The study of the Non-Linear flow of a viscoelastic second-order fluid in the annular
region between two eccentric spheres is investigated. This flow is created by considering the inner
sphere to rotate with angular velocity Ω about the axis passing through the centers of two spheres,
the z-axis, while the outer sphere is kept at rest using the Bispherical coordinates (α ,β ,φ ) . The
equations of motions of second order fluid using retarded motion approximation including inertia
term are formulated and the particular solution of the modified planar second-order equation of
motion which including inertia term is obtained. A modified second-order stream function ψ 2 ,
due to the effect of the inertia, which describes the planar secondary flow field has been properly
obtained