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.
Highlights
There has been significant interest in the stability and transition of the three-dimensional boundary-layer flow due to the rotating disk in recent decades
The seminal study of the stability properties of the Newtonian rotating-disk boundary layer was performed by Gregory et al [2], and there the first experimental observation of stationary crossflow vortices and the first theoretical stability analysis are presented
We have investigated the stability of stationary convective disturbances in the BEK family of boundary-layer flows for shear-thinning power-law fluids
Summary
There has been significant interest in the stability and transition of the three-dimensional boundary-layer flow due to the rotating disk (that is the von Karman [1] flow) in recent decades. With regards to prior studies of the non-Newtonian boundary-layer flow over a rotating disk, Mitschka and Ulbrecht [19] were the first to extend the von Karman similarity solution to incorporate fluids that adhere to a power-law governing viscosity relationship. This work was 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. All newly-derived equations are presented in detail where appropriate in our discussion
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