A case study of non-Fourier heat conduction using internal variables and GENERIC

被引：11

作者：

Szucs, Matyas ^{[1
,2
]}

Pavelka, Michal ^{[3
]}

Kovacs, Robert ^{[1
,2
,4
]}

Fulop, Tamas ^{[1
,2
]}

Van, Peter ^{[1
,2
,4
]}

Grmela, Miroslav ^{[5
]}

机构：

[1] Budapest Univ Technol & Econ, Fac Mech Engn, Dept Energy Engn, Budapest, Hungary

[2] Montavid Thermodynam Res Grp, Budapest, Hungary

[3] Charles Univ Prague, Math Inst, Fac Math, Prague, Czech Republic

[4] Inst Particle & Nucl Phys, Wigner Res Centre Phys, Dept Theoret Phys, Budapest, Hungary

[5] Ecole Polytech Montreal, Montreal, PQ, Canada

来源：

JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS | 2022年 / 47卷 / 01期

关键词：

non-Fourier heat conduction; internal variables; GENERIC; entropy current multiplier; model reduction; 2ND SOUND; THERMAL-CONDUCTIVITY; GUYER-KRUMHANSL; COMPLEX FLUIDS; THERMODYNAMICS; ENTROPY; PROPAGATION; LEQUATION; DEVIATION; PRINCIPLE;

D O I：

10.1515/jnet-2021-0022

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law and its various extensions-the Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type and ballistic-diffusive heat conduction equations-are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

引用

页码：31 / 60

页数：30

共 68 条

[1]

[Anonymous], 1929, The Earth: Its Origin, History and Physical Constitution

[2]

[Anonymous], 1997, Thermodynamics and Rheology

[3] Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory [J].

Asszonyi, Csaba ;

Fueloep, Tamas ;

Van, Peter .

CONTINUUM MECHANICS AND THERMODYNAMICS, 2015, 27 (06) :971-986

[4] New perspectives for modelling ballistic-diffusive heat conduction [J].

Balassa, G. ;

Rogolino, P. ;

Rieth, A. ;

Kovacs, R. .

CONTINUUM MECHANICS AND THERMODYNAMICS, 2021, 33 (05) :2007-2026

[5]

Berezovski A., 2017, INTERNAL VARIABLES T

[6] Energy-momentum-entropy consistent numerical methods for large-strain thermoelasticity relying on the GENERIC formalism [J].

Betsch, Peter ;

Schiebl, Mark .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2019, 119 (12) :1216-1244

[7] Deviation from the Fourier law in room-temperature heat pulse experiments [J].

Both, Soma ;

Czel, Balazs ;

Fulop, Tamas ;

Grof, Gyula ;

Gyenis, Akos ;

Kovacs, Robert ;

Van, Peter ;

Verhas, Jozsef .

JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS, 2016, 41 (01) :41-48

[8] ON ONSAGER PRINCIPLE OF MICROSCOPIC REVERSIBILITY [J].

CASIMIR, HBG .

REVIEWS OF MODERN PHYSICS, 1945, 17 (2-3) :343-350

[9]

CATTANEO C, 1958, CR HEBD ACAD SCI, V247, P431

[10]

deGroot SR., 1963, Non-Equilibrium Thermodynamics, DOI DOI 10.1103/PhysRevE.74.046305

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