented through a system of nonlinear partial differential equations with nonlinear boundary conditions. The non-similar numerical and analytic solutions of the transformed ordinary differential equation are obtained using hybrid homotopy analysis method based on the combination of homotopy analysis and shooting methods. It is observed that extra drag force is required in order to achieve no-slip regime from full slip and thus slip has suppressed the effects of free stream velocity. The results varying from no-slip to full slip case are discussed under the influence of pertinent parameters.

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Section: Introductionmentioning

confidence: 99%

On numerical and approximate solutions for stagnation point flow involving third order fluid

et al. 2015

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“…The first exact solution corresponding to motion of Maxwell fluids in cylindrical domain has been determined by Srivastava [2] .Waters and King [3] published first exact solution corresponding to motion of Oldroyd-B fluids in cylindrical domains. 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].…”

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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“…The aim of this note is to extend the results of Bandelli and Rajagopal [13,Sect. 4] to Burgers and generalized Burgers fluids.…”

Section: Introductionmentioning

confidence: 70%

“…Furthermore, making λ 1 , λ 2 and λ 4 0, Eq. (10a) reduces to the boundary condition (4.3) used by Bandelli and Rajagopal [13]. It corresponds to a problem with a constant shear stress on a part of the boundary, namely…”

Section: Starting Flow Due To a Time Dependent Shear Stressmentioning

confidence: 99%

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Starting solutions for the motion of a generalized Burgers' fluid between coaxial cylinders

Jamil

Fetecău

2012

Bound Value Probl

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The unsteady flow of a generalized Burgers' fluid, between two infinite coaxial circular cylinders, is studied by means of the Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, after the initial moment, applies a longitudinal time dependent shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers' fluids appear as special cases of present results. For large values of t, these solutions are going to the steady solutions that are the same for both kinds of fluids. Finally, the influence of the material parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations. Mathematics Subject Classification (2010). 76A05; 76A10.

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Start-up flows of second grade fluids in domains with one finite dimension

Cited by 180 publications

References 9 publications

On numerical and approximate solutions for stagnation point flow involving third order fluid

On numerical and approximate solutions for stagnation point flow involving third order fluid

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

Starting solutions for the motion of a generalized Burgers' fluid between coaxial cylinders

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