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Non-Newtonian effects in three-dimensional boundary layers

The stability of the boundary-layer on a rotating disk is considered for fluids that adhere to a non-Newtonian governing viscosity relationship. For fluids with shear-rate dependent viscosity the base flow is no longer an exact solution of the Navier-Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary-layer can be determined via a similarity solution. The convective instabilities associated with flows of this nature are described both asymptotically and numerically via separate linear stability analyses. Akin to previous Newtonian studies it is found that there exists two primary modes of instability; the upper-branch type I modes, and the lower-branch type II modes. Results show that both these modes can be stabilised or destabilised depending on the choice of non-Newtonian viscosity model. A number of comments are made regarding the suitability of some of the more well-known non-Newtonian constitutive relationships within the context of the rotating disk model.