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Stokes’ first problem for some non-Newtonian fluids: results and mistakes. (English) Zbl 1272.76018

Summary: The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the analytical solutions are constructed.

MSC:

76A05 Non-Newtonian fluids
76A10 Viscoelastic fluids
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