scholarly journals Emergence of Non-Fourier Hierarchies

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 832 ◽  
Author(s):  
Tamás Fülöp ◽  
Róbert Kovács ◽  
Ádám Lovas ◽  
Ágnes Rieth ◽  
Tamás Fodor ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Room Temperature ◽  
Temperature History ◽  
Fourier’S Law ◽  
Temperature Modeling ◽  
Experimental Side ◽  
Fourier Heat Conduction ◽  
Generalized Heat Equation ◽  
Generalized Heat Conduction ◽  
Fourier's Law

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.

Non-Fourier Heat Conduction in Carbon Nanotubes

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Hai-Dong Wang ◽  
Bing-Yang Cao ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Flux ◽  
Heat Conduction ◽  
Thermal Inertia ◽  
Energy Relation ◽  
Fourier’S Law ◽  
Fourier Heat Conduction ◽  
Fourier's Law

Fourier’s law is a phenomenological law to describe the heat transfer process. Although it has been widely used in a variety of engineering application areas, it is still questionable to reveal the physical essence of heat transfer. In order to describe the heat transfer phenomena universally, Guo has developed a general heat conduction law based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics according to Einstein’s mass–energy relation. The general law degenerates into Fourier’s law when the thermal inertia is neglected as the heat flux is not very high. The heat flux in carbon nanotubes (CNTs) may be as high as 1012 W/m2. In this case, Fourier’s law no longer holds. However, what is estimated through the ratio of the heat flux to the temperature gradient by molecular dynamics (MD) simulations or experiments is only the apparent thermal conductivity (ATC); which is smaller than the intrinsic thermal conductivity (ITC). The existing experimental data of single-walled CNTs under the high-bias current flows are applied to study the non-Fourier heat conduction under the ultrahigh heat flux conditions. The results show that ITC and ATC are almost equal under the low heat flux conditions when the thermal inertia is negligible, while the difference between ITC and ATC becomes more notable as the heat flux increases or the temperature drops.

Non-Fourier Heat Conduction in Carbon Nanotubes

2009 ◽  
Author(s):  
Hai-Dong Wang ◽  
Bing-Yang Cao ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Flux ◽  
Heat Conduction ◽  
Thermal Inertia ◽  
Energy Relation ◽  
Fourier’S Law ◽  
Fourier Heat Conduction ◽  
Fourier's Law

Fourier’s law is a phenomenological law to describe the heat transfer process. Although it has been widely used in a variety of engineering application areas, it is still questionable to reveal the physical essence of heat transfer. In order to describe the heat transfer phenomena universally, Guo has developed a general heat conduction law based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics according to Einstein’s mass-energy relation. The general law degenerates into Fourier’s law when the thermal inertia is neglected as the heat flux is not very high. The heat flux in carbon nanotubes (CNTs) may be as high as 1012 W/m2. In this case Fourier’s law no longer holds. However, what is estimated through the ratio of the heat flux to the temperature gradient by MD simulations or experiments is only the apparent thermal conductivity (ATC); which is smaller than the intrinsic thermal conductivity (ITC). The existing experimental data of single-walled CNTs under the high-bias current flows are applied to study the non-Fourier heat conduction under the ultra-high heat flux conditions. The results show that ITC and ATC are almost equal under the low heat flux conditions when the thermal inertia is negligible, while the difference between ITC and ATC becomes more notable as the heat flux increases or the temperature drops.

Molecular Dynamics Simulation of Non-Fourier Heat Conduction

2007 ◽  
Author(s):  
Qi-Xin Liu ◽  
Pei-Xue Jiang ◽  
Heng Xiang
Keyword(s):  
Thin Films ◽  
Molecular Dynamics ◽  
Heat Conduction ◽  
Dynamics Simulation ◽  
Temperature Profiles ◽  
Fourier’S Law ◽  
Wave Nature ◽  
Unsteady Heat Conduction ◽  
Fourier Heat Conduction ◽  
Fourier's Law

Unsteady heat conduction is known to deviate significantly from Fourier’s law when the system time and length scales are within certain temporal and spatial windows of relaxation. Classical molecular dynamics simulations were used to investigate unsteady heat conduction in argon thin films with a sudden temperature increase at one surface to study the non-Fourier heat conduction effects in argon thin films. The studies were conducted with both pure argon films and films with vacancy defects. The temperature profiles in the argon films showed the wave nature of heat propagation. Comparisons of the MD temperature profiles with the temperature profiles from Fourier’s law conduction show that Fourier’s law is not able to predict the temperature development with the time. Different film thicknesses were also studied to illustrate the variation of the time needed for the films to reach steady-state temperature profiles, which means that the relaxation time varies with film thickness.

