Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

scholarly journals The thermal conductivity of carbon dioxide

1927 ◽  
Vol 114 (767) ◽  
pp. 354-366 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Critical Pressure ◽  
Mean Free Path ◽  
Double System ◽  
Wire Method ◽  
The Mean ◽  
The Absolute ◽  
The Many

Of the many experimental determinations of the thermal conductivity of Co 2 which have been made, the absolute values given by the various observers vary from 3·07 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Winkelman, 1), to 3·39 × 10 -5 cal. sec. -1 cm. -1 deg. -1 (Weber, 2), and generally speaking the experiments were modifications of two principal methods, namely, the electrically heated wire of Schleimacher (3) and the cooling thermometer method. In both of these methods convection losses were present to a degree depending on the dimensions and disposition of the apparatus, and on the pressure of the gas; therefore, in the author’s opinion, the discrepancies amongst various observers are due to the practice of attempting to eliminate these convective losses by diminishing the pressure. Such a procedure is justifiable only if the reduction of pressure is not carried beyond the point at which the mean free path of the molecules becomes comparable with the dimensions of the containing vessel. This is a critical point in the determination of the conductivity of a gas, as the authors’ experiments on Co 2 indicate that the convection becomes negligible only at pressures for which the mean Free Path Effect is such that the significance imposed on the conductivity by Fourier’s law loses its meaning, and below this critical pressure the conductivity varies with the pressure in a manner depending on the dimensions of the vessel containing the gas. In the experiments of Gregory and Archer (4), on the thermal conductivities of air and hydrogen, the use of a double system of electrically-heated wires enabled the authors accurately to identify the critical pressure at which convective losses became negligible. This is an extremely important point in all applications of the hot-wire method to the absolute determination of the conductivities of gases, and alone justifies the procedure of lowering the pressure to eliminate convective losses. Above this critical pressure it is necessary to disentangle the conduction and convection losses, and below, the meaning of conduction loses its ordinary significance.

Lattice Boltzmann Modeling of Phonon Heat Conduction in Superlattice Structures

2010 ◽  
Author(s):  
Cristian J. San Marti´n ◽  
Amador M. Guzma´n ◽  
Rodrigo A. Escobar
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Lattice Boltzmann ◽  
Phonon Dispersion ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
One Dimension ◽  
The Mean ◽  
Superlattice Structures ◽  
Boltzmann Method

The results of temperature prediction and determination of effective thermal conductivity in periodic Si-Ge superlattice in one dimension, at length scale comparable to the mean free path are presented. Classical heat transfer models such as Fourier’s law do not represent what actually happens within electronic devices at these length scales. Phonon-border and phonon-interface scattering effects provide discontinuous jumps in temperature distribution when the mean free path is comparable with the device’s characteristic length, a relation given by the Knudsen number (Kn). For predicting the temperature within the periodic Si-Ge superlattice use is made of the lattice Boltzmann method in one dimension, using Debye’s model in the phonon dispersion relation. The predictions show that as Kn increases, so do the jumps at the borders, the same as at the interfaces. The prediction also shows that the effective conductivity of the Si-Ge superlattice decreases as Kn and the number of layers of material increase, and that keff decreases as the magnitude of p increases, a factor that allows heat flow between one layer and another. Use of gray LBM leads to good approximations of the actual temperature field and thermal conductivity values for the superlattice materials model when the physics of phonons established by Debye’s model is used.

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.

Experimentelle und theoretische Untersuchungen des isothermen und des adiabatischen Hall-Effektes an Se

1953 ◽  
Vol 8 (8) ◽  
pp. 453-459
Author(s):  
Rolf Diestel
Keyword(s):  
Thermal Conductivity ◽  
Theoretical Result ◽  
Free Path ◽  
Hall Coefficient ◽  
Mean Free Path ◽  
Type Semiconductor ◽  
The Mean ◽  
The Difference ◽  
P Type

Supposing an arbitrary dependence of the mean free path on energy, the isothermal and the adiabatic Hall coefficients are calculated for a p-type semiconductor by means of the theory of electrons. The difference between the Hall coefficients calculated in this way decrease considerably with increasing thermal conductivity of the lattice. Even for substances with very small thermal conductivity (i. e. Se etc.), the difference amounts to only about 1% in relation to the isothermal Hall coefficient. This theoretical result is proved by measurements on Se; the measured difference slightly exceeds the limit of error (5,2±4,1)%.

Modeling of Phonon Thermal Conductivity of Two Dimensional Nano and Micro Composites in the Longitudinal Direction

2005 ◽  
Author(s):  
Ravi Prasher
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Longitudinal Direction ◽  
Mean Free Path ◽  
Two Dimensional ◽  
Boltzmann Transport ◽  
Host Medium ◽  
Alumina Composite ◽  
The Mean ◽  
Longitudinal Thermal Conductivity

The three important length scales in composites made from nano/micro wires and fibers are: 1) the ratio of inter fiber distance and mean free path of the phonons in the host medium 2) the ratio of the diameter of the fiber or the wire and the mean free path of the phonons in the host medium and 3) the ratio of the diameter of the fiber and the mean free path of phonons in the fiber. Modeling of longitudinal thermal conductivity of two-dimensional nano and micro composites has not been attempted in the literature. This paper develops analytical modeling for the longitudinal thermal conductivity of nano and micro composites by solving the Boltzmann transport equation (BTE) for phonons. The paper shows the scattering of phonons in the host medium by the fiber boundaries play a very important role in deciding the thermal conductivity of nano and micro composites. The model is in good agreement with data on thermal diffusivity of Bismuth Telluride nanowire/ Alumina composite.

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