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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2011, Volume 7, Number 3, Pages 451–463
(Mi nd270)
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This article is cited in 9 scientific papers (total in 9 papers)
Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions
Dimitri V. Georgievskii M. V. Lomonosov Moscow State University, Vorob’evy gory, Moscow, 119899, Russia
Abstract:
This work deals with tensor-nonlinear constitutive relations connecting the deviators of stress tensor and strain rate tensor in incompressible isotropic media which are called in continuum mechanics as Reiner–Rivlin fluids. The connections of quadratic and cubic invariants of two tensors, where two material functions involve, are presented. The main attention is given to one-dimensional shear flows in various curvilinear coordinate systems. The scheme of obtaining of the material functions for shear on the basis of the steady Poiseuille flow in a plane layer is described. The self-similar solutions corresponding to the generalized diffusion of vortex layer
both in plane and axially symmetric cases are derived.
Keywords:
tensor nonlinearity, invariant, material function, constitutive relation, Reiner–Rivlin fluid, shear, diffusion of vortex, vortex layer.
Received: 05.07.2011 Accepted: 31.08.2011
Citation:
Dimitri V. Georgievskii, “Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions”, Nelin. Dinam., 7:3 (2011), 451–463
Linking options:
https://www.mathnet.ru/eng/nd270 https://www.mathnet.ru/eng/nd/v7/i3/p451
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Abstract page: | 465 | Full-text PDF : | 137 | References: | 68 | First page: | 1 |
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