scholarly journals Evaluation of the thermal conductance of flip-chip bonding structure utilizing the measurement based on Fourier’s law of heat conduction at steady-state

AIP Advances ◽  
2018 ◽  
Vol 8 (6) ◽  
pp. 065208 ◽  
Author(s):  
Chia-Yu Wu ◽  
Yin-Hsien Huang ◽  
Hsin-Han Wu ◽  
Tsung-Eong Hsieh
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Flip Chip ◽  
Thermal Conductance ◽  
Fourier’S Law ◽  
Bonding Structure ◽  
Flip Chip Bonding ◽  
Fourier's Law

scholarly journals Cooling Dynamics of a Gold Nanoparticle in a Host Medium Under Ultrafast Laser Pulse Excitation: A Ballistic-Diffusive Approach

2008 ◽  
Author(s):  
Majid Rashidi-Huyeh ◽  
Sebastian Volz ◽  
Bruno Palpant
Keyword(s):  
Heat Conduction ◽  
Laser Pulse ◽  
Gold Nanoparticle ◽  
Particle Temperature ◽  
Surrounding Medium ◽  
Pulse Excitation ◽  
Fourier’S Law ◽  
Host Medium ◽  
The Matrix ◽  
Fourier's Law

We present a numerical model allowing to determine the electron and lattice temperature dynamics in a gold nanoparticle under subpicosecond pulsed excitation, as well as that of the surrounding medium. For this, we have used the electron-phonon coupling equation in the particle with a source term linked with the laser pulse, and the ballistic-diffusive equations for heat conduction in the host medium. Our results show that the heat transfer rate from the particle to the matrix is significantly smaller than the prediction of Fourier’s law. Consequently, the particle temperature rise is much larger and its cooling dynamics is much slower than that obtained using Fourier’s law, which is attributed to the nonlocal and nonequilibrium heat conduction in the vicinity of the nanoparticle. These results are expected to be of great importance for interpreting pump-probe experiments performed on single nanoparticles or nanocomposite media.

scholarly journals Bragg Mirrors for Thermal Waves

2021 ◽  
Author(s):  
Angela Camacho de la Rosa ◽  
David Becerril ◽  
Guadalupe Gómez-Farfán ◽  
Raul P Esquivel-Sirvent
Keyword(s):  
Heat Conduction ◽  
Numerical Calculation ◽  
Thermal Waves ◽  
Wave Surface ◽  
Fourier’S Law ◽  
Bragg Mirror ◽  
Fourier's Law ◽  
Very High ◽  
Mirror Configuration ◽  
High Reflectance

We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier's law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation's solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved ($>90\%$). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier's law.

scholarly journals Simple One-Dimensional Model of Heat Conduction which Obeys Fourier’s Law

2001 ◽  
Vol 86 (24) ◽  
pp. 5486-5489 ◽  
Author(s):  
P. L. Garrido ◽  
P. I. Hurtado ◽  
B. Nadrowski
Keyword(s):  
Heat Conduction ◽  
Dimensional Model ◽  
Fourier’S Law ◽  
One Dimensional ◽  
Fourier's Law

scholarly journals Deviation from the Fourier law in room-temperature heat pulse experiments

2016 ◽  
Vol 41 (1) ◽  
Author(s):  
Soma Both ◽  
Balázs Czél ◽  
Tamás Fülöp ◽  
Gyula Gróf ◽  
Ákos Gyenis ◽  
...  
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Room Temperature ◽  
Heat Pulse ◽  
Diffusion Regime ◽  
Fourier Law ◽  
Fourier’S Law ◽  
Temperature Heat ◽  
Fourier's Law

AbstractWe report heat pulse experiments at room temperature that cannot be described by Fourier's law. The experimental data are modeled properly by the Guyer–Krumhansl equation, in its over-diffusion regime. The phenomenon may be due to conduction channels with differing conductivities and parallel to the direction of the heat flux.

scholarly journals A Mechanical Model for Fourier’s Law of Heat Conduction

2011 ◽  
Vol 311 (3) ◽  
pp. 755-768 ◽  
Author(s):  
David Ruelle
Keyword(s):  
Heat Conduction ◽  
Mechanical Model ◽  
Fourier’S Law ◽  
Fourier's Law

On Fourier's law of heat conduction

1990 ◽  
Vol 2 (4) ◽  
pp. 301-305 ◽  
Author(s):  
I-Shih Liu
Keyword(s):  
Heat Conduction ◽  
Fourier’S Law ◽  
Fourier's Law
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