Kinetic Theory and Fluid Dynamics

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Springer Science & Business Media, Aug 12, 2002 - Science - 353 pages
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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.
 

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Contents

II
1
III
5
IV
7
V
8
VI
9
VII
10
VIII
11
IX
13
LVI
152
LVII
153
LVIII
157
LIX
160
LX
167
LXI
168
LXII
173
LXIII
185

X
14
XI
15
XII
19
XIII
24
XIV
26
XV
27
XVI
28
XVII
32
XVIII
35
XIX
44
XXI
49
XXII
52
XXIII
53
XXIV
57
XXV
59
XXVI
60
XXVIII
63
XXIX
64
XXX
65
XXXI
70
XXXII
72
XXXIII
81
XXXIV
85
XXXV
86
XXXVII
92
XXXVIII
97
XXXIX
101
XL
102
XLI
103
XLII
104
XLIII
106
XLV
109
XLVI
113
XLVII
116
XLVIII
119
XLIX
123
L
125
LI
135
LII
137
LIII
146
LIV
148
LV
151
LXIV
192
LXV
194
LXVI
196
LXVII
203
LXVIII
204
LXIX
206
LXX
209
LXXI
213
LXXII
216
LXXIII
220
LXXIV
225
LXXV
226
LXXVI
231
LXXVII
235
LXXVIII
237
LXXIX
242
LXXX
244
LXXXI
250
LXXXII
253
LXXXIV
257
LXXXV
269
LXXXVI
271
LXXXVII
280
LXXXVIII
285
LXXXIX
289
XC
292
XCI
295
XCII
297
XCIII
298
XCIV
301
XCV
302
XCVI
304
XCVII
306
XCVIII
311
XCIX
312
CI
313
CII
315
CIII
316
CIV
324
CV
327
CVI
345
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