Thermodynamic Extremum Principles for Nonequilibrium Stationary State in Heat Conduction
- 4 April 2017
- journal article
- research article
- Published by ASME International in Journal of Heat Transfer
- Vol. 139 (7), 071303
- https://doi.org/10.1115/1.4036086
Abstract
Minimum entropy production principle (MEPP) is an important variational principle for the evolution of systems to nonequilibrium stationary state. However, its restricted validity in the domain of Onsager's linear theory requires an inverse temperature square-dependent thermal conductivity for heat conduction problems. A previous derivative principle of MEPP still limits to constant thermal conductivity case. Therefore, the present work aims to generalize the MEPP to remove these nonphysical limitations. A new dissipation potential is proposed, the minimum of which thus corresponds to the stationary state with no restriction on thermal conductivity. We give both rigorous theoretical verification of the new extremum principle and systematic numerical demonstration through 1D transient heat conduction with different kinds of temperature dependence of the thermal conductivity. The results show that the new principle remains always valid while MEPP and its derivative principle fail beyond their scopes of validity. The present work promotes a clear understanding of the existing thermodynamic extremum principles and proposes a new one for stationary state in nonlinear heat transport.Keywords
This publication has 41 references indexed in Scilit:
- Thermodynamic analysis of gas flow and heat transfer in microchannelsInternational Journal of Heat and Mass Transfer, 2016
- Phonon hydrodynamics and its applications in nanoscale heat transportPhysics Reports, 2015
- A Continuum Approach to Thermomass TheoryJournal of Heat Transfer, 2012
- Nonlinear evolution and stability of the heat flow in nanosystems: Beyond linear phonon hydrodynamicsPhysical Review B, 2010
- On the Entropy Generation Formula of Radiation Heat Transfer ProcessesJournal of Heat Transfer, 2005
- Dynamics and thermodynamics of complex fluids. I. Development of a general formalismPhysical Review E, 1997
- The Minimum Entropy Production PrincipleAnnual Review of Physical Chemistry, 1980
- Principle of Minimum Entropy ProductionPhysical Review B, 1954
- Reciprocal Relations in Irreversible Processes. II.Physical Review B, 1931
- Reciprocal Relations in Irreversible Processes. I.Physical Review B, 1931