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.

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.

A Novel Approach for Lattice Boltzmann Modeling of Energy Transport

2012 ◽  
Author(s):  
Dadong Wang ◽  
Yanbao Ma
Keyword(s):  
Heat Conduction ◽  
Lattice Boltzmann ◽  
Thermal Transport ◽  
Energy Transport ◽  
Transient Heat Conduction ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Nano Scale ◽  
Novel Approach ◽  
Boltzmann Method

It is well known that Fourier law breaks down for the prediction of heat conduction in nano-scale, where the length scale is comparable to the mean free path of energy carriers. Over the past decade, Boltzmann transport equation (BTE) has been used to predict thermal transport in dielectrics and semiconductors at micro-scale and nano-scale. In this work, a new modified gray model is obtained from BTE. The implicit lattice Boltzmann method (LBM) is developed to simulate the thermal transport process. Based on the new model, we can derive Guyer-Krumhansl equation. Transient heat conduction through a thin nano-film and hotspot self-heating in sub-micron transistors are examined. The numerical results are compared with those provided by Fourier, Cattaneo, and Guyer-Krumhansl equation.

Simulation and Optimization Design of the Heat Waveguide Optical Switch on Non-Fourier Heat Conduction Theory

2014 ◽  
Vol 556-562 ◽  
pp. 2093-2096
Author(s):  
Ji Yun Song ◽  
Xiao Min Zhang ◽  
Zhong Xiang Chu ◽  
Long Zhang
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Optical Switch ◽  
Thermal Relaxation ◽  
Core Layer ◽  
Response Speed ◽  
Thermal Relaxation Time ◽  
Simulation And Optimization ◽  
Conduction Theory ◽  
Fourier Heat Conduction

The temperature distribution of the heat waveguide optical switch with different cladding materials is simulated on Fourier heat conduction theory and non-Fourier heat conduction theory, discussing effect of the cladding materials on the power consumption and the response speed of the device. The main conclusions as follows: (1)The response speed of waveguide optical switch with silica as cladding is faster than that with PMMA as cladding. (2)Thermal relaxation time has significant influence on the temperature of the core layer: the variation of optical switch core layer temperature gets bigger with the increase of material thermal relaxation time.

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.

Micro/Nanoscale Heat Transfer: Interfacial Effects Dominate the Heat Transfer

2012 ◽  
Author(s):  
X. Zhang ◽  
Z. Y. Guo
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Near Field ◽  
Mean Free Path ◽  
Viscous Force ◽  
Inertia Force ◽  
Relative Importance ◽  
Interfacial Effects ◽  
Nanoscale Heat Transfer ◽  
The Continuum

This paper describes the effects of size on heat conduction in nanofilms, convective heat transfer in micro/nanochannels, and near-field radiation in nanogaps. As the size is reduced, the ratio of the surface area to the volume increases; therefore, the relative importance of the interfacial effects also increases. The physical mechanisms for these size effects have been classified into two classes. When the scale is reduced to the order of micrometers (except for gases), the interfaces only affect the macro parameters and the continuum assumption still holds, but the relative importance of the various forces (inertia force, viscous force, buoyancy, etc.) and effects (interfacial effect, axial heat conduction in the tube wall, etc.) changes, resulting in changes in the heat transfer characteristics from normal conditions. As the size is further reduced to the order of submicrometers or nanometers, the interface affects not only the macro parameters but also the micro parameters (mean free path, relaxation time, etc.) so the continuum assumption breaks down and Newton’s viscosity law and Fourier’s heat conduction law are no longer applicable. Thus, the major characteristic of micro/nanoscale heat transfer is that the interfacial effects dominate the heat transfer.

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.

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.

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