A Broad Range of Phonon Mean Free Paths Is Important for Heat Conduction

2008 ◽  
Author(s):  
C. Dames
Keyword(s):  
Thermal Conductivity ◽  
Distribution Function ◽  
Heat Conduction ◽  
Mean Free Path ◽  
Angular Frequency ◽  
Boundary Scattering ◽  
Spectral Form ◽  
Einstein Distribution ◽  
K 13 ◽  
Bose Einstein

The thermal conductivity is modeled with a spectral form of kinetic theory k=13∫CωνLdω(1) where ω is the angular frequency, Cω is the specific heat per unit frequency, ν = ∂ω/∂q is the group velocity, and L is the effective mean free path (MFP) which combines bulk and boundary scattering using Matthiessen’s rule: Cω=ħωDOS∂f/∂T(2)L−1=Lbulk−1+Lboundary−1.(3) Here q is the wavevector, DOS is the density of states (acoustic modes only), T is the temperature, and f is the Bose-Einstein distribution function.

Thermal Rectification by Ballistic Phonons

2008 ◽  
Author(s):  
John Miller ◽  
Wanyoung Jang ◽  
Chris Dames
Keyword(s):  
Distribution Function ◽  
Mean Free Path ◽  
Temperature Gradients ◽  
Reverse Direction ◽  
Large Temperature ◽  
Thermal Rectification ◽  
Einstein Distribution ◽  
Ballistic Phonons ◽  
Dimensional Electron Gas ◽  
Bose Einstein

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.

scholarly journals Lattice Boltzmann method simulation of the gas heat conduction of nanoporous material

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3749-3756
Author(s):  
Ya Han ◽  
Shuai Li ◽  
Hai-Dong Liu ◽  
Weipeng Cui
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Size Effects ◽  
Temperature Jump ◽  
Boundary Scattering ◽  
Nanoporous Material ◽  
Boltzmann Method

In order to deeply investigate the gas heat conduction of nanoporous aerogel, a model of gas heat conduction was established based on microstructure of aerogel. Lattice Boltzmann method was used to simulate the temperature distribution and gas thermal conductivity at different size, and the size effects of gas heat conduction have had been obtained under micro-scale conditions. It can be concluded that the temperature jump on the boundary was not obvious and the thermal conductivity remained basically constant when the value of Knudsen number was less than 0.01; as the value of Knudsen number increased from 0.01 to 0.1, there was a clear temperature jump on the boundary and the thermal conductivity tended to decrease and the effect of boundary scattering increased drastically, as the value of Knudsen number was more than 0.1, the temperature jump increased significantly on the boundary, furtherly, the thermal conductivity decreased dramatically, and the size effects were significantly.

scholarly journals On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Kazi Ashraful Alam ◽  
Mir Mehedi Faruk
Keyword(s):  
Black Holes ◽  
Distribution Function ◽  
Phase Space ◽  
Partition Function ◽  
Boltzmann Distribution ◽  
Einstein Distribution ◽  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime ◽  
Bose Einstein

Entropy bound for the photon gas in a noncommutative (NC) spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.

Electron and Phonon Thermal Conduction in Epitaxial High-Tc Superconducting Films

1993 ◽  
Vol 115 (1) ◽  
pp. 17-25 ◽  
Author(s):  
K. E. Goodson ◽  
M. I. Flik
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Size Effect ◽  
Free Path ◽  
Fluid Model ◽  
Mean Free Path ◽  
Boundary Scattering ◽  
High Tc ◽  
Two Fluid Model ◽  
Electron Mean Free Path

Electrons and phonons are the carriers of heat in the a-b plane of the high-Tc superconductor YBa2Cu3O7. In the absence of boundary scattering, the a-b plane thermal conductivity and the mean free path of each carrier type are calculated as functions of temperature using kinetic theory, the two-fluid model of the superconducting state, and experimental data for the thermal conductivity and electrical resistivity of a single crystal. The reduction by boundary scattering of the effective a-b plane thermal conductivity along an epitaxial YBa2Cu3O7 film is predicted as a function of temperature and film thickness. The size effect on the phonon conductivity dominates over the size effect on the electron conductivity. The predicted electron mean free path is limited by scattering on defects and is in very good agreement with experimental data from infrared spectroscopy.

