Kinetic Theory and Fluid DynamicsSpringer Science & Business Media, 12 aug 2002 - 353 pagina's This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit. |
Inhoudsopgave
II | 1 |
III | 5 |
IV | 7 |
V | 8 |
VI | 9 |
VII | 9 |
IX | 9 |
X | 11 |
LXIII | 105 |
LXIV | 106 |
LXV | 107 |
LXVI | 111 |
LXVII | 114 |
LXVIII | 121 |
LXXI | 127 |
LXXII | 135 |
XI | 12 |
XII | 13 |
XIII | 17 |
XIV | 22 |
XV | 23 |
XVI | 23 |
XIX | 23 |
XXI | 23 |
XXII | 23 |
XXIII | 32 |
XXIV | 37 |
XXV | 40 |
XXVI | 41 |
XXVII | 45 |
XXVIII | 47 |
XXIX | 48 |
XXXII | 51 |
XXXIII | 52 |
XXXIV | 53 |
XXXV | 58 |
XXXVI | 60 |
XXXVII | 69 |
XXXVIII | 71 |
XL | 71 |
XLII | 71 |
XLIII | 75 |
XLIV | 79 |
XLV | 79 |
XLVI | 79 |
XLVII | 79 |
XLVIII | 79 |
L | 79 |
LI | 79 |
LII | 82 |
LIII | 85 |
LIV | 89 |
LVII | 91 |
LVIII | 99 |
LIX | 101 |
LX | 103 |
LXI | 103 |
LXXIII | 135 |
LXXIV | 135 |
LXXV | 135 |
LXXVI | 139 |
LXXIX | 139 |
LXXX | 139 |
LXXXI | 139 |
LXXXII | 141 |
LXXXIII | 144 |
LXXXIV | 148 |
LXXXV | 153 |
LXXXVII | 154 |
LXXXVIII | 159 |
LXXXIX | 163 |
XCII | 165 |
XCIV | 165 |
XCV | 172 |
XCVI | 175 |
XCVII | 179 |
C | 181 |
CI | 183 |
CII | 192 |
CIII | 197 |
CIV | 201 |
CV | 204 |
CVI | 207 |
CVII | 209 |
CVIII | 210 |
CIX | 213 |
CXII | 214 |
CXIII | 216 |
CXV | 218 |
CXVI | 223 |
CXVII | 224 |
CXIX | 225 |
CXX | 227 |
CXXIII | 228 |
CXXIV | 233 |
CXXV | 233 |
CXXVI | 247 |
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Veelvoorkomende woorden en zinsdelen
analysis Appendix asymptotic theory behavior BKW equation BKW model Boltzmann equation boundary condition classical gas coefficients collision integral complete condensation component function condensed phase continuum limit corresponding Couette flow cylinder derived determined diffuse reflection discussion Euler set expansion expressed Əxi Əxj finite flow induced Fluids Gas Dynamics given Golse Grad-Hilbert solution hard-sphere gas inhomogeneous term integral equation ÎSBO Îvo kinetic Knudsen-layer correction layer linearized Mach number macroscopic variables Maxwellian mean free path molecules Navier-Stokes set nondimensional nonlinear obtained orthogonal pairs it,iu parameters particle Phys pipe pressure PSBO relation right-hand side rotation SB solution Section set of equations simple boundary slip solvability condition Sone Sone & Aoki spherical subscript Sugimoto symmetric Takata tensor thermal conductivity thermal creep flow thermal-stress tion TSBO velocity distribution function viscous boundary-layer windmill X₁ θα біз მე მყ