广义二阶流体绕圆柱旋转流动的精确解
Exact Solutions for a Rotational Flow of Generalized Second Grade Fluids Through a Circular Cylinder
摘要：
本文用Laplace变换和Hankel变换确定了无限长圆柱内广义二阶流体旋转流动的速度场和相应的切向应力。在时间t=0时，流体处于静止状态，运动是由圆柱体绕其轴线以角速度$Ω.t$旋转产生的。速度场和适当的剪应力的积分和级数形式的广义G-函数。此外，它们被呈现为牛顿解和适当的非牛顿贡献之间的总和。作为$β= 1$解的特例，分别得到了普通二阶流体和牛顿流体的相应解，即$α= 0$和$β= 1$。
英文摘要：
In this note the velocity field and the associated tangential stress corresponding to the rotational flows of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and Hankel transforms. At time t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder, around its axis, with the angular velocity $Ω.t$. The velocity field and the adequate shear stress are presented under integral and series forms in terms of the generalized G-functions. Furthermore, they are presented as a sum between the Newtonian solutions and the adequate non-Newtonian contributions. The corresponding solutions for the ordinary second grade fluid and Newtonian fluid are obtained as particular cases of our solutions for $β= 1$, respectively $α= 0$ and $β= 1$.
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