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 A nonlocal Fourier's law and its application to the heat conduction of one-dimensional and two-dimensional thermal lattices

2016 ◽  
Vol 344 (6) ◽  
pp. 388-401 ◽  
Author(s):  
Noël Challamel ◽  
Cécile Grazide ◽  
Vincent Picandet ◽  
Arnaud Perrot ◽  
Yingyan Zhang
Keyword(s):  
Heat Conduction ◽  
Two Dimensional ◽  
Fourier’S Law ◽  
One Dimensional ◽  
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 Fourier’s Law for a Microscopic Model of Heat Conduction

2005 ◽  
Vol 121 (3-4) ◽  
pp. 271-289 ◽  
Author(s):  
Cédric Bernardin ◽  
Stefano Olla
Keyword(s):  
Heat Conduction ◽  
Microscopic Model ◽  
Fourier’S Law ◽  
Fourier's Law

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.

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