Ferziger J.H., Kaper H.G. — Mathematical theory of transport processes in gases :: Электронная библиотека попечительского совета мехмата МГУ

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Ferziger J.H., Kaper H.G. — Mathematical theory of transport processes in gases

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Название: Mathematical theory of transport processes in gases

Авторы: Ferziger J.H., Kaper H.G.

Аннотация:

The present book offers a more or less complete theory for deriving transport properties of gases from first principles - that is, in terms of the intermolecular potentials which determine the forces between any two molecules in the gas. Both neutral gases and ionized gases are discussed, and, for the neutral gases, the theory of monatomic as well as polyatomic gases is covered. The principal results of these investigations are based on Boltzmann's equation for a dilute gas; however, extensions into the areas of dense gases and rarefied gases are also given.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 568

Добавлена в каталог: 07.04.2019

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Предметный указатель

Gakhov, F. D.      477 553
Gandhi, J. M.      296 553
Garcia-Colin, L. S.      6 387 390 395 396 398 553
Gas constant      16
Gas-surface interaction      77—79 469—472
Generalized Boltzmann equation, for dense gas      380
Geometrical collision variables      see "Collision variables" "Deflection
Gibson, R. O.      372 556
Goldman, R.      51 421 553
Goldstein, H.      33 85 553
Gorter, C. J.      351 553
Grad, H.      6 87 102 114 122 132 151 154 159 161 162 553
Gradient vector      497
Gray, P.      290 552
Green, H. S.      36 550
Green, M. S.      6 23 387 390 395 396 398 403 553
Grew, K. E.      287 553
Gross, E. P.      467 550 553
Guernsey, R.      424 554
Guiraud, J. P.      79 97 154 552 554
Gyrofrequency      429 453 455
Gyromagnetic radius      429 430
gyromagnetic ratio      351
H-function      71 79
H-function, behavior at local Maxwellian state      86
H-function, connection with entropy      75
H-function, information-theoretical interpretation of      75
H-theorem, for Boltzmann's equation      72 83
H-theorem, for generalized Boltzmann equation, absence of      386 392
H-theorem, for Waldmann — Snider equation      334
H-theorem, for Wang Chang — Uhlenbeck equation      315
H-theorem, interpretation of      70—71 75
Haines, L. K.      421 554
Hall current      444
Hamiltonian function      33 335 354
Hamiltonian operator      33 377
Hard molecule      239
Harris, E. G.      424 557
Heat conduction      see "Thermal conductivity"
Heat conduction, Eucken's theory of, for polyatomic gas      307—312
Heat conduction, phenomenological theory of      198
Heat flow vector, Chapman — Enskog approximation, for binary gas mixture      190
Heat flow vector, Chapman — Enskog approximation, for dense gas, Enskog's theory      365 368—369
Heat flow vector, Chapman — Enskog approximation, for dense gas, general theory      391 399
Heat flow vector, Chapman — Enskog approximation, for gas mixture      169 177—179
Heat flow vector, Chapman — Enskog approximation, for ionized gas      444—445
Heat flow vector, Chapman — Enskog approximation, for Lorentz gas      195
Heat flow vector, Chapman — Enskog approximation, for polyatomic gas, quantum mechanical      348 352
Heat flow vector, Chapman — Enskog approximation, for polyatomic gas, quasi-classical      319
Heat flow vector, Chapman — Enskog approximation, for simple gas      121 123 130—131 149—150 152—153
Heat flow vector, definition of, for dense gas      386
Heat flow vector, definition of, for gas mixture      18
Heat flow vector, definition of, for polyatomic gas, quantum mechanical      335
Heat flow vector, definition of, for polyatomic gas, quasi-classical      315
Heat flow vector, definition of, for simple gas      16
Heat, specific      see "Specific heat"
Hecke, E.      116 554
Hess, S.      354 554
Hilbert class      see "Normal solutions of Boltzmann's equation"
