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Fluids 2016, 1(2), 19; doi:10.3390/fluids1020019

On Thermomechanics of a Nonlinear Heat Conducting Suspension

1,†,* and 2,†
1
U. S. Department of Energy, National Energy Technology Laboratory (NETL), 626 Cochrans Mill Road, Pittsburgh, PA 15236, USA
2
School of Marine Science and Policy, University of Delaware, 103 Robinson Hall, Newark, DE 19711, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Bekir S. Yilbas
Received: 10 March 2016 / Revised: 12 June 2016 / Accepted: 12 June 2016 / Published: 18 June 2016
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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Abstract

In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of Massoudi (International Journal of Non-Linear Mechanics, 2001, 36(1), pp. 25–37.) and Massoudi (Mathematical Methods in the Applied Sciences, 2006, 29(13), pp. 1599–1613.) where the entropy law is used and restrictions are also obtained on the constitutive parameters. In most thermomechanical studies of nonlinear fluids using the entropy law, the stress tensor is assumed to be nonlinear and the heat flux vector still has the form of the Fourier type, i.e., it is proportional to the temperature gradient. In this paper, we use a generalized (nonlinear) form for the heat flux vector. When our model is linearized we obtain constraints, due to the entropy inequality, which are in agreement with the earlier results. View Full-Text
Keywords: heat flux vector; non-Fourier heat conduction; nonlinear fluids; continuum mechanics; Korteweg-type fluids; entropy inequality; Clausius-Duhem inequality; J0101 heat flux vector; non-Fourier heat conduction; nonlinear fluids; continuum mechanics; Korteweg-type fluids; entropy inequality; Clausius-Duhem inequality; J0101
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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Massoudi, M.; Kirwan, A.D. On Thermomechanics of a Nonlinear Heat Conducting Suspension. Fluids 2016, 1, 19.

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