Shear flows of a new class of power-law fluids

Christiaan Le Roux; Kumbakonam R. Rajagopal

Applications of Mathematics (2013)

  • Volume: 58, Issue: 2, page 153-177
  • ISSN: 0862-7940

Abstract

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We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new models and then consider some simple boundary-value problems, namely steady planar Couette and Poiseuille flows with no-slip and slip boundary conditions. We show that these problems can have more than one solution and that the multiplicity of the solutions depends on the values of the model parameters as well as the choice of boundary conditions.

How to cite

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Le Roux, Christiaan, and Rajagopal, Kumbakonam R.. "Shear flows of a new class of power-law fluids." Applications of Mathematics 58.2 (2013): 153-177. <http://eudml.org/doc/252502>.

@article{LeRoux2013,
abstract = {We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new models and then consider some simple boundary-value problems, namely steady planar Couette and Poiseuille flows with no-slip and slip boundary conditions. We show that these problems can have more than one solution and that the multiplicity of the solutions depends on the values of the model parameters as well as the choice of boundary conditions.},
author = {Le Roux, Christiaan, Rajagopal, Kumbakonam R.},
journal = {Applications of Mathematics},
keywords = {non-Newtonian fluid; Couette flow; Poiseuille flow; slip boundary condition; non-Newtonian fluid; Couette flow; Poiseuille flow; slip boundary condition},
language = {eng},
number = {2},
pages = {153-177},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shear flows of a new class of power-law fluids},
url = {http://eudml.org/doc/252502},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Le Roux, Christiaan
AU - Rajagopal, Kumbakonam R.
TI - Shear flows of a new class of power-law fluids
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 153
EP - 177
AB - We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Průša, K. R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new models and then consider some simple boundary-value problems, namely steady planar Couette and Poiseuille flows with no-slip and slip boundary conditions. We show that these problems can have more than one solution and that the multiplicity of the solutions depends on the values of the model parameters as well as the choice of boundary conditions.
LA - eng
KW - non-Newtonian fluid; Couette flow; Poiseuille flow; slip boundary condition; non-Newtonian fluid; Couette flow; Poiseuille flow; slip boundary condition
UR - http://eudml.org/doc/252502
ER -

References

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