Book excerpt: The stability of flow of certain non-Newtonian fluids between two rotating coaxial cylinders in the presence of a circular magnetic field is examined. The fluid in question is assumed to be an incmpressible Reiner-Rivlin fluid. The equations of motion for these non-Newtonian fluids governing marginal stability are derived, and boundary conditions for perfectly conducting cylinders (Fermi boundary conditions) are formulated for the cases of corotating and counterrotating cylinders, when the gap between the cylinders is small. The underlying characteristic value problem is solved by using an expansion in orthogonal functions method developed by Chandrasekhar to determine the critical Taylor numbers for marginal stability as stability criteria. Numerical calculations have been performed. It is found that the effect of crossviscosaty is to facilitate the onset of instability; whereas the effect of viscosity under similar conditions would be a stabilizing one. Thus the effect of cross-viscosity is found to be opposite that of viscosity in the stability analysis of the present case. (Author).