TITLE:
Restrictions on the Material Coefficients in the Constitutive Theories for Non-Classical Viscous Fluent Continua
AUTHORS:
K. S. Surana, A. D. Joy, J. N. Reddy
KEYWORDS:
Non-Classical Continua, Polar Continua, Eulerian Description, Viscous Fluids, Material Coefficients
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.1,
January
30,
2018
ABSTRACT:
This paper considers conservation and balance laws and the constitutive theories
for non-classical viscous fluent continua without memory, in which internal
rotation rates due to the velocity gradient tensor are incorporated in the
thermodynamic framework. The constitutive theories for the deviatoric part
of the symmetric Cauchy stress tensor and the Cauchy moment tensor are derived
based on integrity. The constitutive theories for the Cauchy moment
tensor are considered when the balance of moments of moments 1) is not a
balance law and 2) is a balance law. The constitutive theory for heat vector
based on integrity is also considered. Restrictions on the material coefficients
in the constitutive theories for the stress tensor, moment tensor, and heat
vector are established using the conditions resulting from the entropy inequality,
keeping in mind that the constitutive theories derived here based on integrity
are in fact nonlinear constitutive theories. It is shown that in the case of
the simplest linear constitutive theory for stress tensor used predominantly
for compressible viscous fluids, Stokes' hypothesis or Stokes'assumption has
no thermodynamic basis, hence may be viewed incorrect. Thermodynamically
consistent derivations of the restrictions on various material coefficients are
presented for non-classical as well as classical theories that are applicable to
nonlinear constitutive theories, which are inevitable if the constitutive theories
are derived based on integrity.