The neutral curve for stationary disturbances in rotating disk flow for power-law fluids

P. T. Griffiths, S. J. Garrett, S. O. Stephen

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.

Original languageEnglish
Pages (from-to)73-81
Number of pages9
JournalJournal of Non-Newtonian Fluid Mechanics
Volume213
DOIs
Publication statusPublished - 1 Nov 2014
Externally publishedYes

Fingerprint

Power-law Fluid
Rotating Disk
Shear Thinning
shear thinning
Shear thinning
rotating disks
Rotating disks
Streamlines
Branch
disturbances
Disturbance
Curvature
curvature
Convective Instability
Coriolis force
Coriolis Force
Cross-flow
Curve
Fluids
cross flow

Keywords

  • Instability
  • Neutral curve
  • Power-law fluid
  • Rotating disk flow

ASJC Scopus subject areas

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

Cite this

The neutral curve for stationary disturbances in rotating disk flow for power-law fluids. / Griffiths, P. T.; Garrett, S. J.; Stephen, S. O.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 213, 01.11.2014, p. 73-81.

Research output: Contribution to journalArticle

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AB - This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.

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