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2010 | Buch

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An Introduction to the Boltzmann Equation and Transport Processes in Gases

verfasst von: Gilberto Medeiros Kremer

Verlag: Springer Berlin Heidelberg

Buchreihe : Interaction of Mechanics and Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Inhaltsverzeichnis

Frontmatter

Basic Principles of the Kinetic Theory

Abstract

One of the main objectives of the kinetic theory is to describe the macroscopic properties of gases—such as pressure, temperature, thermal conductivity, viscosity, diffusion, etc.—from microscopic quantities that are associated with the molecules which compose the gases—such as mass, velocity, kinetic energy, internal degrees of freedom and interaction forces between the molecules.

Gilberto Medeiros Kremer

The Boltzmann Equation

Abstract

Consider a monatomic gas with N molecules enclosed in a recipient of volume V. One molecule of this gas can be specified at a given time by its position x = (x₁,x₂,x₃) and velocity c = (c₁,c₂,c₃). Hence, a molecule can be specified as a point in a six-dimensional space spanned by its coordinates and velocity components, the so-called μ-phase space. In the μ-phase space, a system of N molecules is described by N points with coordinates (x_α, c_α) for each α= 1,2,...,N.

Gilberto Medeiros Kremer

The Chapman-Enskog Method

Abstract

In this section, a single fluid is analyzed within the framework of the thermodynamic theory of irreversible processes, the so-called TIP.

In this theory, the fluid is described macroscopically by the five scalar fields of mass density $\varrho({\bf x},t)$, hydrodynamic velocity v_i(x,t) and temperature T(x,t).

Gilberto Medeiros Kremer

Moment Methods

Abstract

The macroscopic description of a rarefied gas within Grad’s moment method is based on thirteen scalar fields, namely, mass density $\varrho({\bf x},t)$, hydrodynamic velocity v_i(x,t), pressure tensor p_ij(x,t) and heat flux vector q_i(x,t).

Gilberto Medeiros Kremer

Polyatomic Gases

Abstract

The molecules of polyatomic gases have internal variables that are associated with their internal energy states, namely: (a) the rotational state, (b) the vibrational state, (c) the electronic state and (d) the nuclei state.

Monatomic and polyatomic gases differ from each other concerning the behaviors of the specific heat at constant volume c_v and the ratio of the coefficients of thermal conductivity and shear viscosity λ/μ. These two differences will be explained below.

Gilberto Medeiros Kremer

Dense Gases

Abstract

The equation proposed by van der Waals is the oldest equation of state which takes into account the volume occupied by the molecules of the gas as well as the attractive forces between its molecules. Here, the van der Waals equation of state will be determined from the virial theorem proposed by Clausius.

Gilberto Medeiros Kremer

Granular Gases

Abstract

As it was discussed in the previous chapters, the mechanical energy of a gas is conserved when its molecules undergo elastic collisions and, in this case, the gas relaxes toward an equilibrium state characterized by a Maxwellian distribution function. The inelastic collisions of the gas molecules transform the translational kinetic energy into heat, and the mechanical energy lost implies a temperature decay of the gas. Gases whose molecules undergo inelastic collisions are known in the literature as granular gases.

Gilberto Medeiros Kremer

Mixtures of Monatomic Gases

Abstract

The state of a mixture of n monatomic gases in the μ-phase space is characterized by a set of distribution functions f_α ≡ f(x,c_α,t) with α = 1,2,...,n, such that f(x,c_α,t)dx dc_α gives at time t the number of molecules of constituent α in the volume element whose position vectors are within the range x and x + dx, while the velocity vectors are within the range c_α and c_α + dc_α.

Gilberto Medeiros Kremer

Chemically Reacting Gas Mixtures

Abstract

Consider the following independent reactions in the gaseous phase:

$$ N_2+3H_2\rightleftharpoons 2NH_3, \qquad O_2+2H_2\rightleftharpoons 2H_2O, \qquad H_2+Cl\rightleftharpoons HCl+H. $$

The above expressions indicate the amounts of the elements which correspond to the reagents and products of the reactions. For example, in the formation of ammonia, 1 mole of N₂ with 3 moles of H₂ results in 2 moles of NH₃. From now on, only a single uncoupled chemical reaction will be analyzed.

Gilberto Medeiros Kremer

Backmatter

Titel: An Introduction to the Boltzmann Equation and Transport Processes in Gases
verfasst von: Gilberto Medeiros Kremer
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-11696-4
Print ISBN: 978-3-642-11695-7
DOI: https://doi.org/10.1007/978-3-642-11696-4

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