scholarly journals Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011 ◽  
Vol 468 (2141) ◽  
pp. 1217-1229 ◽  
Author(s):  
A. Sellitto ◽  
D. Jou ◽  
J. Bafaluy
Keyword(s):  
Heat Transport ◽  
Local Equilibrium ◽  
Mean Free Path ◽  
Thin Layers ◽  
Graphene Sheets ◽  
Fourier Law ◽  
Local Effects ◽  
Radial Heat ◽  
Non Local ◽  
The Mean

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

scholarly journals Non-local effects in the mean-field disc dynamo: II – numerical and asymptotic solutions

2004 ◽  
Vol 98 (4) ◽  
pp. 345-363 ◽  
Author(s):  
Ashley P. Willis ◽  
Anvar Shukurov ◽  
Andrew M. Soward ◽  
Dmitry Sokoloff
Keyword(s):  
Mean Field ◽  
Asymptotic Solutions ◽  
Local Effects ◽  
Non Local ◽  
The Mean

Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach

2010 ◽  
Author(s):  
Aydin Nabovati ◽  
Daniel P. Sellan ◽  
Cristina H. Amon
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Fourier Law ◽  
Transport Models ◽  
Size Dependent ◽  
Semiconductor Electronic ◽  
Ballistic Heat Transfer ◽  
The Mean ◽  
Boltzmann Method

It is well known that continuum-based thermal transport models, such as the Fourier law, fail when the characteristic size of a system becomes comparable to the mean free path of carriers that transport thermal energy. The current work uses the lattice Boltzmann method to develop two modifications to the Fourier heat equation so that it can capture sub-continuum effects. The two modifications are: (i) a size-dependent thermal conductivity and (ii) a size-dependent temperature jump at the system boundaries.

Thermal transport of small systems

2017 ◽  
Author(s):  
Takahiro Yamamoto ◽  
Kazuyuki Watanabe ◽  
Satoshi Watanabe
Keyword(s):  
Thermal Transport ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Fourier Law ◽  
Small Systems ◽  
One Dimensional ◽  
Sample Dimension ◽  
The Mean

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

scholarly journals Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond

Nanomaterials ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 414 ◽  
Author(s):  
Miguel-Ángel Sanchez-Martinez ◽  
Francesc Alzina ◽  
Juan Oyarzo ◽  
Clivia Sotomayor Torres ◽  
Emigdio Chavez-Angel
Keyword(s):  
Heat Transport ◽  
Free Path ◽  
Regularization Parameter ◽  
Physical Nature ◽  
Mean Free Path ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Energy Carriers ◽  
The Mean ◽  
The Impact

The understanding of the mean free path (MFP) distribution of the energy carriers in materials (e.g., electrons, phonons, magnons, etc.) provides a key physical insight into their transport properties. In this context, MFP spectroscopy has become an important tool to describe the contribution of carriers with different MFP to the total transport phenomenon. In this work, we revise the MFP reconstruction technique and present a study on the impact of the regularization parameter on the MFP distribution of the energy carriers. By using the L-curve criterion, we calculate the optimal mathematical value of the regularization parameter. The effect of the change from the optimal value in the MFP distribution is analyzed in three case studies of heat transport by phonons. These results demonstrate that the choice of the regularization parameter has a large impact on the physical information obtained from the reconstructed accumulation function, and thus cannot be chosen arbitrarily. The approach can be applied to various transport phenomena at the nanoscale involving carriers of different physical nature and behavior.

scholarly journals Temperature Distribution through a Nanofilm by Means of a Ballistic-Diffusive Approach

Inventions ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 2 ◽  
Author(s):  
Hatim Machrafi
Keyword(s):  
Heat Transport ◽  
Temperature Jump ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Behavior Changes ◽  
Heat Management ◽  
Qualitative Comparison ◽  
Microelectronic Devices ◽  
Order Of Magnitude ◽  
Non Local

As microelectronic devices are important in many applications, their heat management needs to be improved, in order to prolong their lifetime, and to reduce the risk of damage. In nanomaterials, heat transport shows different behaviors than what can be observed at macroscopic sizes. Studying heat transport through nanofilms is a necessary tool for nanodevice thermal management. This work proposes a thermodynamic model incorporating both ballistic, introduced by non-local effects, and diffusive phonon transport. Extended thermodynamics principles are used in order to develop a constitutive equation for the ballistic behavior of heat conduction at small-length scales. Being an irreversible process, the present two-temperature model contains a one-way transition of ballistic to diffusive phonons as time proceeds. The model is compared to the classical Fourier and Cattaneo laws. These laws were not able to present the non-locality that our model shows, which is present in cases when the length scale of the material is of the same order of magnitude or smaller than the phonon mean free path, i.e., when the Knudsen number K n ≤ O ( 1 ) . Moreover, for small K n numbers, our model predicted behaviors close to that of the classical laws, with a weak temperature jump at both sides of the nanofilm. However, as K n increases, the behavior changes completely, the ballistic component becomes more important, and the temperature jump at both sides of the nanofilms becomes more pronounced. For comparison, a model using Fourier’s and Cattaneo’s laws with an effective thermal conductivity has shown, with reasonable qualitative comparison for small Knudsen numbers and large times.

scholarly journals Non-local effects in the mean-field disc dynamo I. An asymptotic expansion

2000 ◽  
Vol 93 (1-2) ◽  
pp. 97-114 ◽  
Author(s):  
Vladimir Priklonsky ◽  
Anvar Shukurov ◽  
Dmitry Sokoloff ◽  
Andrew Soward
Keyword(s):  
Asymptotic Expansion ◽  
Mean Field ◽  
Local Effects ◽  
Non Local ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document