Hilbert paradox      115 172
Hilbert space      100
Hilbert's method, for solving Boltzmann's equation      109—115
Hilbert's method, for solving Boltzmann's equation, relation with Chapman — Enskog method      121—122
Hilbert's uniqueness theorem      109—115
Hilbert, D.      4 5 88 93 108 109 467 552 554
Hille, E.      102 106 554
Hirschfelder, J. O.      176 207 233 238 251 253 256—259 262 304 311 371 372 554
Holway, L. H.      488 554
Hydrodynamic velocity, definition of, for dense gas      381
Hydrodynamic velocity, definition of, for gas mixture      17
Hydrodynamic velocity, definition of, for polyatomic gas, quantum mechanical      335
Hydrodynamic velocity, definition of, for simple gas      12
Hydrodynamics      see "Fluid dynamics"
Hydrostatic pressure      15 16 18 365 391
Hydrostatic pressure, influence of gradient on diffusion      see "Diffusion driving force"
Ideal gas law      see "Perfect gas law"
Ideal hydrodynamic equations      see "Euler equations"
Ikenberry, E.      132 554
Impact parameter      28
Impact parameter, reduced      252
Index of repulsion      239
Inelastic collisions      see "Collisions"
Initial layer      154 158 see
Initial value problem      see "Existence theory"
Intermolecular force, nature of, between charged molecules      236—237
Intermolecular force, nature of, between monatomic molecules      232—234
Intermolecular force, nature of, between polyatomic molecules      234—236
Intermolecular potential, and temperature dependence of transport properties      255
Internal energy, definition of, for dense gas      381
Internal energy, definition of, for gas mixture      19
Internal energy, definition of, for polyatomic gas, quantum mechanical      335
Internal energy, definition of, for polyatomic gas, quasi-classical      315
Internal energy, definition of, for simple gas      12
Internal energy, equation of      see "Conservation equations"
Invariants, summational or collisional      see "Collisional invariants"
Inverse collisions      see "Collisions"
Inverse thermo-electric effect      see "Electro-thermal effect"
Inversion temperature      226
Ionized gas, non-equilibrium      456
Irreversibility      50 58 69—70
Isotopes, self-diffusion in a mixture of      190
Isotropic tensor      344 495 see
Jackson, E. A.      467 553
James, E. M.      159 552
Jancel, R.      132 427 554
Jaynes, E. T.      75 554
Jeans, J. H.      312 554
Jeffreys, H.      491 554
Jensen's inequality      82
Jones, R. C.      226 553
Kagan, Yu.      334 554
Kahan, Th.      132 427 554
Kahn, B.      23 554
Katz, A.      75 554
Kawasaki, K.      421 554
Keller, J. M.      278 279 285 554
Kestin, J.      268 269 555
Kihara approximation      139—143 271—274 see "Thermal "Thermal "Viscosity"
Kihara model potential      242
Kihara, T.      242 555
Kim, S. K.      375 555
Kinetic energy, molecular      12
Kinetic theory, historical summary      3—8
Kinetic theory, outline of      1—3
Kinetic theory, relation with fluid dynamics      153—162
Kirkwood, J. G.      36 555
Knudsen number      464
Kogan, M. N.      465 555
Kohler, M.      134 555
Kramer's problem      see "Slip flow problem"
Kronecker symbol      see "Unit tensor"
Krook, M.      467 550
Ku ${\check{s}\check{c}}$ er, I.      161 467 555
Kumar, K.      132 555
Ladyzhenskaia, O. A.      150 555
Lampis, H.      472 551
Landau, L. D.      231 260 261 263 555
Landoldt-B ${\ddot{o}}$ rnstein      302 555
Langevin, P.      4
Laranjeira, M. F.      287 555
Lenard, A.      424 555
Lennard — Jones model potential      240 252 275—279 288
Lennard — Jones model potential, application to polyatomic gases      303
Lennard — Jones model potential, parameters for noble gases      276 284—285
Lennard — Jones model potential, transport integral ratios, numerical tables      528—532
Lennard — Jones model potential, transport integrals, numerical tables      522—525
Lennard-Jones, J. E.      240 555
Liepmann, H. W.      486 555
Lifshitz, E. M.      231 260 261 263 555
Linearized Boltzmann equation      87 465

