Poiseuille gas flow in the transition regime II. Application of the general theory

1967 ◽  
Vol 301 (1467) ◽  
pp. 401-409 ◽  
Keyword(s):  
Relaxation Time ◽  
Gas Flow ◽  
Capillary Tube ◽  
Collision Operator ◽  
Mean Free Path ◽  
Transition Regime ◽  
Tube Radius ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Flow Through

The general formulae given in the previous paper are investigated in detail using a simple relaxation-time approximation for the collision operator, and numerical results are obtained for the total gas flow through a capillary tube at various values of the ratio of tube radius to collision mean free path. For all values of this ratio, the results obtained agree with experiment to within about 2%.

Poiseuille gas flow in the transition regime I. Formulation of the general theory

1967 ◽  
Vol 301 (1467) ◽  
pp. 387-400 ◽  
Keyword(s):  
Cross Section ◽  
Gas Flow ◽  
Circular Cross Section ◽  
Collision Operator ◽  
Mean Free Path ◽  
Theoretical Treatment ◽  
Transition Regime ◽  
Velocity Dependence ◽  
Tube Radius ◽  
Intermolecular Collision

A theoretical treatment is given of gas flow along a tube of circular cross-section for arbitrary ratio of intermolecular collision mean free path to tube radius. A general solution is obtained of the Boltzmann equation which is valid for any intermolecular collision operator. The spatial variation of this solution is exhibited explicitly and its velocity dependence is given in terms of the solution of certain integral equations.

scholarly journals Bulk viscosity of strongly interacting matter in the relaxation time approximation

2018 ◽  
Vol 97 (4) ◽  
Author(s):  
Alina Czajka ◽  
Sigtryggur Hauksson ◽  
Chun Shen ◽  
Sangyong Jeon ◽  
Charles Gale
Keyword(s):  
Relaxation Time ◽  
Bulk Viscosity ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Strongly Interacting

scholarly journals Calculations of the thermal conductivity of Si1-xGex films with nonuniform composition

2018 ◽  
Vol 19 (1) ◽  
pp. 48-52
Author(s):  
V. V. Kuryliuk ◽  
O. M. Krit
Keyword(s):  
Thermal Conductivity ◽  
Relaxation Time ◽  
Boltzmann Equation ◽  
Temperature Interval ◽  
Thermoelectric Properties ◽  
Bulk Material ◽  
Nonuniform Distribution ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
Available Information

SiGe films have attracted much attention recently due to experimental demonstrations of improved thermoelectric properties over those of the corresponding bulk material. However, despite this increasing attention, available information on the thermoelectric properties of Si1-xGex films is quite limited, especially for nonuniform composition in wide temperature interval. In this paper we have used the Boltzmann equation under the relaxation-time approximation to calculate the thermal conductivity of Si1-xGex films with nonuniform composition. It is confirmed that SiGe films with nonuniform composition has significantly lower thermal conductivity than its uniform counterpart. This suggests that an improvement in thermoelectric properties is possible by using the SiGe films with nonuniform distribution of germanium.

Longitudinal magnetoresistance in silver and copper between 4.2 and 35 °K

1967 ◽  
Vol 302 (1468) ◽  
pp. 83-98 ◽  
Keyword(s):  
Relaxation Time ◽  
Electron Scattering ◽  
Small Angle ◽  
Time Approximation ◽  
Long Wavelength ◽  
Relaxation Time Approximation ◽  
Angle Scattering ◽  
Different Types ◽  
Pure Single Crystal ◽  
Longitudinal Magnetoresistance

Longitudinal magnetoresistance has been measured in a number of single crystals of silver and one very pure single crystal of copper in fields up to 65 kG and at temperatures between 4.2 and 35 °K. The purpose of the work has been to investigate the effects of different types of electron scattering, in particular small angle scattering. It has been found that at 4.2 °K impure crystals obey the relaxation time approximation fairly well, whereas crystals that have been purified (by oxidation at 800 °C) do not. Above 4.2 °K, the addition of long wavelength phonons has caused the magnetoresistance to increase substantially, as predicted by Pippard (1964), but agreement with Pippard’s theory is only qualitative. To account for the results a more detailed treatment of the scattering is required.

LATTICE THERMAL CONDUCTIVITY IN A HOLLOW SILICON NANOWIRE

2005 ◽  
Vol 19 (06) ◽  
pp. 1017-1027 ◽  
Author(s):  
WEI-QING HUANG ◽  
KE-QIU CHEN ◽  
Z. SHUAI ◽  
LINGLING WANG ◽  
WANGYU HU
Keyword(s):  
Thermal Conductivity ◽  
Relaxation Time ◽  
Lattice Thermal Conductivity ◽  
Silicon Nanowire ◽  
Boundary Scattering ◽  
Phonon Confinement ◽  
Time Approximation ◽  
Si Nanowire ◽  
Scattering Mechanisms ◽  
Relaxation Time Approximation

We theoretically investigate the lattice thermal conductivity of a hollow Si nanowire under the relaxation time approximation. The results show that the thermal conductivity in such structure is decreased markedly below the bulk value due to phonon confinement and boundary scattering. The thermal conductivities under different scattering mechanisms are given, and it is found that the boundary scattering is dominant resistive process for the decrease of the thermal conductivity.

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