Erratum: “Non-Fourier Heat Conduction in Carbon Nanotubes” [ASME J. Heat Transfer, 2012, 134(5), p. 051004; DOI: 10.1115/1.4005634 ]

2019 ◽  
Vol 141 (3) ◽  
pp. 037001
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Heat Conduction ◽  
Fourier Heat Conduction

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.

Heat conduction in double-walled carbon nanotubes with intertube additional carbon atoms

2015 ◽  
Vol 17 (25) ◽  
pp. 16476-16482 ◽  
Author(s):  
Liu Cui ◽  
Yanhui Feng ◽  
Peng Tan ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Heat Conduction ◽  
Heat Transfer Performance ◽  
Transfer Performance ◽  
Reduction Mechanisms ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Theoretical insights into the heat transfer performance and its reduction mechanisms in double-walled carbon nanotubes with intertube additional carbon atoms.

Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles

1996 ◽  
Vol 118 (3) ◽  
pp. 539-545 ◽  
Author(s):  
G. Chen
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Particle Temperature ◽  
Approximate Expression ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Host Medium ◽  
Conduction Theory ◽  
Fourier Heat Conduction ◽  
Thermal Phenomena

Heat transfer around nanometer-scale particles plays an important role in a number of contemporary technologies such as nanofabrication and diagnosis. The prevailing method for modeling thermal phenomena involving nanoparticles is based on the Fourier heat conduction theory. This work questions the applicability of the Fourier heat conduction theory to these cases and answers the question by solving the Boltzmann transport equation. The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium. In the opposite limit, however, the heat transfer rate from the particle is significantly smaller, and thus the particle temperature rise is much larger than the prediction of the Fourier conduction theory. The differences are attributed to the nonlocal and nonequilibrium nature of the heat transfer processes around nanoparticles. This work also establishes a criterion to determine the applicability of the Fourier heat conduction theory and constructs a simple approximate expression for calculating the effective thermal conductivity of the host medium around a nanoparticle. Possible experimental evidence is discussed.

Nonclassical Heat Transfer Models for Laser-Induced Thermal Damage in Biological Tissues

2011 ◽  
Author(s):  
Jianhua Zhou ◽  
J. K. Chen ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Thermal Wave ◽  
Thermal Damage ◽  
Blood Perfusion ◽  
Biological Tissues ◽  
Phase Lag ◽  
Fourier Heat Conduction

To ensure personal safety and improve treatment efficiency in laser medical applications, one of the most important issues is to understand and accurately assess laser-induced thermal damage to biological tissues. Biological tissues generally consist of nonhomogeneous inner structures, in which heat flux equilibrates to the imposed temperature gradient via a thermal relaxation mechanism which cannot be explained by the traditional parabolic heat conduction model based on Fourier’s law. In this article, two non-Fourier heat conduction models, hyperbolic thermal wave model and dual-phase-lag (DPL) model, are formulated to describe the heat transfer in living biological tissues with blood perfusion and metabolic heat generation. It is shown that the non-Fourier bioheat conduction models could predict significantly different temperature and thermal damage in tissues from the traditional parabolic model. It is also found that the DPL bioheat conduction equations can be reduced to the Fourier heat conduction equations only if both phase lag times of the temperature gradient (τT) and the heat flux (τq) are zero. Effects of laser parameters and blood perfusion on the thermal damage simulated in tissues are also studied. The result shows that the overall effects of the blood flow on the thermal response and damage are similar to those of the time delay τT. The two-dimensional numerical results indicate that for a local heating with the heated spot being smaller than the tissue bulk, the variations of the non-uniform distributions of temperature suggest that the multi-dimensional effects of thermal wave and diffusion not be negligible.

Numerical simulation of non-Fourier effects in combined heat transfer

2010 ◽  
Vol 225 (2) ◽  
pp. 429-436
Author(s):  
E Izadpanah ◽  
S Talebi ◽  
M H Hekmat
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Splitting Method ◽  
Thermal Relaxation ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction ◽  
Wave Nature ◽  
Fourier Heat Conduction ◽  
Combined Heat Transfer

The non-Fourier effects on transient and steady temperature distribution in combined heat transfer are studied. The processes of coupled conduction and radiation heat transfer in grey, absorbing, emitting, scattering, one-dimensional medium with black boundary surfaces are analysed numerically. The hyperbolic heat conduction equation is solved by flux splitting method, and the radiative transfer equation is solved by P1 approximate method. The transient thermal responses obtained from non-Fourier heat conduction equation are compared with those obtained from the Fourier heat conduction equation. The results show that the non-Fourier effect can be important when the conduction to radiation parameter and the thermal relaxation time are larger. Further, the radiation effect is more pronounced at small values of single scattering albedo and conduction to radiation parameters. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature.

Topics of Heat Transfer Related to Single-Walled Carbon Nanotubes

2007 ◽  
Author(s):  
Shigeo Maruyama
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Heat Conduction ◽  
Single Walled Carbon Nanotubes ◽  
Phonon Transport ◽  
Hot Water ◽  
Single Walled Carbon ◽  
Stationary Heat ◽  
Stationary Heat Conduction ◽  
Walled Carbon Nanotubes

Using an alcohol catalytic CVD method shown to produce high-quality single-walled carbon nanotubes (SWNTs), films of vertically aligned (VA-)SWNTs were synthesized on quartz substrates. The VA-SWNTs can be removed from the substrate and transferred onto an arbitrary surface—without disturbing the vertical alignment—using a hot-water assisted technique. This ability makes experimental measurements of the anisotropic properties of SWNTs considerably less challenging. A series of molecular dynamics simulations have been performed to investigate a variety of heat conduction characteristics of SWNTs. Investigations of stationary heat conduction identifies diffusive-ballistic heat conduction regime in a wide range of nanotube-lengths. Furthermore, studies on non-stationary heat conduction show that the extensive ballistic phonon transport gives rise to wave-like non-Fourier heat conduction. Finally, several case studies are presented for SWNT heat transfer in more practical situations.

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