On the stability of the BEK family of rotating boundary-layer flows for power-law fluids

M. A. Abdulameer; P. T. Griffiths; B. Alveroğlu; S. J. Garrett

doi:10.1016/j.jnnfm.2016.08.006

On the stability of the BEK family of rotating boundary-layer flows for power-law fluids

M. A. Abdulameer
, P. T. Griffiths
, B. Alveroğlu
, S. J. Garrett

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

7 Citations (Scopus)

43 Downloads (Pure)

Abstract

We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.

Original language	English
Pages (from-to)	63-72
Number of pages	10
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	236
Early online date	26 Aug 2016
DOIs	https://doi.org/10.1016/j.jnnfm.2016.08.006
Publication status	Published - 1 Oct 2016
Externally published	Yes

Keywords

Bödewadt flow
Convective instability
Ekman layer
Flow control
Power-law fluid
Von Kármán flow

ASJC Scopus subject areas

General Chemical Engineering
General Materials Science
Condensed Matter Physics
Mechanical Engineering
Applied Mathematics

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10.1016/j.jnnfm.2016.08.006

Abdulameer_et_al_Stability_BEK_family_Non-Newtonian_Fluid_MechanicsAccepted author manuscript, 1.33 MBLicence: CC BY-NC-ND

https://lra.le.ac.uk/handle/2381/38547Licence: CC BY-NC-ND

Cite this

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title = "On the stability of the BEK family of rotating boundary-layer flows for power-law fluids",

abstract = "We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The B{\"o}dewadt, Ekman and von K{\'a}rm{\'a}n flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.",

keywords = "B{\"o}dewadt flow, Convective instability, Ekman layer, Flow control, Power-law fluid, Von K{\'a}rm{\'a}n flow",

author = "Abdulameer, \{M. A.\} and Griffiths, \{P. T.\} and B. Alveroğlu and Garrett, \{S. J.\}",

year = "2016",

month = oct,

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doi = "10.1016/j.jnnfm.2016.08.006",

language = "English",

volume = "236",

pages = "63--72",

journal = "Journal of Non-Newtonian Fluid Mechanics",

issn = "0377-0257",

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}

TY - JOUR

T1 - On the stability of the BEK family of rotating boundary-layer flows for power-law fluids

AU - Abdulameer, M. A.

AU - Griffiths, P. T.

AU - Alveroğlu, B.

AU - Garrett, S. J.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.

AB - We consider the convective instability of the BEK family of rotating boundary-layer flows for shear-thinning power-law fluids. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. A linear stability analysis is conducted using a Chebyshev polynomial method in order to investigate the effect of shear-thinning fluids on the convective type I (inviscid crossflow) and type II (viscous streamline curvature) modes of instability. The results reveal that an increase in shear-thinning has a universal stabilising effect across the entire BEK family. Our results are presented in terms of neutral curves, growth rates and an analysis of the energy balance. The newly-derived governing equations for both the steady mean flow and unsteady perturbation equations are given in full.

KW - Bödewadt flow

KW - Convective instability

KW - Ekman layer

KW - Flow control

KW - Power-law fluid

KW - Von Kármán flow

UR - https://www.scopus.com/pages/publications/84984852185

U2 - 10.1016/j.jnnfm.2016.08.006

DO - 10.1016/j.jnnfm.2016.08.006

M3 - Article

AN - SCOPUS:84984852185

SN - 0377-0257

VL - 236

SP - 63

EP - 72

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

ER -

On the stability of the BEK family of rotating boundary-layer flows for power-law fluids

Abstract

Keywords

ASJC Scopus subject areas

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