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Sone Y. — Molecular Gas Dynamics Theory, Techniques, and Applications
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Название: Molecular Gas Dynamics Theory, Techniques, and ApplicationsАвтор: Sone Y. Аннотация: This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The progress in the field over the last thirty years has greatly enhanced the original theory and has stimulated interesting and critical gas dynamic phenomena and problems. 'Molecular Gas Dynamics,' unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and application.
Язык: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2007Количество страниц: 665Добавлена в каталог: 09.11.2008Операции: Положить на полку |
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Integral form of the Boltzmann equation 531 Integral-equation expression of the Boltzmann equation 531 Integral-equation expression of the linearized BKW equation 532 Integrated form of the Boltzmann equation 531 Internal energy, specific 2 Inverse-power potential 505 Inverted temperature gradient phenomenon 339 Inviscid region 166 Isotropic operator 509 Jensen inequality 558 Jump condition 83 see Kernel form of the linearized collision integral 523 Kernel of the linearized collision integral (hard-sphere molecules) 527 Kernel of the linearized collision integral (pseudo inverse-power potential) 527 Kinetic boundary condition 8 see Knudsen compressor 272 Knudsen layer 79 283 Knudsen layer, analysis of, infinitesimal-curvature problem 455 Knudsen layer, analysis of, linear problem 79 Knudsen layer, analysis of, nonlinear problem 115 130 139 Knudsen layer, analysis of, weakly nonlinear problem 102 Knudsen layer, equation for 80 103 116 131 139 562 Knudsen minimum 183 Knudsen number 15 Knudsen number expansion see "Grad — Hilbert expansion" "Hilbert "Knudsen-layer "Sexpansion" " "SB "Fluid-dynamic-type "Viscous Knudsen number expansion, modified 606 Knudsen-layer correction (time-dependent problem) 163 Knudsen-layer correction (time-independent problem), infinitesimal-curvature problem 456 Knudsen-layer correction (time-independent problem), linear problem 79 83 89 Knudsen-layer correction (time-independent problem), nonlinear problem 113 115 130 136 138 139 Knudsen-layer correction (time-independent problem), weakly nonlinear problem 102 104 Knudsen-layer function 85 90 105 106 564 Knudsen-layer function (data) 85 86 Knudsen-layer part see "Knudsen-layer correction" Knudsen-layer variables 79 103 115 130 Knudsen-layer-type solution 363 Law of large number 584 586 Law of large number, extended 587 Linear problem (time-dependent problem) 150 155 164 Linear problem (time-independent problem) 74 Linearized collision integral see "Collision integral" Liouville equation 481 Local Maxwell distribution 7 Local Maxwell distribution, satisfying the Boltzmann equation see "Local Maxwell distribution" Local Maxwellian see "Local Maxwell distribution" Loss term of the collision integral 4 505 Lubrication problem in a rarefied gas 196 Mach number 95 Macroscopic variable, relation between a macroscopic variable and the velocity distribution function 2 Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (linearized form) 23 Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (nondimensional variables) 16 Macroscopic variable, relation between a macroscopic variable and the velocity distribution function (perturbed variables) 20 Marginal velocity distribution function 223 303 544 Mass, conservation equation of 6 Mass, flow from a cylindrical condensed phase 307 310 316 319 Mass, flow from a spherical condensed phase 325 326 330 Mass, transfer to a boundary (relation to the velocity distribution function) 2 Mass, transfer to a closed body 94 109 Maxwell distribution 6 546 Maxwell distribution, absolute 551 Maxwell distribution, local 7 Maxwell molecule 506 Maxwell molecule, pseudo 507 Maxwell-type condition 8 Maxwell-type condition in perturbed variables 22 Maxwell-type condition, linearized 24 Maxwell-type condition, nondimensional 17 Maxwellian see "Maxwell distribution" Maxwellian, linearized expression for the perturbed local Maxwellian 24 Maxwellian, local see "Local Maxwell distribution" Maxwellian, nondimensional local 16 Mean collision frequency 7 Mean collision frequency for a Maxwellian 7 552 Mean free path 7 Mean free path (numerical data) 619 Mean free path (numerical data) for a Maxwellian 7 551 Mean free path (numerical data) for the BKW equation 13 Mean free time 7 Measure zero 4 Micro flow 196 Mixed-type condition (on an interface) 9 Mixed-type condition (on an interface) in perturbed variables 22 Mixed-type