الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The isochoric and isothermal flow of a viscoelasticfluid of the
second-order in the annular region between two confocal ellipsoids is
investigated theoretically. The study is carried out in terms of the three
dimensional ellipsoidal (prolate spheroidal) coordinates (s,{J,rp) where
the inner and the outer ellipsoids are uniformly rotating with angular
velocities il, and il~: respectively, about the axis connecting theirfoci.
Up to thefirst-order the equation of motion had been solved .Hence a
first-order velocity field WI (~, 8) which represents the primary.flow in
the <p -direction about the z-axis is calculated.
A second-order stream-function ’412 (s,B ) which describes the
secondary flow field superimposed onto the primary one has been
properly formulated by solving the three-dimensional inhomogenious
biharmonic vector equation . The particular solution of the planar
second-order equation of motion is obtained via the three dimensional
Green ’sfunction ofthe ellipsoidal coordinates.
On the basis of the obtained velocity field, the stresses, forces and
torques acting on the outer ellipsoid when it is being at rest has been
calculated. for viscoelastic third- order fluids. An important resultfor
i
rheometry is that the resultant torques can be used to determine the
coefficient of viscosity Jl and the third-order shear viscosity(J32 + J3,,).