Multicomponent transport algorithms

Description

This book presents a general and self-contained theory of iterative algorithms for evaluating transport coefficients of dilute polyatomic gas mixtures, including the Enskog-Chapman procedure with its extension to reactive mixtures, the variational framework for polynomial expansions, the mathematical properties of the linear systems, the singular case of vanishing concentrations, iterative methods with convergence theorems, and explicit, accurate, approximate expressions for all the transport coefficients.This book contains mostly new developments and is written for the broadest audience of potentially interested readers, including engineers, physicists, chemists, numerical modelers, applied mathematicians, and mathematicians. Therefore, every mathematical step is carefully explained and only introductory linear algebra and kinetic theory concepts are needed.The authors made a special effort in presenting the material rigorously and comprehensively, thereby providing a complete source of reference for evaluating multicomponent transport coefficients. Read more... 1. Introduction. 1.1. Detailed Modeling of Dilute Polyatomic Gas Mixtures -- 2. Transport Linear Systems. 2.1. Transport Coefficients of Dilute Polyatomic Gas Mixtures. 2.2. Derivation of the Transport Linear Systems. 2.3. Mathematical Structure of the Transport Linear Systems. 2.4. The Shear Viscosity. 2.5. The Volume Viscosity. 2.6. The Diffusion Matrix. 2.7. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 2.8. The Thermal Conductivity and the Thermal Diffusion Ratios. 2.9. Comparison with the Systems of Monchick, Yun, and Mason. 2.10. The Mason and Monchick approximations -- 3. Rescaled Transport Linear Systems. 3.1. Transport Linear System for Nonnegative Mass Fractions. 3.2. The Shear Viscosity. 3.3. The Volume Viscosity. 3.4. The Flux Diffusion Matrix. 3.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 3.6. The Thermal Conductivity and the Thermal Diffusion Ratios. 3.7. The Mason and Monchick Approximations -- 4. Mathematical Properties. 4.1. Mathematical Preliminaries. 4.2. The Shear Viscosity. 4.3. The Volume Viscosity. 4.4. The Diffusion Matrix and the Flux Diffusion Matrix. 4.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 4.6. The Thermal Conductivity and the Thermal Diffusion Ratios. 4.7. The Dilution Limit -- 5. Convergent Iterative Methods. 5.1. Iterative Methods for Constrained Singular Systems. 5.2. The Shear Viscosity. 5.3. The Volume Viscosity. 5.4. The Diffusion Matrix and the Flux Diffusion Matrix. 5.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 5.6. The Thermal Conductivity and the Thermal Diffusion Ratios -- 6. Numerical Experiments. 6.1. Computational Considerations. 6.2. The Shear Viscosity. 6.3. The Volume Viscosity. 6.4. The Diffusion Matrix and the Flux Diffusion Matrix. 6.5. The Partial Thermal Conductivity and the Thermal Diffusion Vector. 6.6. The Thermal Conductivity and the Thermal Diffusion Ratios -- 7. Concluding Remarks