The shear-driven Rayleigh problem for generalised Newtonian fluids

Brian R. Duffy; David Pritchard; Stephen K. Wilson

doi:10.1016/j.jnnfm.2014.02.001

The shear-driven Rayleigh problem for generalised Newtonian fluids

Brian R. Duffy, David Pritchard, Stephen K. Wilson

Mathematics And Statistics

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Abstract

We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.

Original language	English
Pages (from-to)	11-17
Number of pages	7
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	206
Early online date	11 Feb 2014
DOIs	https://doi.org/10.1016/j.jnnfm.2014.02.001
Publication status	Published - 30 Apr 2014

Keywords

boundary layer
generalised Newtonian fluid
rayleigh problem
stokes’s first problem

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10.1016/j.jnnfm.2014.02.001

DuffyPritchardWilson-JNNFM2014-shear-driven-rayleigh-problemAccepted author manuscript, 250 KBLicence: CC BY-NC-ND 4.0

Cite this

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title = "The shear-driven Rayleigh problem for generalised Newtonian fluids",

abstract = "We consider a variant of the classical {\textquoteleft}Rayleigh problem{\textquoteright} ({\textquoteleft}Stokes{\textquoteright}s first problem{\textquoteright}) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.",

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note = "Notice: This is the author's version of a work that was accepted for publication in Journal of Non-Newtonian Fluid Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Non-Newtonian Fluid Mechanics, [206, April, (2014)], http://dx.doi.org/10.1016/j.jnnfm.2014.02.001",

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doi = "10.1016/j.jnnfm.2014.02.001",

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T1 - The shear-driven Rayleigh problem for generalised Newtonian fluids

AU - Duffy, Brian R.

AU - Pritchard, David

AU - Wilson, Stephen K.

N1 - Notice: This is the author's version of a work that was accepted for publication in Journal of Non-Newtonian Fluid Mechanics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Non-Newtonian Fluid Mechanics, [206, April, (2014)], http://dx.doi.org/10.1016/j.jnnfm.2014.02.001

PY - 2014/4/30

Y1 - 2014/4/30

N2 - We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.

AB - We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.

KW - boundary layer

KW - generalised Newtonian fluid

KW - rayleigh problem

KW - stokes’s first problem

UR - http://www.journals.elsevier.com/journal-of-non-newtonian-fluid-mechanics

U2 - 10.1016/j.jnnfm.2014.02.001

DO - 10.1016/j.jnnfm.2014.02.001

M3 - Article

SN - 0377-0257

VL - 206

SP - 11

EP - 17

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

ER -

The shear-driven Rayleigh problem for generalised Newtonian fluids

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Keywords

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