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Stagnation and rotating-disk flows over a compliant surface. (English) Zbl 1037.76065
Summary: We obtain exact solutions to the stagnation flow over a compliant surface and to the flow about rotating disk coated by a compliant layer. The compliant layer is modelled by Mooney rubberlike material. In the stagnation flow, the deformation of the rubber layer depends on two dimensionless groups: one is the ratio of pressure to the shear modulus of the material, and the other is the ratio of boundary layer thickness to the thickness of the layer. It is shown that this deformation has a limit point at a critical value of the pressure force, beyond which the solution does not exist. In the rotating-disk flow, the deformation of the rubber layer depends on two dimensionless groups, one is a material parameter, and the other is a flow loading parameter, the ratio of the flow-induced viscous stress to the shear modulus multiplied by the ratio of the thickness of the layer to the boundary layer thickness. At large value of a material parameter, it is found that this deformation has a limit point at a critical value of the flow loading parameter.
MSC:
76U05 General theory of rotating fluids
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74B20 Nonlinear elasticity
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