On the Kinetic Theory of the Enskog Fluid. Viscosity and Viscoelasticity, Heat Conduction and Thermal Pressure

1981 ◽  
Vol 36 (6) ◽  
pp. 545-553 ◽  
Author(s):  
G. Schmidt ◽  
W. E. Köhler ◽  
S. Hess
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Moment Method ◽  
Solution Procedure ◽  
Fluid Viscosity ◽  
Thermal Pressure ◽  
Dense Fluid ◽  
The Moment ◽  
Dependent Viscosity

Abstract The moment method is applied to the linearized Enskog-Boltzmann equation for a dense gas. Thus an enlarged set of equations of thermo-hydrodynamics is obtained which allows to go beyond ordinary hydrodynamics. The resulting expressions for the density dependent viscosity and heat conductivity coincide with those previously obtained with the help of the Chapman- Enskog solution procedure. In addition, however, the frequency dependence of the viscosity is treated and it is demonstrated that the thermal pressure does not vanish in a dense fluid

scholarly journals The development and application of the moment method in the gas kinetic theory

2016 ◽  
Vol 46 (10) ◽  
pp. 1465-1488 ◽  
Author(s):  
Ruo LI ◽  
Zhicheng HU ◽  
Heyu WANG ◽  
Yuwei FAN ◽  
Zhenning CAI
Keyword(s):  
Kinetic Theory ◽  
Moment Method ◽  
Gas Kinetic Theory ◽  
The Moment

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

scholarly journals Spectral gap in random bipartite biregular graphs and applications

2021 ◽  
pp. 1-39
Author(s):  
Gerandy Brito ◽  
Ioana Dumitriu ◽  
Kameron Decker Harris
Keyword(s):  
Community Detection ◽  
Adjacency Matrix ◽  
Moment Method ◽  
Coding Theory ◽  
High Probability ◽  
Spectral Gap ◽  
Matrix Completion ◽  
Full Rank ◽  
The Moment ◽  
Deterministic Matrix

Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

1998 ◽  
Vol 12 (02) ◽  
pp. 191-205 ◽  
Author(s):  
Vu Van Hung ◽  
Nguyen Thanh Hai
Keyword(s):  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Phase Change ◽  
Specific Heat ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Moment Method ◽  
Adiabatic Compressibility ◽  
Relative Displacement ◽  
The Moment

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat Cv and Cp, the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat Cv and Cp… of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye–Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

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