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Flow of a Viscoelastic Fluid Between Two Rotating Confocal Ellipsoids
Proc. Math. Phys. Soc. Egypt. • 2004
Publication Information
Authors
Abu-El Hasan, A.,Abdel Wahab, M., El-Bakry, M.,Hemaid,S. andZidan,M
Keywords
Viscoelastic fluid- ellipsoidal (prolate spheroid) coordinates - Confocal ellipsoids - Biharmonic vector equation - Secondary flow
Journal
Proc. Math. Phys. Soc. Egypt.
Publisher
Not Available
Volume
No.81
Issue
Not Available
Pages
pp.37-57
publication.type
Local
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
The isochoric and isothermal flow of a viscoelastic fluid in the annular region between two confocal ellipsoids is investigated . This study is carried out in terms of the elliptic (prolate spheroidal) coordinates , where the inner and the outer ellipsoids are uniformly rotating; respectively, with angular velocities about the axis connecting their foci.
The equations of motion of first and second orders are formulated and solved for the first order only . However, the equation of second order indicates the presence of secondary flow superimposed onto the primary one. The stress distributions are computed and used to determine the resultant forces and torques acting on the outer elllipsoid when it is being at rest. An important result for rheometry is that the resultant torques can be used to determine the coefficient of viscosity .
The equations of motion of first and second orders are formulated and solved for the first order only . However, the equation of second order indicates the presence of secondary flow superimposed onto the primary one. The stress distributions are computed and used to determine the resultant forces and torques acting on the outer elllipsoid when it is being at rest. An important result for rheometry is that the resultant torques can be used to determine the coefficient of viscosity .