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Entropy 2017, 19(12), 689; https://doi.org/10.3390/e19120689

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

1
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
2
U. S. Department of Energy, National Energy Technology Laboratory (NETL), P. O. Box 10940, Pittsburgh, PA 15236, USA
3
School of Marine Science and Policy, University of Delaware, Robinson Hall, Newark, DE 19716, USA
*
Author to whom correspondence should be addressed.
Received: 19 October 2017 / Revised: 5 December 2017 / Accepted: 11 December 2017 / Published: 14 December 2017
(This article belongs to the Section Thermodynamics)
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Abstract

Flowing media in both industrial and natural processes are often characterized as assemblages of densely packed granular materials. Typically, the constitutive relations for the stress tensor and heat flux vector are fundamentally nonlinear. Moreover, these equations are coupled through the Clausius–Duhem inequality. However, the consequences of this coupling are rarely studied. Here we address this issue by obtaining constraints imposed by the Clausius–Duhem inequality on the constitutive relations for both the stress tensor and the heat flux vector in which the volume fraction gradient plays an important role. A crucial result of the analysis is the restriction on the dependency of phenomenological coefficients appearing in the constitutive equations on the model objective functions. View Full-Text
Keywords: heat flux vector; nonlinear heat conduction; granular materials; nonlinear fluids; continuum mechanics heat flux vector; nonlinear heat conduction; granular materials; nonlinear fluids; continuum mechanics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Yang, H.; Massoudi, M.; Kirwan, A.D., Jr. Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector. Entropy 2017, 19, 689.

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