Emergence of Non-Fourier Hierarchies

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs, and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier’s law for room-temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermo-mechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier’s law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.

[1]  Henning Struchtrup,et al.  Heat pulse experiments revisited , 1993 .

[2]  M. K. Moallemi,et al.  Experimental evidence of hyperbolic heat conduction in processed meat , 1995 .

[3]  P. Ván,et al.  Models of Ballistic Propagation of Heat at Low Temperatures , 2015, 1506.05578.

[4]  Csaba Asszonyi,et al.  Elastic, thermal expansion, plastic and rheological processes – theory and experiment , 2015 .

[5]  Robert A. Guyer,et al.  Thermal Conductivity, Second Sound, and Phonon Hydrodynamic Phenomena in Nonmetallic Crystals , 1966 .

[6]  R. J. Jenkins,et al.  Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity , 1961 .

[7]  Róbert Kovács,et al.  Analytic solution of Guyer-Krumhansl equation for laser flash experiments , 2018, International Journal of Heat and Mass Transfer.

[8]  Kurt Frischmuth,et al.  Numerical reconstruction of heat pulse experiments , 1995 .

[9]  P. Ván,et al.  Kinematic quantities of finite elastic and plastic deformation , 2010, 1007.2892.

[10]  P. V'an,et al.  Thermodynamic hierarchies of evolution equations , 2014, 1412.4490.

[11]  I. Müller,et al.  Rational Extended Thermodynamics , 1993 .

[12]  T. F. McNelly,et al.  Second Sound and Anharmonic Processes in Isotopically Pure Alkali-Halides , 1974 .

[13]  Wenjing Ye,et al.  Modified Ballistic-diffusive Equations for Transient non-continuum Heat Conduction , 2015 .

[14]  P. V'an,et al.  Guyer-Krumhansl–type heat conduction at room temperature , 2017, 1704.00341.

[15]  K. V. Zhukovsky,et al.  Exact solution of Guyer–Krumhansl type heat equation by operational method , 2016 .

[16]  Róbert Kovács,et al.  Thermodynamical consistency of the dual-phase-lag heat conduction equation , 2017, 1709.06825.

[17]  H. Herwig,et al.  Fourier Versus Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure , 2000 .

[18]  Tam'as Fulop.  Objective thermomechanics , 2015 .

[19]  Tamás Fülöp,et al.  Deviation from the Fourier law in room-temperature heat pulse experiments , 2015, 1506.05764.

[20]  L. Tisza,et al.  Transport Phenomena in Helium II , 1938, Nature.

[21]  S. Rukolaine,et al.  Unphysical effects of the dual-phase-lag model of heat conduction: higher-order approximations , 2017 .

[22]  Péter Ván,et al.  Evolutsioonivõrrandite termodünaamilised hierarhiad , 2015 .

[23]  M Barrett,et al.  HEAT WAVES , 2019, The Year of the Femme.

[24]  R. Guyer,et al.  Solution of the Linearized Phonon Boltzmann Equation , 1966 .

[25]  G Chen,et al.  Ballistic-diffusive heat-conduction equations. , 2001, Physical review letters.

[26]  Vito Antonio Cimmelli,et al.  Nonequilibrium Thermodynamics and Heat Transport at Nanoscale , 2016 .

[27]  Hubert M. James,et al.  Some extensions of the flash method of measuring thermal diffusivity , 1980 .

[28]  Paul Steinmann,et al.  Finite Element Approaches to Non-classical Heat Conduction in Solids , 2005 .

[29]  Peter Van.  Weakly nonlocal irreversible thermodynamics—the Guyer–Krumhansl and the Cahn–Hilliard equations , 2001 .

[30]  P. V'an,et al.  Generalized heat conduction in heat pulse experiments , 2014, 1409.0313.

[31]  Konstantin V. Zhukovsky,et al.  Operational Approach and Solutions of Hyperbolic Heat Conduction Equations , 2016, Axioms.

[32]  Vito Antonio Cimmelli,et al.  A thermodynamic model for heat transport and thermal wave propagation in graded systems , 2015 .

[33]  W. Roetzel,et al.  Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure , 2003 .

[34]  Luigi Preziosi,et al.  Addendum to the paper "Heat waves" [Rev. Mod. Phys. 61, 41 (1989)] , 1990 .

[35]  Vito Antonio Cimmelli,et al.  Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview , 2016 .

[36]  Da Yu Tzou,et al.  Macro- to Microscale Heat Transfer: The Lagging Behavior , 2014 .

[37]  J. Fourier.  Théorie analytique de la chaleur , 2009 .

[38]  Robert A. Guyer,et al.  SECOND SOUND IN SOLID HELIUM , 1966 .

[39]  Vito Antonio Cimmelli,et al.  Generalized heat-transport equations: parabolic and hyperbolic models , 2017, 1709.05502.

[40]  H. Jackson,et al.  Thermal Conductivity, Second Sound, and Phonon-Phonon Interactions in NaF , 1971 .

[41]  Vincenzo Tibullo,et al.  Stability and Thermodynamic Restrictions for a Dual-Phase-Lag Thermal Model , 2017 .

[42]  Hari M. Srivastava,et al.  Analytical solutions for heat diffusion beyond Fourier law , 2017, Appl. Math. Comput..

[43]  P'eter V'an,et al.  Second sound and ballistic heat conduction: NaF experiments revisited , 2017, 1708.09770.

[44]  L. Tisza,et al.  Theory of liquid helium , 1947 .

[45]  Lev Davidovich Landau,et al.  THE THEORY OF SUPERFLUIDITY OF HELIUM II , 1971 .