Mass Nature of Heat and Its Applications II: Non-Fourier Heat Conduction in Carbon Nanotubes

2010 ◽  
Author(s):  
Bing-Yang Cao ◽  
Quan-Wen Hou
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Heat Flux ◽  
Heat Conduction ◽  
Driving Force ◽  
Inertial Force ◽  
Momentum Conservation ◽  
Fourier’S Law ◽  
Fourier's Law ◽  
Very High

Carbon nanotubes (CNTs) have attracted much attention in nanotechnology fields because of their unique thermal properties. The thermal conductivity of CNTs was reported to be as high as several thousand W/mK. The heat flux in CNTs can reach 109−1012 W/m2 under normal heat conduction conditions. In this paper we demonstrate that Fourier’s heat conduction law breaks down for so high heat flux. Based on a novel concept of thermomanss, which is defined as the equivalent mass of thermal energy according to Einstein’s mass-energy relation, heat conduction in CNTs can be regarded as the flow of a phonon gas governed by its mass and momentum conservation equations like in fluid mechanics. The momentum conservation equation, including driving force, inertial force and resistance terms, reduces to Fourier’s law as the heat flux is not very high and the inertial force of phonon gas is negligible with respect to the driving force. However, Fourier’s law of heat conduction no longer holds if the heat flux is very high such that the inertial force of the phonon gas is not negligible. The heat conduction behavior deviates from Fourier’s law even for steady state conditions so that the heat conduction is characterized by a non-linear relationship between the heat flux and the temperature gradient. In this case, the thermal conductivity of the CNTs can no longer be defined as the ratio of the heat flux to the temperature gradient in experiments or numerical computations. Furthermore, the ratio of the phonon gas velocity to the thermal sound speed can be defined as the thermal Mach number. Heat flow in CNTs will be choked, just like gas flows in a converging nozzle, and a temperature jump will be observed when the thermal Mach number equals or exceeds unity. In this case, the predicted temperature profile of the CNTs based on Fourier’s law is much lower than that based on the thermomass theory considering a CNT electrically heated by high-bias current flows. The intrinsic thermal conductivity can be only calculated by the present thermomass theory, rather than Fourier’s heat conduction law. The present study shows that the thermomass based theory should be applied for high flux heat conduction in CNTs where Fourier’s heat conduction law breaks down.

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.

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 Bragg Mirrors for Thermal Waves

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7452
Author(s):  
Angela Camacho de la Rosa ◽  
David Becerril ◽  
María Guadalupe Gómez-Farfán ◽  
Raúl 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.

Molecular Dynamic Study on Thermal Conductivity of Methyl-Chemisorption Carbon Nanotubes

2015 ◽  
Vol 1096 ◽  
pp. 520-523
Author(s):  
Yun Peng Song ◽  
Yan He ◽  
Yuan Zheng Tang
Keyword(s):  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Heat Conduction ◽  
Covalent Bonding ◽  
Methyl Groups ◽  
Leading Role ◽  
Adsorbed Carbon ◽  
Adsorption Density ◽  
Rapid Drop

The thermal conductivity at 300K of (6, 6) carbon nanotubes and chemi-adsorbed carbon nanotubes with methyl groups at random positions through covalent bonding (chemisorption) has been calculated as a function of adsorption density using molecular dynamics. The results exhibit a rapid drop in thermal conductivity with chemisorptions, even chemisorption as little as 1.0% of the nanotube carbon atoms reduces the thermal conductivity significantly. Investigate its reason, defects caused by chemisorption blocking the transmission of phonons which plays a leading role in the heat conduction of nanotubes, affecting the temperature distribution and energy transmission, leading to the thermal conductivity decline.

