Communications in Applied and Industrial Mathematics
Special Issue on Constitutive Equations for Heat Conduction in Nanosystems and Non-equilibrium Processes. Guest Editors: Vito Antonio Cimmelli and David Jou
Published Online: May 20, 2016
Page range: 167 - 176
Received: Dec 25, 2014
Accepted: May 04, 2015
DOI: https://doi.org/10.1515/caim-2016-0012
Keywords
© 2016 Yangyu Guo et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.