The steady flow of an incompressible Oldroyd
8-constant fluid in the annular region between two
concentric cylinders, or so-called cylindrical Couette
flow, is investigated. The inner cylinder rotates with an
angular velocity W about its own axis, z-axis, while the
outer cylinder is kept at rest. The viscoelasticity of the
fluid is assumed to dominate the inertia such that the
latter can be neglected in the momentum equation. An
analytical solution is obtained through the expansion of
the dynamical variables in power series of the
dimensionless retardation time. The primary velocity term
denotes the Newtonian rotation about the z-axis. The
first-order is a vanishing term. The second-order results
in a secondary flow represented by the stream-function.
This second-order term is the viscoelastic contribution to
the primary viscous flow. The second-order
approximation depends on the four viscometric
parameters of the fluid.