Abstract
This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works.
Highlights
The conservation and balance laws for non-classical thermofluids incorporating internal rotation rates due to antisymmetric part of the velocity gradient tensor have been presented by Surana et al [1,2,3,4]
These consist of usual conservation and balance laws of classical continuum mechanics: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), first and second laws of thermodynamics (FLT, second law of thermodynamics (SLT)), but require some modification and/or re-derivations and a new balance law, balance of moment of moment (BMM), is needed due to presence of new physics associated with the rotation rates
A clear explanation of the use of higher order convected time derivatives of the strain tensors as argument tensors of deviatoric Cauchy stress for thermoviscous fluids based on classical continuum mechanics (CCM) and consistency of the resulting constitutive theory and the rationale supporting such derivations is essential in explaining the use of these concepts in non-classical fluent continua hincorporating internal rotation rates
Summary
The conservation and balance laws for non-classical thermofluids incorporating internal rotation rates due to antisymmetric part of the velocity gradient tensor have been presented by Surana et al [1,2,3,4]. A clear explanation of the use of higher order convected time derivatives of the strain tensors as argument tensors of deviatoric Cauchy stress for thermoviscous fluids based on CCM and consistency of the resulting constitutive theory and the rationale supporting such derivations is essential in explaining the use of these concepts in non-classical fluent continua hincorporating internal rotation rates. Initial selection of the argument tensors of the constitutive variables based on conjugate pairs in the entropy inequality is augmented in the present work to include additional desired physics based on the higher order convected time derivatives of the Green’s strain tensor for the deviatoric Cauchy stress tensor and higher order convected rotation rates for Cauchy moment tensor. Their convected time derivatives are considered in the derivation of the conservation and balance laws and the constitutive theories
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
