TITLE:
Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates
AUTHORS:
K. S. Surana, S. W. Long, J. N. Reddy
KEYWORDS:
Rate Constitutive Theories, Non-Classical Thermofluids, With Memory, Convected Time Derivatives, Internal Rotation Gradient Tensor, Generators and Invariants, Cauchy Moment Tensor
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.8,
August
22,
2018
ABSTRACT:
The paper presents constitutive theories for non-classical thermoviscoelastic
fluids with dissipation and memory using a thermodynamic framework based
on entirety of velocity gradient tensor. Thus, the conservation and the balance
laws used in this work incorporate symmetric as well as antisymmetric part of
the velocity gradient tensor. The constitutive theories derived here hold in coand
contra-variant bases as well as in Jaumann rates and are derived using
convected time derivatives of Green’s and Almansi strain tensors as well as
the Cauchy stress tensor and its convected time derivatives in appropriate
bases. The constitutive theories are presented in the absence as well as in the
presence of the balance of moment of moments as balance law. It is shown
that the dissipation mechanism and the fading memory in such fluids are due
to stress rates as well as moment rates and their conjugates. The material
coefficients are derived for the general forms of the constitutive theories
based on integrity. Simplified linear (or quasi-linear) forms of the constitutive
theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive
models for non-classical thermoviscoelastic fluids are derived and are compared
with those derived based on classical continuum mechanics. Both,
compressible and incompressible thermoviscoelastic fluids are considered.