condition (on an interface), linearized 25 Mixed-type condition (on an interface), nondimensional 18 Model equation 12 molar mass 618 Molecular chaos 485 Moment method 601 Moment method (Grad thirteen-moment method) 604 Moment method (Mott — Smith analysis of a plane shock wave) 603 Momentum, conservation equation of 6 Momentum, transfer to a boundary (relation to the velocity distribution function) 2 Navier — Stokes set 6 110 Navier — Stokes set of equations for a compressible fluid 108 Navier — Stokes set of equations for an incompressible fluid 107 108 144 159 Navier — Stokes system, discrepancy (or incompleteness or inappropriateness) of the Navier — Stokes system in describing the behavior of a gas in the continuum limit 122 402 see "Ghost "Non-Navier "Non-Navier Navier — Stokes-type set 99 Negative temperature gradient phenomenon 339 Negative thermophoresis see "Thermophoresis" Non-Navier — Stokes effect in the continuum limit 120 144 162 416 Non-Navier — Stokes stress 121 459 Nondimensional expression 13 Nondimensional expression in perturbed variables 19 Nondimensional variables, definition of nondimensional variables I 13 Nondimensional variables, definition of nondimensional variables II (perturbed variables) 19 Nonlinear problem (time-dependent problem) 153 160 164 165 Nonlinear problem (time-independent problem) 112 126 137 Nonlinear-thermal-stress flow 121 242 Nonslip condition 86 Normal temperature 325 One-way flow without average temperature and pressure gradients (pipe with ditches) 261 One-way flow without average temperature and pressure gradients (pipe with shelves) 267 Overall solution 73 Overall solution (linear problem) 79 Overall solution (nonlinear problem) 113 131 138 Overall solution (weakly nonlinear problem) 102 Parallel temperature 325 Parity of the collision integral 517 Parity of the linearized collision integral 514 Peculiar velocity 548 Plane Couette flow see "Couette flow" Poiseuille flow 178 Poiseuille flow for a square cross section (data) 269 Poiseuille flow for various cross sections (data) 183 Poiseuille flow in a quasi-unidirectional flow 195 Poiseuille flow, software for 183 607 Prandtl boundary layer see "Viscous boundary layer" Prandtl number 96 Pressure 2 Pressure stress 79 Pressure, nondimensional 16 Pressure, nondimensional linearized perturbed 23 Pressure, nondimensional perturbed 20 Pressure, work done by see "Work" Probability density function, N-particle 481 Probability density function, truncated 482 Pseudo inverse-power molecule 507 Pseudo inverse-power potential, collision integral for the 507 Pseudo Maxwell molecule 507 Quasi-unidirectional flow 189 Quasi-unidirectional flow, Couette flow in a 196 Quasi-unidirectional flow, hear-transfer problem in a 196 Quasi-unidirectional flow, Poiseuille flow in a 195 Quasi-unidirectional flow, thermal transpiration in a 195 Radiometer 234 Rankine — Hugoniot relation 220 Rayleigh number 382 Reynolds number 95 S expansion 97 S layer 93 S solution 97 Saturated gas pressure 10 Saturated gas pressure (numerical data) 619 SB solution 113 Scattering kernel 8 10 Scattering kernel, nondimensional (on a simple boundary) 17 Scattering kernel, nondimensional (on an interface) 18 Second law of thermodynamics, the negative temperature gradient phenomenon and the 339 Self-adjoint property of the linearized collision operator 21 498 Shock condition 220 Shock layer 221 283 Shock wave 166 219 221 Shock wave, formation and propagation of a 222 Shock wave, weak 369 Similarity solution 540 Simple boundary 8 Slightly rarefied gas 73 Slip boundary condition (time-dependent problem) 163 Slip boundary condition (time-independent problem), linear problem 83 89 Slip boundary condition (time-independent problem), nonlinear problem 117 132 140 Slip boundary condition (time-independent problem), weakly nonlinear problem 102 104 Slip coefficient 85 89 105 106 118 135 564 Slip coefficient (data) 85 90 106 119 135 Slip condition 83 see Slit, flow through a 70 183 Slowly varying approximation 186 Slowly varying function 487 Slowly varying solution 357 365 Sonic speed 96 Sound wave 152 153 Sound wave, speed of 96 Sound wave, speed of, (numerical data) 619 Specular-reflection condition 8 Specular-reflection condition, linearized 24 Specular-reflection condition, nondimensional 17 Speed of sound 96 Speed of sound (numerical data) 619 Spherical symmetry of the velocity distribution function 324 Spherically symmetric state 324 Spherically symmetric tensor field 509 Standard state 618 Stokes set 76 144 157 Stress tensor 2 Stress tensor of the Grad — Hilbert solution 78 Stress tensor of the S solution 101 Stress tensor, Knudsen — layer