Stokes' first problem for some non-Newtonian fluids: Results and mistakes
arXiv:1009.4416 · doi:10.1016/j.mechrescom.2010.09.006
Abstract
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.
10 pages, 2 figures; accepted for publication in Mechanics Research Communications; v2 corrects a few typos
References in corpus (1)
Cited by in corpus (8)
- Stress retardation versus stress relaxation in linear viscoelasticity
- On a difficulty in the formulation of initial and boundary conditions for eigenfunction expansion solutions for the start-up of fluid flow
- Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]
- Comments on: "Energetic balance for the Rayleigh--Stokes problem of an Oldroyd-B fluid" [Nonlinear Anal. RWA 12 (2011) 1]
- Comments on "Scattering Cancellation-Based Cloaking for the Maxwell--Cattaneo Heat Waves"
- Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler
- On the flow of Oldroyd-B fluids with fractional derivatives over a plate that applies shear to the fluid
- Comment on: "Stokes' first problem for heated flat plate with Atangana--Baleanu fractional derivative" [Chaos Solitons Fractals 117 (2018) 68]