Elephant ivory: A low thermal conductivity, high strength nanocomposite

2006 ◽  
Vol 21 (1) ◽  
pp. 287-292 ◽  
Author(s):  
Michael B. Jakubinek ◽  
Champika J. Samarasekera ◽  
Mary Anne White
Keyword(s):  
Thermal Conductivity ◽  
Room Temperature ◽  
High Strength ◽  
Mean Free Path ◽  
Boundary Scattering ◽  
Low Thermal Conductivity ◽  
Recent Interest ◽  
Elephant Ivory ◽  
Nanocomposite Structures ◽  
Structure Properties

There has been much recent interest in heat transport in nanostructures, and alsoin the structure, properties, and growth of biological materials. Here we present measurements of thermal properties of a nanostructured biomineral, ivory. The room-temperature thermal conductivity of ivory is anomalously low in comparison with its constituent components. Low-temperature (2–300 K) measurements ofthermal conductivity and heat capacity reveal a glass-like temperature dependenceof the thermal conductivity and phonon mean free path, consistent with increased phonon-boundary scattering associated with nanostructure. These results suggest that biomineral-like nanocomposite structures could be useful in the design of novel high-strength materials for low thermal conductivity applications.

Thermal Transport Property of Silicon Membranes With Asymmetric Porous Structure

2015 ◽  
Author(s):  
Harutoshi Hagino ◽  
Koji Miyazaki
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Thermal Conduction ◽  
Transport Theory ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Boundary Scattering ◽  
Rectification Effect ◽  
Thermal Rectification ◽  
Asymmetric Pores

The size effect on thermal conduction due to phonon boundary scattering in films was studied as controlling heat conduction. Thermal rectifier was proposed as a new heat control concept by a ballistic rectifier relies on asymmetric scattering of phonons in asymmetric linear structure. We focus on the thermal rectification effect in membrane with asymmetric pores. We discussed on the thermal rectification effect from the calculation and thermal conductivity measurement of asymmetric structured membrane. Thermal conduction was calculated by using radiation calculation of ANSYS Fluent based on Boltzmann transport theory which is development of equation of phonon radiative transfer from view point of phonon mean free path and boundary scattering condition. In-plane thermal conductivities of free standing membranes with microsized asymmetric pores were measured by periodic laser heating measurement. From the result of calculation, phonons were transition to ballistic transport in the membranes with asymmetric shaped pores and thermal rectification effect was obtained on the condition of specular scattering because of the asymmetric back-scattering of ballistic phonons from asymmetric structure. The thermal rectification effect was increased with decreasing thickness of membrane shorter and shorter than mean free path of phonon. From the result of measurements, we were able to confirm the reduction of thermal conductivity based on ballistic phonon transport theory, but the strong thermal rectification effect was not confirmed.

The thermal conductivity of tin and indium below 1°K

1958 ◽  
Vol 248 (1255) ◽  
pp. 522-538 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Superconducting State ◽  
Size Dependence ◽  
Mean Free Path ◽  
Fermi Velocity ◽  
Boundary Scattering ◽  
Simple Analysis ◽  
Phonon Field ◽  
Size Dependent

An experimental study has been made of some aspects of the thermal conductivity of superconducting tin and indium below 1°K. Experiments at the lowest temperatures, where the thermal conductivity of the lattice is dominant, and for tin varies as T 3 , have been mainly directed towards studying the size effect in the conductivity due to the scattering of phonons at the specimen surface. Electropolishing tin has been found to increase the thermal conductivity considerably; a simple analysis of the results shows that almost complete specular reflexion of phonons is attainable. The analysis confirms the existence of an internal scattering of phonons, describable at the lowest temperatures by a temperature-independent mean free path which does not vary when the diameter of the specimen is reduced, but is very sensitive to any damage suffered by the crystal. The lattice conductivity of indium, which is anomalous in having a T 4 rather than a T 3 variation, appears to be limited mainly by internal scattering and it is tentatively suggested that the internal scattering is mainly due to the reradiation from dislocations oscillating in the phonon field. At somewhat higher temperatures (above about 0.7 but below 1°K) the thermal conductivity is predominantly electronic and the results indicate that here too the ‘effective’ electronic mean free path is size-dependent due to boundary scattering. From an analysis of this size-dependence in tin, the ‘intrinsic’ electronic mean free path in the superconducting state is deduced and found to be between ten and thirty times as long as in the normal state. The results suggest also that the electronic velocity in the superconducting state is something like one-third of the Fermi velocity.

Theoretical and DSMC Studies on Heat Conduction of Gas Confined in a Cuboid Nanopore

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Chuan-Yong Zhu ◽  
Zeng-Yao Li ◽  
Wen-Quan Tao
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Numerical Study ◽  
Direct Simulation Monte Carlo ◽  
Mean Free Path ◽  
Confined Space ◽  
Temperature Jumps ◽  
Side Walls ◽  
The Impact

This paper presents a theoretical and numerical study on the heat conduction of gas confined in a cuboid nanopore, in which there exists a temperature difference between the top and bottom walls and the side walls are adiabatic. A modified gas mean free path in confined space is proposed by considering the impact of collisions between molecules and solid surfaces, with which an effective thermal conductivity model of gas in the transition regime is derived. A direct simulation Monte Carlo (DSMC) study on the heat conduction of argon and helium in a cuboid nanopore is carried out to validate the present model. The influences of the Knudsen number and the treatments of boundary conditions on the heat conduction and effective thermal conductivity of gas in nanopores are studied. The temperature jumps and the reduction of heat flux near side walls are analyzed.

