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

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.

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

“…Much more recently Griffiths et al [22] considered a rigorous asymptotic stability analysis of the shear-thinning boundary-layer flow over a rotating disk. This work was then extended by the same authors Griffiths et al [23] to compute the neutral curves of convective instability (working under the parallel-flow assumption) and complete agreement was found with their prior asymptotic analysis. These two papers can be considered as the non-Newtonian generalisations of Hall [4] and Malik [3], respectively.…”

“…In this current paper we extend the non-Newtonian, inelastic study of Griffiths et al [23], to the entire BEK family of rotating boundary-layer flows. A Chebyshev polynomial method is used to consider the effects shear-thinning power-law fluids have on the type I and type II modes of instability.…”

Stability of the shear-thinning boundary-layer flow over a flat inclined plate

“…More recent studies have addressed the linear stability characteristics of unconfined non-Newtonian shear flows. The effect of shear-thinning has been shown to delay the onset of convective instability when considering the three-dimensional boundary-layer flow due to a rotating disc [4,5]. However, the results presented in these investigations consider only the 'power-law' formulation of the problem.…”

Quantifying non-Newtonian effects in rotating boundary-layer flows

“…6. The governing equations for shear-thinning fluids that adhere to the power-law viscosity model can be found in Griffiths et al [17], the equivalent equations for fluids that adhere to the Carreau viscosity model can be easily inferred therein. In all that follows the eigenvalue problem defined by the stability equations is solved with the homogeneous boundary conditions…”