Linearized Boltzmann equation, existence and uniqueness theory for      97—106
Linearized collision operator      87—88 161 409
Linearized collision operator, BGK-model      467 484
Linearized collision operator, model construction      467—469
Linearized collision operator, properties of      88—96 465—466
Linearized ternary collision operator      410
Liouville equation      35 39 56
Liouville's law for elastic collisions      27
Loaded sphere      312
London, F.      233 555
Longmire, C. L.      430 555
Lorentz force      429
Lorentz gas      191
Lorentz gas, convergence of Chapman — Cowling and Kihara approximations      271—274
Lorentz gas, perturbation methods based on      196
Lorentz gas, transport properties      191—196
Lorentz, H. A.      4 191 555
Loyalka, S. K.      468 482 555
Lunn, A. C.      5 555
Macroscopic observables, vector of      113 116
Magnetic field, effect of, on transport properties, for ionized gas      444 445
Magnetic field, effect of, on transport properties, for polyatomic gas (Senftleben — Beenakker effect)      351—355
Magnetodynamics or magnetohydrodynamics or MHD      425
Magnetogasdynamic (or magnetohydrodynamic or MHD-) equations      433
Marshall, W.      430 440 449 555
Mason, E. A.      175 196 199 221 244 259 262 271 273 286 287 294—296 298 303 306 325—328 511 519 523 526 528 555—559
Mass density, definition of, for dense gas      381
Mass density, definition of, for gas mixture      17
Mass density, definition of, for polyatomic gas, quantum mechanical      335
Mass density, definition of, for simple gas      11
Mass, molecular      10
Mass, molecular, reduced      205
Massey, H. S. W.      231 556
Material derivative      see "Substantial derivative"
Maximum principle      134 181
Maxwell molecules, ${\Omega}$ -integrals      251
Maxwell molecules, definition of      239
Maxwell molecules, eigenfunctions of collision operator for      239 252 466 467
Maxwell, J. C.      3 4 64 74 556
Maxwellian velocity distribution function      see "Equilibrium solution"
Maxwellian velocity distribution function, definition of      74
Maxwellian velocity distribution function, linearization with respect to      87 98
Maxwellian velocity distribution function, properties of      76—77
Mazur, P.      176 340 348 351 450 552
McCourt, F. R. W.      7 334 337 340 342 552 556
McCoy, B. J.      370 556
McCune, J. E.      116 556
McGee, I. J.      243 550
Mean collision time      51
Mean free path      19 20 154 158 197
Mean free time      19 108 154 158
Michels, A,      372 556
Mixing rules      244—245
Mixing rules, verification of, for Lennard — Jones (6—12) potential parameters      282—284
Model potentials      237 244
Modeling, of collision operator      467—469
Modified Buckingham (6-exp) model potential      241 252 275
Modified Buckingham (6-exp) model potential, transport integral ratios, numerical tables      519—521
Modified Buckingham (6-exp) model potential, transport integrals, numerical tables      511—518
Molecular chaos      58 379 see Stosszahlansatz"
Molecular fraction      219
Molecular fraction, dependence of transport properties on      280 290
Molecular interaction operator      35 377
Moment of inertia      329
Momentum, molecular      11
Momentum, molecular, equation of      see "Conservation equations" "Angular
Monchick, L.      175 196 199 244 286 303 305 306 325—328 523 526 528 556
Monte Carlo method, for solving Boltzmann's equation      488—490
Montgomery, D.      424 556
Morgenstern, D.      5 153 556
Morse model potential      242 279 283
Morse model potential, transport integrals and transport integral ratios, numerical tables      534—535
Morse, T. F.      116 556
Mott, N. F.      231 556
Muckenfuss, C      229 312 552 556
Mundy, J. N.      287 553
Munn — Smith model potential      277 287—288
Munn, R. J.      259 262 277 286—288 534 556 557
Murphy, T. J.      402
Muskhelishvili, N. I.      478 556
Narasimha, R.      486 555
Navier — Stokes equations      131
Navier, C. L. M. H.      150 556
Neutron transport theory      468
Newton's law, of viscosity      68
Noble gas mixtures, transport properties of      279—298
Noble gases, transport properties of      274—279
Normal pressure      15
Normal solutions of Boltzmann's equation, class of      114
Number density, definition of, for dense gas      381
Number density, definition of, for gas mixture      17
Number density, definition of, for polyatomic gas, quantum mechanical      333
Number density, definition of, for simple gas      11
O'Neal, C      274 557
Ohm's law      443
Ohmic heating      433
Onsager relations      176 349
Onsager, L.      226 553
Oppenheim, I.      421 554
Orbiting collisions      see "Collisions"
Order-of-magnitude estimates, of successive terms in Chapman — Enskog approximation      151—153
Pair correlation function      389
Pair distribution function      381
Partial bracket integrals      see "Bracket integrals"
Partition function, for internal states of polyatomic molecules      316 317 336
Pauling, L.      233 557
Peculiar velocity, definition of      12 18
Pekeris, C. L.      93 557
Perfect (or ideal) gas law      77 112 123
Phase mixing operator      38 377
Phase shift      261
Phase space ( ${\mu}$ -space)      33
Phenomenological theory of transport properties      196—200
Phillips, R. S.      102 106 554
Pidduck, F. B.      312 557
Planck's constant      259 260 331
Plasma frequency      425
Plasma physics      423
Point center of repulsion model potential      239 272—273
Point center of repulsion model potential, ${\Omega}$ -integrals for      250—252
Poisson bracket      35
Polarizability, numerical table      302
Polarization      232
Polyatomic gas, classical theory      328—330
Polyatomic gas, Eucken's theory      307—312
Polyatomic gas, quantum mechanical theory      330—350
Polyatomic gas, quasi-classical theory      313—328
Position vector      10
Potential energy, effective      253
Povzner, A. Ja.      153 557
Pressure      see "Hydrostatic pressure"
Pressure tensor, Chapman — Enskog approximation, for dense gas, Enskog's theory      365 368—369
Pressure tensor, Chapman — Enskog approximation, for dense gas, general theory      390 400
Pressure tensor, Chapman — Enskog approximation, for gas mixture      169
Pressure tensor, Chapman — Enskog approximation, for ionized gas      449—450
Pressure tensor, Chapman — Enskog approximation, for polyatomic gas, quantum mechanical      345 352
Pressure tensor, Chapman — Enskog approximation, for polyatomic gas, quasi-classical      319
Pressure tensor, Chapman — Enskog approximation, for simple gas      121 123 129—130 147—149 152—153
Pressure tensor, definition of, for dense gas      383
Pressure tensor, definition of, for gas mixture      18
Pressure tensor, definition of, for polyatomic gas, quantum mechanical      335
Pressure tensor, definition of, for polyatomic gas, quasi-classical      315
Pressure tensor, definition of, for simple gas      15
Pseudovector      497
Quantum theory of scattering      260—263
Range, of intermolecular force      50 377
Rankine — Hugoniot relations      485
Rarefied gas      152 464—490
Rate-of-shear tensor      129 345
Rate-of-strain tensor      129

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