Size Effects of Heat Conduction for Silicon Nanograins

2014 ◽  
Vol 633-634 ◽  
pp. 34-37
Author(s):  
Ya Fen Han ◽  
Hai Dong Liu
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Kinetic Theory ◽  
Free Path ◽  
Size Effects ◽  
Mean Free Path ◽  
Structure Model ◽  
The Mean

The structure model of silicon nanograins was built. And then based the modification of the mean free path of phonons according to the size of nanograins, the expression of thermal conductivity in nanograins was obtained according to the phonon kinetic theory. The dependence of the thermal conductivity of silicon nanograins on size was investigated. The results showed that thermal conductivity of nanograins decrease with the reduction of characteristic sizes when the characteristic sizes of nanograins are comparable to or smaller than the phonon mean free path.

Heat Conduction Across Nanoscale Interfaces and Nanomaterials for Thermal Management and Thermoelectric Energy Conversion

2010 ◽  
Author(s):  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Thermal Management ◽  
Contact Area ◽  
Silicon Substrate ◽  
Mean Free Path ◽  
Contact Mode ◽  
Nanoscale Interfaces ◽  
Air Conduction

Nanoscale heat conduction plays a critical role in applications ranging from thermal management of nanodevices to nanostructured thermoelectric materials for solid state refrigeration and power generation. This lecture presents recent investigations in our group. The first part of the lecture demonstrates heat conduction across nanoscale interfaces formed between individual nanoscale heaters and the silicon substrate [1]. A systematic experimental study was performed of thermal transport from individual nanoscale heaters with widths ranging between 77nm-250nm to bulk silicon substrates in the temperature range of 80–300K. The effective substrate thermal conductivity was measured by joule heating thermometry. We report up to two orders of magnitude reductions in the measured effective thermal conductivity of the silicon substrate when the heater widths are smaller than the mean free path of the heat carriers in the substrate, as summarized in Fig. 1. The effective mean free path of the silicon substrate was extracted from the measurements and was found to be comparable with recent molecular dynamics simulations. A proof of concept demonstration of a novel Thermal Interface Material (TIM) is presented next. The high thermal conductivity TIM is based on a highly connected high thermal conductivity nanostructured filler network embedded in a polymer matrix where the contribution of filler-matrix interfaces to thermal resistance is minimized. It was found [2] that the thermal conductivity could be varied from ∼0.2 to 20 W/mK when the volume fraction of metallic nanoparticles was varied from 0–20%. For similar volume fractions and filler composition, microparticle based composites have two orders of magnitude lower thermal conductivities. SEM characterization and thermal transport modeling are employed to support the conclusion that morphological changes in the nano-TIM are responsible for the thermal conductivity reduction. Thermoelectric transport investigations are discussed for a novel class of highly scalable nanostructured bulk chalcogenides developed at Rensselaer Polytechnic Institute [3]. Un-optimized, single-component bulk assemblies of Bi2Te3 and Sb2Te3 single crystal nanoplates show large enhancements (25–60%) in the room temperature thermoelectric figure of merit compared with individual bulk counterparts (Table 1). Nanostructuring was found to lead to strong thermal conductivity reduction without significantly affecting the mobility of the charge carriers, as shown in Table 2. A scanning thermal microprobe technique developed for simultaneous thermal conductivity (κ) and Seebeck coefficient (α) measurements in thermoelectric films is also presented [4]. In this technique, an AC alternative current joule-heated V-shaped microwire that serves as heater, thermometer and voltage electrode, locally heats the thin film when contacted with the surface (Fig. 2). The κ is extracted from the average DC temperature rise thermal resistance of the microprobe and α from the DC Seebeck voltage measured between the probe and unheated regions of the film by modeling the heat transfer in the probe, sample and their contact area, and by calibrations with standard reference samples. Application of the technique on sulfur-doped porous Bi2Te3 and Bi2Se3 films reveals α = −105.4 and 1.96 μV/K, respectively, which are within 2% of the values obtained by independent measurements carried out using microfabricated test structures. The respective κ values are 0.36 and 0.52 W/mK, which are significantly lower than the bulk values due to film porosity, and are consistent with effective media theory. The dominance of air conduction at the probe-sample contact area determines the microscale spatial resolution of the technique and allows probing samples with rough surfaces. Non-contact mode measurement of thermal conductivity was also demonstrated and confirmed by independent characterization [5]. In non-contact mode the technique utilizes ballistic air conduction as the dominant heat transfer mechanism between the thermal probe and the sample and thus eliminates uncertainties due to solid contact and liquid meniscus conduction.

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