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 journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)63-72
Number of pages10
JournalJournal of Non-Newtonian Fluid Mechanics
Volume236
Early online date26 Aug 2016
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Fingerprint

Rotating Flow
Power-law Fluid
Shear Thinning
shear thinning
boundary layer flow
Shear thinning
Boundary layer flow
Boundary Layer Flow
Fluids
fluids
Convective Instability
Cross-flow
Polynomial Methods
Linear stability analysis
Chebyshev's Method
Energy Balance
Linear Stability Analysis
Chebyshev Polynomials
Streamlines
Energy balance

Keywords

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

ASJC Scopus subject areas

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

Cite this

On the stability of the BEK family of rotating boundary-layer flows for power-law fluids. / Abdulameer, M. A.; Griffiths, P. T.; Alveroğlu, B.; Garrett, S. J.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 236, 01.10.2016, p. 63-72.

Research output: Contribution to journalArticle

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AU - Abdulameer, M. A.

AU - Griffiths, P. T.

AU - Alveroğlu, B.

AU - Garrett, S. J.

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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.

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