The instability of non-Newtonian boundary-layer flows over rough rotating disks

A.A Alqarni; B. Alveroğlu; Paul Griffiths; S. J. Garrett

doi:10.1016/j.jnnfm.2019.104174

The instability of non-Newtonian boundary-layer flows over rough rotating disks

A.A Alqarni, B. Alveroğlu, Paul Griffiths, S. J. Garrett

University of Leicester

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

21 Citations (Scopus)

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Abstract

We are concerned with the local linear convective instability of the incompressible boundary-layer flows over rough rotating disks for non-Newtonian fluids. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness. The subsequent linear stability analyses of these flows (to disturbances stationary relative to the disk) indicate that isotropic and azimuthally-anisotropic (radial grooves) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.

Original language	English
Article number	104174
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	273
Early online date	9 Oct 2019
DOIs	https://doi.org/10.1016/j.jnnfm.2019.104174
Publication status	Published - Nov 2019

Bibliographical 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, 273 (2019) DOI: 10.1016/j.jnnfm.2019.104174

© 2019, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Carreau fluid
Convective instability
Laminar boundary layer
Non-Newtonian

ASJC Scopus subject areas

Chemical Engineering(all)
Materials Science(all)
Condensed Matter Physics
Mechanical Engineering
Applied Mathematics

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10.1016/j.jnnfm.2019.104174

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Cite this

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title = "The instability of non-Newtonian boundary-layer flows over rough rotating disks",

abstract = "We are concerned with the local linear convective instability of the incompressible boundary-layer flows over rough rotating disks for non-Newtonian fluids. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness. The subsequent linear stability analyses of these flows (to disturbances stationary relative to the disk) indicate that isotropic and azimuthally-anisotropic (radial grooves) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.",

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AU - Griffiths, Paul

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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, 273 (2019) DOI: 10.1016/j.jnnfm.2019.104174 © 2019, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2019/11

Y1 - 2019/11

N2 - We are concerned with the local linear convective instability of the incompressible boundary-layer flows over rough rotating disks for non-Newtonian fluids. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness. The subsequent linear stability analyses of these flows (to disturbances stationary relative to the disk) indicate that isotropic and azimuthally-anisotropic (radial grooves) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.

AB - We are concerned with the local linear convective instability of the incompressible boundary-layer flows over rough rotating disks for non-Newtonian fluids. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness. The subsequent linear stability analyses of these flows (to disturbances stationary relative to the disk) indicate that isotropic and azimuthally-anisotropic (radial grooves) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.

KW - Carreau fluid

KW - Convective instability

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KW - Non-Newtonian

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DO - 10.1016/j.jnnfm.2019.104174

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JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

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The instability of non-Newtonian boundary-layer flows over rough rotating disks

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