Mass Nature of Heat and Its Applications I: Motion of Thermomass Fluid and General Heat Conduction Law

2010 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Bing-Yang Cao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Gas Flow ◽  
Short Pulse ◽  
Rest Mass ◽  
Inertial Force ◽  
High Heat Flux ◽  
Phase Lag ◽  
Energy Relation ◽  
Inertial Terms

The concept of thermomass is defined as the equivalent mass of thermal energy according to the Einstein’s mass-energy relation. Hence, the phonon gas in dielectrics can be regarded a weighty, compressible fluid. Heat conduction in the medium, where the rest mass lattices or molecules acts the porous framework, resembles the gas flow through the porous medium. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, since the drift velocity of a phonon gas is normally much less than the speed of light. The momentum equation of the thermomass gas, including the driving, inertial and resistant forces, is a damped wave equation, which is in fact the general conduction law. This is because it reduces to the CV (Cattaneo-Vernotte) model or the single phase-lag model as the heat flux related inertial terms are neglected, and reduces to Fourier’s heat conduction law as all inertial terms are neglected. Therefore, the underlying physics of Fourier’s heat conduction law is the balance between the driving force and the resistant force of the heat motion, and Fourier’s law will break down when the inertial force is comparable to the resistant force, for instance, in the case of ultra-short pulse laser heating or heat conduction in carbon nanotubes at ultra-high heat flux.

THE INFLUENCE OF THICKNESS ON THE MEASURED THERMAL CONDUCTIVITY OF FIBREBOARD AND ROCK WOOL

1938 ◽  
Vol 16a (4) ◽  
pp. 82-87
Author(s):  
J. D. Babbitt
Keyword(s):  
Thermal Conductivity ◽  
Surface Effects ◽  
Fourier’S Law ◽  
Hot Plate ◽  
Fourier's Law ◽  
Rock Wool ◽  
Measured Thermal Conductivity ◽  
Plate Apparatus

The thermal conductivity of samples of rock wool and fibreboard of various thicknesses (0.5 to 2.0 in.) was measured by means of a hot-plate apparatus. It was found that when surface effects were eliminated the conductivity obeyed Fourier's law.

scholarly journals Nonlinear Heat Transport in Superlattices with Mobile Defects

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1200 ◽  
Author(s):  
David Jou ◽  
Liliana Restuccia
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Conduction ◽  
Thermal Resistance ◽  
Heat Transport ◽  
Concentration Dependence ◽  
Transport Coefficients ◽  
Nonlinear Behavior ◽  
Strongly Nonlinear

We consider heat conduction in a superlattice with mobile defects, which reduce the thermal conductivity of the material. If the defects may be dragged by the heat flux, and if they are stopped at the interfaces of the superlattice, it is seen that the effective thermal resistance of the layers will depend on the heat flux. Thus, the concentration dependence of the transport coefficients plus the mobility of the defects lead to a strongly nonlinear behavior of heat transport, which may be used in some cases as a basis for thermal transistors.

Investigation of Interfacial Thermal Resistance on Nano-Structures Using Molecular Dynamics Simulations

2010 ◽  
Author(s):  
Navdeep Singh ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Thermal Resistance ◽  
Md Simulations ◽  
Interfacial Thermal Resistance ◽  
Filler Materials ◽  
Nano Structures ◽  
Dynamics Simulations ◽  
Very High

Due to their very high thermal conductivity carbon nanotubes have been found to be an excellent material for thermal management. Experiments have shown that the heaters coated with carbon nanotubes increase the heat transfer by as much as 60%. Also when nanotubes are used as filler materials in composites, they tend to increase the thermal conductivity of the composites. But the increase in the heat transfer and the thermal conductivity has been found to be much less than the calculated values. This decrease has been attributed to the interfacial thermal resistance between the carbon nanotubes and the surrounding material. MD simulations were performed to study the interfacial thermal resistance between the carbon nanotubes and the liquid molecules. In the simulations, the nanotube is placed at the center of the simulation box and a temperature of 300K is imposed on the system. Then the temperature of the nanotube is raised instantaneously and the system is allowed to relax. From the temperature decay, the interfacial thermal resistance between the carbon nanotube and the liquid molecules is calculated. In this study the liquid molecules under investigation are n-heptane, n-tridecane and n-nonadecane.

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