Stokes' first problem for some non-Newtonian fluids: Results and mistakes

Details Stokes' first problem for some non-Newtonian fluids: Results and mistakes Stokes' first problem for some non-Newtonian fluids: Results and mistakes

2010-09-22

arxiv.org/abs/1009.4416v2

Mechanics Research Communications 37 (8), 2010, pp. 717-723

Physics

Fluid Dynamics

10 pages, 2 figures; accepted for publication in Mechanics Research Communications; v2 corrects a few typos

Scientific paper

10.1016/j.mechrescom.2010.09.006

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.

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