# Interdisciplinary Applied Mathematics

Скачать в pdf «Interdisciplinary Applied Mathematics»

For a hard sphere molecular gas, the continuum equations governing the macroscopic variables at their leading-order term are given as follows (Sone, 2002):

dP0    dP1

—- = 0, —-

dxi ’ dxi

0,

(15.44a)

d ujQUji dxj

(15.44b)

UjQUjl

дщ i

dxj

1 дР2    1 d

2 dxi    2 71 dxj

1    1 d

‘-q’

2 » Pq dxj

1    1 d

‘2

1/2

q

дт0дт0 dxi dx

tq

j

д2т0

dxidxj

duii    duji

—1——

dxj    dxi

2 ^

з ~d^7 ij)

Это

k

1 d2 Tq

2

дх: I 6ij

Sin

3 dx

дт0 _ 1 d f1/2 <9 T0

“ 272 ax

q

dxn

(15.44c)

(15.44d)

where

CTq = 1 + Wq, Tq = 1 + Tq, Pq = 1 + Pq = LTq Tq,

71 = 1.270042427, y2 = 1.922284066, = 1.947906335,77 = 0.188106.

In the present expansion, ui1 is the leading term of the flow velocity, since the case with uiQ = 0 is considered.

The boundary conditions are

TQ — тwQ,    ui1

1/2

Tq’ d TQ

Pq ® XJ

( Sij    ni nj ),

(15.45)

for the temperature and velocity, respectively.

Remark: The third and fourth terms on the right-hand side of equation (15.44c) are    due    to thermal    stress.    The    thermal    stress    contribution    is    not

Скачать в pdf «Interdisciplinary Applied Mathematics»