Михатулин Д.С., Чирков А.Ю. Конспект лекций по тепломассообмену
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., ., 2009
– 51 –
, :
)(
2
Re)2(Re
*Re*
0
b
C
Hf
dX
d
f
LL
, (5.43)
)(StRe
ReRe
0 TSL
TT
b
dX
Td
T
dX
d
, (5.44)
)(StRe
ReRe
0 DDDL
DD
b
dX
Cd
C
dX
d
, (5.45)
/***Re* v ;
/Re
T
T
v ;
/Re
D
D
v ;
CCC
w
;
L
x
X
/
; L – -
;
/Re L
L
v ; C
f0
, St
0
, St
D0
– ,
«»
Re
**
;
0
/
ff
CC
– ;
vC
v
b
f
ww
0
2
– , 2/
0f
C ;
0
St/St
S
– ;
0
St
v
v
b
ww
T
– -
;
0
St/St
D
D
D
–
;
0
St
D
ww
D
v
v
b
– .
-
, .
(5.43)–(5.45) , -
, , . C
f
, St, St
D
.
C
f
, St, St
D
.
,
. -
-
.
,
.
(dp/dx=0) -
, .
., ., 2009
– 52 –
5.3.
0
/
x
p
. : y=0 0
x
v ,
0
y
v ; y=
vv
x
, 0
y
v .
(x, y), -
: y
x
/v , x
y
/v . -
x y )/( xy
v (
),
x
v
y
v –
xf
v/)( . -
(5.12), , -
02
fff . (5.46)
:
f
yy
x
vv
, (5.47)
)(
2
1
ff
xx
y
v
v . (5.48)
0
'
f
f
=0;
1
'
f
=. (5.49)
(5.46) .
. f, f
f
,
, .
12
-
x
f
xy
x
w
x
w
v
v
v
v
v
332,0)0('')( . (5.50)
12
.: / . . . . .:
. . , 1997.
., ., 2009
– 53 –
, b l
vv lbdxxb
l
w
664,0)(
0
. (5.51)
,
v/5 x . (5.52)
v/73,1* x . (5.53)
v/664,0** x . (5.54)
(5.13)
0
2
Pr
2
2
d
d
f
d
d
, (5.55)
)/()(
w
w
TTTT
.
(5.55) :
=0
0
; =
1
. (5.56)
(5.55)
0
Pr
0
Pr
)(/)( dfdf
. (5.57)
Pr = 1 (5.57)
v
v
x
w
w
f
f
TT
TT
)(
)(
)(
)(
, (5.58)
-
.
()
-
., ., 2009
– 54 –
0
Pr
Pr
00
)(
)0(
)(
df
f
xxy
T
TT
y
w
x
vv
. (5.59)
3
0
Pr332,0)/(
,
x
x
v
3
Pr332,0 . (5.60)
L
dx
L
L
x
v
3
0
Pr664,0
1
. (5.61)
xx
RePr332,0Nu
3
, (5.62)
L
RePr664,0Nu
3
, (5.63)
/Re x
x
v ,
/Re L
L
v .
3/2
0
PrRe
332,0
PrRe
Nu
St
Re
Re
x
x
x
x
T
d
d
. (5.64)
,
x
T
dd Re/Re
, -
3/4
0
PrRe
22,0
St
T
. (5.65)
-
, . «» , –
.
-
., ., 2009
– 55 –
. , -
, *Re*/22,02/
0
f
C .
,
,
.
5.4.
, -
().
0)0(
wy
y vv .
,
x
v x.
0/
x
x
v ,
wy
const vv
.
2
2
y
y
xx
w
vv
v , (5.66)
:
y = 0 0
x
v ; y =
vv
x
. (5.67)
(5.66) (5.67 )
y
w
x
v
vv exp1 . (5.68)
, , -
w
v
* , (5.69)
w
v2
**
, (5.70)
., ., 2009
– 56 –
vv
v
w
w
x
w
y
, (5.71)
w
f
C
v2
. (5.72)
-
, ,
2
4
w
v
x
v
v
. (5.73)
.
0
/
x
T
2
2
Pr
y
y
w
v ; (5.74)
y
TT
TT
w
w
w
vPr
1 . (5.75)
,
w
w
y
T
q
)(
St
wp
w
TTc
q
v
, -
:
v
v
w
St . (5.76)
-
, -
.
., ., 2009
– 57 –
1exp
1exp
w
w
x
y
v
v
v
v
, (5.77)
1exp
1exp
T
w
w
w
w
a
y
a
TT
TT
v
v
, (5.78)
:
1exp
1
2
2
C
w
www
f
v
v
v
v
, (5.79)
1exp
1
1exp
1
St
T
w
ww
T
w
wp
wwpw
a
a
)T(Tc
)T(T
v
v
v
v
v
v
. (5.80)
1exp
1
1
0
*
dy
w
w
x
v
vv
v
, (5.81)
1exp
1
2
1
0
**
dy
w
w
xx
v
vv
v
v
v
. (5.82)
5.5.
, -
(M > 0,25), (5.55)
2
/ y
x
v .
., ., 2009
– 58 –
2
2
2
2
)(
)(
Pr
2
Pr
f
TTcd
d
f
d
d
wp
v
. (5.83)
(5.83) ,
, -
. T
w
-
T
.
TT
w
-
(. . 5.3).
y
x
q
>0
w
q =
0
w
q <
0
w
T
Tw
w
T
T
T
T
*
*
*
8
8
. 5.3.-
(M < 1)
-
2
2
M
2
1
1
2
k
rT
c
v
rTT
p
w
, (5.84)
TT
TT
rr
ww
*
*
(Pr) (5.85)
– , M
–
., ., 2009
– 59 –
, k – ,
*
T – -
.
Pr
r
(
6
Pr
6
,
0
), –
3
Pr
r
. -
)
5
9
/(
4
Pr
k
k
.
-
.
13
5,0
ReNu
xx
B
x
, (5.86)
2/1
Pr564,0B
0
Pr
,
3/1
Pr33,0B
6
,
0
Pr
.
11040
43080
PrRe029,0Nu
,
*
w
,
*
w
w
,
w
,
w,x
w
w,x
T
T
T
T
x
. (5.87)
11,0
*
w
w
/TT , 5,45,2
M
106
M .
13
.: / . . . . . .:
. . , 2004.
., ., 2009
– 60 –
6.
-
. x
, r – , -
. , -
dp/dx<0, .
,
dx
dp
dr
d
r
dr
d
r
x
11
v
. (6.1)
, . 0
x
v r=d/2, d – -
. (6.1)
2
0
2
0
1)(
r
r
r
x
vv , (6.2)
dx
dp
4
1
0
v – , r
0
=d/2. -
0
5,0 vv
.
Re/Re
dv .
,
4
10...2300Re .
.
-
(. .
6.1).
, x,
. , -
.
-
. -
, (6.2) . -
.