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Non-Linear Flow of a Viscoelastic Fluid between Two Eccentric Spheres
Adv. Studies Theor. Phys. • 2010
Publication Information
Authors
Mostafa Y. El-Bakry
Keywords
Non-Linear flow- Viscoelastic fluid-Bispherical coordinates - Biharmonic vector
equation -Secondary flow- Stream function
Journal
Adv. Studies Theor. Phys.
Publisher
Hikari Ltd
Volume
4
Issue
No.16
Pages
781 - 796
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
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
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