On the first problem of Stokes for Burgers' fluids. II: The cases γ = λ2/4 and γ > λ2/4

D. Vieru; T. Hayat; Corina Fetecau; C. Fetecau

doi:10.1016/j.amc.2007.07.033

On the first problem of Stokes for Burgers' fluids. II: The cases γ = λ²/4 and γ > λ²/4

D. Vieru
, T. Hayat
, Corina Fetecau
, C. Fetecau

Gh. Asachi Technical University
Quaid-I-Azam University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The velocity fields and the associated tangential stresses corresponding to the flow of a Burgers' fluid over a suddenly moved flat plate are established when the relaxation times satisfy the conditions γ = λ²/4 and γ > λ²/4. Using the Laplace transform, the solutions are presented in forms of simple or multiple integrals in term of Bessel functions J₀( · ), J₁( · ), I₀ ( · ) and I₁( · ). The simplest solutions are obtained when γ = λ_r ² and λ = 2λ_r. The corresponding diagrams for velocity and shear stress are compared with those for a Newtonian fluid.

Original language	English
Pages (from-to)	76-86
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	197
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2007.07.033
State	Published - 15 Mar 2008
Externally published	Yes

Keywords

Burgers' fluid
Shear stress
Stokes' first problem
Velocity field

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10.1016/j.amc.2007.07.033

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title = "On the first problem of Stokes for Burgers' fluids. II: The cases γ = λ2/4 and γ > λ2/4",

abstract = "The velocity fields and the associated tangential stresses corresponding to the flow of a Burgers' fluid over a suddenly moved flat plate are established when the relaxation times satisfy the conditions γ = λ2/4 and γ > λ2/4. Using the Laplace transform, the solutions are presented in forms of simple or multiple integrals in term of Bessel functions J0( · ), J1( · ), I0 ( · ) and I1( · ). The simplest solutions are obtained when γ = λr 2 and λ = 2λr. The corresponding diagrams for velocity and shear stress are compared with those for a Newtonian fluid.",

keywords = "Burgers' fluid, Shear stress, Stokes' first problem, Velocity field",

author = "D. Vieru and T. Hayat and Corina Fetecau and C. Fetecau",

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T1 - On the first problem of Stokes for Burgers' fluids. II

T2 - The cases γ = λ2/4 and γ > λ2/4

AU - Vieru, D.

AU - Hayat, T.

AU - Fetecau, Corina

AU - Fetecau, C.

PY - 2008/3/15

Y1 - 2008/3/15

N2 - The velocity fields and the associated tangential stresses corresponding to the flow of a Burgers' fluid over a suddenly moved flat plate are established when the relaxation times satisfy the conditions γ = λ2/4 and γ > λ2/4. Using the Laplace transform, the solutions are presented in forms of simple or multiple integrals in term of Bessel functions J0( · ), J1( · ), I0 ( · ) and I1( · ). The simplest solutions are obtained when γ = λr 2 and λ = 2λr. The corresponding diagrams for velocity and shear stress are compared with those for a Newtonian fluid.

AB - The velocity fields and the associated tangential stresses corresponding to the flow of a Burgers' fluid over a suddenly moved flat plate are established when the relaxation times satisfy the conditions γ = λ2/4 and γ > λ2/4. Using the Laplace transform, the solutions are presented in forms of simple or multiple integrals in term of Bessel functions J0( · ), J1( · ), I0 ( · ) and I1( · ). The simplest solutions are obtained when γ = λr 2 and λ = 2λr. The corresponding diagrams for velocity and shear stress are compared with those for a Newtonian fluid.

KW - Burgers' fluid

KW - Shear stress

KW - Stokes' first problem

KW - Velocity field

UR - https://www.scopus.com/pages/publications/38949148950

U2 - 10.1016/j.amc.2007.07.033

DO - 10.1016/j.amc.2007.07.033

M3 - Article

AN - SCOPUS:38949148950

SN - 0096-3003

VL - 197

SP - 76

EP - 86

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

On the first problem of Stokes for Burgers' fluids. II: The cases γ = λ²/4 and γ > λ²/4

Abstract

Keywords

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