A variational principle for extended irreversible thermodynamics: heat conducting viscous fluids
Abstract
Extended irreversible thermodynamics is a theory that expands the classical framework of nonequilibrium thermodynamics by going beyond the local-equilibrium assumption. A notable example of this is the Maxwell–Cattaneo heat flux model, which introduces a time lag in the heat flux response to temperature gradients. In this paper, we develop a variational formulation of the equations of extended irreversible thermodynamics by introducing an action principle for a nonequilibrium Lagrangian that treats thermodynamic fluxes as independent variables. A key feature of this approach is that it naturally extends both Hamilton’s principle of reversible continuum mechanics and the earlier variational formulation of classical irreversible thermodynamics. The variational principle is initially formulated in the material (Lagrangian) description, from which the Eulerian form is derived using material covariance (or relabeling symmetries). The tensorial structure of the thermodynamic fluxes dictates the choice of objective rate in the Eulerian description, and plays a central role in the emergence of nonequilibrium stresses – arising from both viscous and thermal effects – that are essential to ensure thermodynamic consistency. This framework naturally results in the Cattaneo–Christov model for heat flux. We also investigate the extension of the approach to accommodate higher-order fluxes and the general form of entropy fluxes. The variational framework presented in this paper has promising applications in the development of structure-preserving and thermodynamically consistent numerical methods. It is particularly relevant for modeling systems where entropy production is a delicate issue that requires careful treatment to ensure consistency with the laws of thermodynamics.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The author states no conflict of interest.
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Research funding: This work was supported by a Start-up grant from the Nanyang Technological University and by the Ministry of Education, Singapore, under Tier 1 Grant.
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Data availability: Not applicable.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical and optimization analysis of natural convection and entropy-generation in wavy triangular cavity with Casson fluid under magnetohydrodynamics and radiation
- Anisotropic turbulent flow of water through converging wavy-aluminum-circular pipe with five half-cycles: insight into the significance of four-branch minor-inlet angle
- A Hydrogen-fueled hybrid system based on HT-PEMFCs for simultaneous electrical power generation and high-value heat storage
- Optimization of two-cold one-hot reservoir low-dissipation heat engines
- Numerical and experimental heat transfer analysis of two-phase flow through microchannel for development of heat dissipation correlation
- Applying irreversible thermodynamics to the paradigmatic secondary transporter: lactose permease (LacY)
- Single-, two-, three-, and four-objective optimizations for an irreversible vacuum thermionic generator via finite-time thermodynamics, NSGA-II and three decision-making techniques
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- Heat transfer analysis of plate versus pin fin heat sinks with GnP-MWCNT/water hybrid nanofluid
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical and optimization analysis of natural convection and entropy-generation in wavy triangular cavity with Casson fluid under magnetohydrodynamics and radiation
- Anisotropic turbulent flow of water through converging wavy-aluminum-circular pipe with five half-cycles: insight into the significance of four-branch minor-inlet angle
- A Hydrogen-fueled hybrid system based on HT-PEMFCs for simultaneous electrical power generation and high-value heat storage
- Optimization of two-cold one-hot reservoir low-dissipation heat engines
- Numerical and experimental heat transfer analysis of two-phase flow through microchannel for development of heat dissipation correlation
- Applying irreversible thermodynamics to the paradigmatic secondary transporter: lactose permease (LacY)
- Single-, two-, three-, and four-objective optimizations for an irreversible vacuum thermionic generator via finite-time thermodynamics, NSGA-II and three decision-making techniques
- A variational principle for extended irreversible thermodynamics: heat conducting viscous fluids
- Heat transfer analysis of plate versus pin fin heat sinks with GnP-MWCNT/water hybrid nanofluid
- The internal energy as a function of state parameters in steady and unsteady Poiseuille flows