part of 88 90 105 107 Stress tensor, nondimensional 16 Stress tensor, nondimensional linearized perturbed 23 Stress tensor, nondimensional perturbed 20 Strouhal number 15 Suction boundary layer 145 Summation convention in Cartesian tensor notation 1 Summational invariant of the collision 499 Supersonic accelerating flow 369 Symmetry relation 5 495 Symmetry relation (nondimensional form) 16 System in the overall region see "Fluid-dynamic-type equations" "Slip System in the overall region = equations and boundary conditions for the overall region (flow with a finite Mach number around a simple boundary) 132 Taylor — Couette problem 121 403 Taylor — Couette problem, ghost effect in the 416 Temperature 2 Temperature in the 306 Temperature in the r direction 306 Temperature in the z direction 306 Temperature, bifurcated temperature field under infinitesimal velocity 396 410 Temperature, flows induced by temperature fields see "Flow" Temperature, nondimensional 16 Temperature, nondimensional linearized perturbed 23 Temperature, nondimensional perturbed 20 Temperature, normal 325 Temperature, parallel 325 Tensor see "Stress tensor" Tensor, axially symmetric 509 Tensor, axially symmetric field of a symmetric tensor, general form of 511 Tensor, Cartesian tensor notation 1 Tensor, curvature 84 Tensor, spherically symmetric 509 Tensor, spherically symmetric field of a symmetric tensor, general form of 510 Test function 601 thermal conductivity 6 Thermal conductivity (numerical data) 619 Thermal conductivity, mistaken discussion of thermal conductivity in a free molecular flow 41 Thermal conductivity, positivity of 522 Thermal conductivity, relation between thermal conductivity and mean free path 95 Thermal creep flow 86 121 233 Thermal edge flow 246 Thermal force 249 see Thermal polarization 88 204 280 Thermal stress 79 102 118 120 121 157 Thermal stress slip flow 88 239 Thermal stress, nonlinear thermal stress flow 121 242 Thermal transpiration 178 261 Thermal transpiration for a square cross section (data) 269 Thermal transpiration for various cross sections (data) 183 Thermal transpiration in a quasi-unidirectional flow 195 Thermal transpiration, software for 183 607 Thermal velocity 548 Thermal-edge compressor 278 Thermal-stress slip flow 88 239 Thermophoresis 249 Thermophoresis, negative 261 Transport coefficient, nondimensional 78 100 117 521 Transport coefficient, nondimensional, (data) 78 102 117 522 Truncated probability density function 482 Two-surface problem of evaporation and condensation 338 Two-surface problem of evaporation and condensation under a generalized kinetic boundary condition 352 Unidirectional flow see "Flow (flows through a channel or pipe)" Uniqueness of solution of the boundary-value problem of the linearized Boltzmann equation (a bounded domain) 566 Uniqueness of solution of the boundary-value problem of the linearized Boltzmann equation (a half-space) see "Grad — Bardos theorem" Uniqueness of solution of the half-space problem of the nonlinear Boltzmann equation (simple boundary) see "Half-space problem" Vacuum pump without a moving part (Knudsen compressor) 272 Vacuum pump without a moving part (thermal-edge compressor) 277 Velocity distribution function 2 Velocity distribution function, discontinuity of the velocity distribution function around a convex body 311 319 331 Velocity distribution function, marginal see "Marginal velocity distribution function" viscosity 6 Viscosity (numerical data) 619 Viscosity, mistaken discussion of viscosity in a free molecular flow 41 Viscosity, positivity of 522 Viscosity, relation between viscosity and mean free path 95 Viscous boundary layer 126 128 165 461 464 Viscous boundary layer, equations and boundary conditions for the 133 Viscous boundary layer, natural variables in the 128 Viscous boundary-layer set 144 Viscous boundary-layer solution 129 Viscous region 166 Von Karman relation 96 Wave, formation and propagation of a shock wave 222 Wave, speed of sound see "Speed of sound" Wave, weak shock 369 Waves formed by a heated or cooled wall see "Section 4.8" Waves in condensing flows onto a plane condensed phase see "Section 6.1.3" Waves in evaporating flows from a plane condensed phase see "Section 6.1.2" Weak form of the Boltzmann equation 579 Weak shock wave 369 Weak solution of the Euler set 166 Weakly nonlinear problem (time-dependent problem) 152 158 164 Weakly nonlinear problem (time-independent problem) 96 Well-posed problem of a partial differential equation 111 Work, done by pressure in the Grad — Hilbert solution 157 Work, done by pressure in the S solution 107 160
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