The Convective instability of non-Newtonian of boundary-layer flow over rough rotating-disk

Abstract

This thesis considers the local linear convective stability behaviour of non- Newtonian boundary-layer flows over rotating disks and the effects of surface roughness. A non-Newtonian fluid is modelled via the Carreau model, which represents a type of generalised Newtonian fluid. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface rough- ness. The partial-slip approach of Miklavčič & Wang [1] is modified in such a way that the viscosity is no longer constant and depends on the shear rate. The non-linear ordinary differential equations are reduced via the introduction of a suitable similarity solution. The stability equations are solved to obtain the disturbance eigenfunctions and to plot curves showing neutral stability using the Chebyshev collocation method. The stability of a non-Newtonian boundary-layer flows is investigated with different boundary conditions: the no-slip boundary conditions and the partial-slip. Thereby the neutral curves for the convective instabilities associated with the boundary-layer flow due to a rotating disk can be determined over a broad range of parameter values. The subsequent linear stability analyses of these flows indicate that isotropic and azimuthally anisotropic (radial groove) surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of in- stability. The underlying physical mechanisms are clarified using an integral energy equation.