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.

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.

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.

An alternative criterion in heat transfer optimization

2010 ◽  
Vol 467 (2128) ◽  
pp. 1012-1028 ◽  
Author(s):  
Qun Chen ◽  
Hongye Zhu ◽  
Ning Pan ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Entropy Generation ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Optimization Criterion ◽  
Entransy Dissipation ◽  
Minimum Entropy ◽  
Fourier’S Law ◽  
Fourier's Law

Entropy generation is recognized as a common measurement of the irreversibility in diverse processes, and entropy generation minimization has thus been used as the criterion for optimizing various heat transfer cases. To examine the validity of such entropy-based irreversibility measurement and its use as the optimization criterion in heat transfer, both the conserved and non-conservative quantities during a heat transfer process are analysed. A couple of irreversibility measurements, including the newly defined concept entransy , in heat transfer process are discussed according to different objectives. It is demonstrated that although thermal energy is conserved, the accompanied system entransy and entropy in heat transfer process are non-conserved quantities. When the objective of a heat transfer is for heating or cooling, the irreversibility should be measured by the entransy dissipation, whereas for heat-work conversion, the irreversibility should be described by the entropy generation. Next, in Fourier’s Law derivation using the principle of minimum entropy production, the thermal conductivity turns out to be inversely proportional to the square of temperature. Whereas, by using the minimum entransy dissipation principle, Fourier’s Law with a constant thermal conductivity as expected is derived, suggesting that the entransy dissipation is a preferable irreversibility measurement for heat transfer.

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.

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.

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.

Enhanced thermal conductivity by aggregation in heat transfer nanofluids containing metal oxide nanoparticles and carbon nanotubes

2008 ◽  
Vol 92 (2) ◽  
pp. 023110 ◽  
Author(s):  
Jesse Wensel ◽  
Brian Wright ◽  
Dustin Thomas ◽  
Wayne Douglas ◽  
Bert Mannhalter ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Metal Oxide ◽  
Metal Oxide Nanoparticles ◽  
Oxide Nanoparticles ◽  
Enhanced Thermal Conductivity

scholarly journals Design and Implementation of a Laboratory Equipment for Studying Heat Transfer by Conduction

2019 ◽  
Vol 11 (1) ◽  
pp. 153-156
Author(s):  
István Padrah ◽  
Judit Pásztor ◽  
Rudolf Farmos
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Thermal Conduction ◽  
Transfer Mechanism ◽  
Measuring Instrument ◽  
Heat Transfer Mechanism ◽  
Laboratory Equipment ◽  
Insulating Materials ◽  
Design And Implementation

Abstract Thermal conduction is a heat transfer mechanism. It is present in our everyday lives. Studying thermal conductivity helps us better understand the phenomenon of heat conduction. The goal of this paper is to measure the thermal conductivity of various materials and compare results with the values provided by the manufacturers. To achieve this we assembled a measuring instrument and performed measurements on heat insulating materials.

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