Steady flow of a second-grade fluid in an annulus with porous walls. (English) Zbl 1151.76005
Summary: An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of confluent hypergeometric functions and is valid for all values of the cross-Reynolds number and elastic number. The solutions for \( - 2, +\infty \), and \( - \infty \) values of cross-Reynolds number are obtained, and a comparison with those for Newtonian’s fluids is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, elastic number, and the ratio of radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.
MSC:
| 76A05 | Non-Newtonian fluids |
| 76S05 | Flows in porous media; filtration; seepage |
| 76U05 | General theory of rotating fluids |
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