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Energetic balance for the Rayleigh-Stokes problem of an Oldroyd-B fluid. (English) Zbl 1205.35223
Summary: The dissipation, the power due to the shear stress at the wall, the change of kinetic energy with time as well as the boundary layer thickness corresponding to the Rayleigh-Stokes problem for an Oldroyd-B fluid are established. The corresponding expressions of Maxwell, second grade and Newtonian fluids, performing the same motions, are obtained as the limiting cases of our general results. Specific features of the four models are emphasized by means of the asymptotic approximations and graphical representations. It is worth mentioning that in comparison with the Newtonian model, the power of the shear stress at the wall and the dissipation for Oldroyd-B fluids increase while the boundary layer thickness decreases.

MSC:
35Q35PDEs in connection with fluid mechanics
76A05Non-Newtonian fluids
76D08Lubrication theory
76M45Asymptotic methods, singular perturbations (fluid mechanics)
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