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Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders 被引量:4
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作者 A.Mahmood C.Fetecau +1 位作者 N.A.Khan M.Jamil 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2010年第4期541-550,共10页
The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of th... The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0+ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles. 展开更多
关键词 Generalized second grade fluid Velocity field Shear stress Longitudinal oscillatory flow Laplace and Hankel transforms
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Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders
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作者 Amir Mahmood Saima Parveen Najeeb Alam Khan 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第2期222-227,共6页
The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and H... The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 + , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions. 展开更多
关键词 Second grade fluid · Velocity field · Shear stress · Longitudinal oscillatory flow · Laplace and Hankel transforms
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