Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

Abstract The present investigation is concerned with basic flows of generalized second grade fluids based on a Sisko fluid. After formulation of the general equations of motion three simple flows of viscoplastic fluids of a Sisko type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow in a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation the Sisko model one was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.

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Stability of modulated finite-gap cylindrical Couette flow: linear theory

Journal of Fluid Mechanics ◽

10.1017/s0022112081001961 ◽

1981 ◽

Vol 108 ◽

pp. 19-42 ◽

Cited By ~ 31

Author(s):

S. Carmi ◽

J. I. Tustaniwskyj

Keyword(s):

Unsteady Flow ◽

Couette Flow ◽

Floquet Theory ◽

Analytic Solution ◽

Outer Cylinder ◽

Three Dimensional ◽

Linear Perturbation ◽

Cylindrical Couette Flow ◽

The Stability ◽

The Galerkin Method

The linear stability of an extensively modulated cylindrical Couette flow is investigated in the finite-gap range. A closed form analytic solution is obtained for the basic unsteady flow after modulation is introduced through the boundary conditions. The general linear perturbation equations for three-dimensional disturbances are then derived and subsequently solved using the Galerkin method with the stability analysed by the Floquet theory. Modulation is found to destabilize the flow in most cases and results compare very favourably with the ones obtained experimentally. Stabilization is possible only for some cases of outer cylinder modulation.

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Modeling turbulent couette flow in a plane channel

Journal of Applied Mechanics and Technical Physics ◽

10.1007/bf00852168 ◽

1989 ◽

Vol 30 (2) ◽

pp. 223-229 ◽

Cited By ~ 2

Author(s):

B. L. Rozhdestvenskii ◽

I. N. Simakin ◽

M. I. Stoinov

Keyword(s):

Couette Flow ◽

Plane Channel

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Simple Flows of Pseudoplastic Fluids Based on Dehaven Model

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2017-0066 ◽

2017 ◽

Vol 22 (4) ◽

pp. 1035-1044

Author(s):

A. Walicka

Keyword(s):

Couette Flow ◽

Poiseuille Flow ◽

Equations Of Motion ◽

Plane Channel ◽

Coaxial Cylinders ◽

Flow Through ◽

Solutions Of Equations ◽

Simple Flows ◽

Pseudoplastic Fluids ◽

Plastic Fluids

Abstract In this paper three simple flows of visco-plastic fluids of DeHaven type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow through a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation DeHaven model it was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.

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