Next Article in Journal
An Information-Theoretic Analysis of Flexible Efficient Cognition for Persistent Sustainable Production
Previous Article in Journal
A Combination Prediction Model of Long-Term Ionospheric foF2 Based on Entropy Weight Method
Open AccessArticle

Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality

Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66048, USA
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 443; https://doi.org/10.3390/e22040443
Received: 30 January 2020 / Revised: 5 April 2020 / Accepted: 11 April 2020 / Published: 14 April 2020
(This article belongs to the Special Issue Thermodynamics of Materials)
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 n ε 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 n Θ . 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. View Full-Text
Keywords: ordered rate; constitutive theories; convected time derivatives; strain rate; gradients of rotation rates; representation theorem; integrity ordered rate; constitutive theories; convected time derivatives; strain rate; gradients of rotation rates; representation theorem; integrity
MDPI and ACS Style

Surana, K.S.; Long, S.W. Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality. Entropy 2020, 22, 443.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop