Михатулин Д.С., Чирков А.Ю. Конспект лекций по тепломассообмену
Подождите немного. Документ загружается.
., ., 2009
– 31 –
k – ; a, b, c, d, e, f –
, -
.
,
(3.21)
fedcba
k )TL()LMT()MTL()ML()LT(L)MT(
12213113113
.
(3.22)
,
f
e
d
c
b
a
2
3
0
, (3.23)
f
e
d
b
2
3
3
, (3.24)
e
d
c
1
, (3.25)
f
e
1
. (3.26)
(3.23)–(3.26) -
, ,
.
c f, . -
,
f
e
1
,
c
f
d
,
c
b
1
c
a
.
(3.21)
f
p
fcfccc
cvDkD
1
. (3.27)
-
, (3.27)
f
p
c
c
D
k
D
v
(3.28)
fc
k
Pr
Re
Nu
. (3.29)
,
., ., 2009
– 32 –
-
: k, c f. , -
(3.21) .
,
.
11
PrGrNu
1
fc
k . (3.30)
-
D, , , , c
p
fw
TTT
.
, -
, . -
, -
, .
T
f
, T
w
2)/T(TT
wfm
. -
«f», «w» «m», .
, .
, . -
, .
., ., 2009
– 33 –
4.
4.1.
-
, -
, .
,
(2.33). ,
.
0
TT
, T
0
–
(). -
.
pgxpp
0
0
, (4.1)
p
0
– ; g – ; x
;
p – ,
p gxp
0
0
.
-
. -
, ,
gg
00000
ppppp
, (4.2)
g – , .
(4.2) -
,
vgvv
v
2
0
)(
p
, (4.3)
2
av , (4.4)
0
v
. (4.5)
,
., ., 2009
– 34 –
, (4.3) (4.4) -
. -
: – h, – h
2
/, – a/h, – T.
vevv
v
211
RaPr)(Pr
z
p , (4.6)
2
Pr v , (4.7)
e
z
– x, Pr=/a – ,
a
Tgl
3
0
Ra –
. (4.5)
.
, (4.6) (4.7) , -
, –
Ra ( Gr) Pr.
4.2. -
.
, T
w
-
.
T
0
< T
w
(. . 4.1). x,
y ( ). z,
x y, .
( 0
v ). -
.
, x.
. , .
. -
.
,
. -
2
)1( y
w
, (4.8)
0
TT
w
w
.
., ., 2009
– 35 –
y
x
=
9
0
dx
x
w
T
=const
TT
v
<
=0
w
8
8
. 4.1.
T
w
T
0
v
x
v
x
T
T
y
0
0,38
. 4.2.
., ., 2009
– 36 –
(2.31)
(
0
/
T
) -
constxTT
x
/)( vv .
(4.8),
2
0
0
y
ww
w
yTT
q
. (4.9)
. 4.2 -
.
,
2
2
1
y
g
x
p
yx
xx
y
x
x
vv
v
v
v (4.10)
:
0
x
v ,
w
(T=T
w
) y = 0; (4.11)
0
x
v ,
0
(T=T
0
), 0
y y = . (4.12)
, -
(2.33).
gxp
0
/
, , .
0
yx
y
x
v
v
. (4.13)
, 0
y
v , , , -
(4.13) 0/
x
x
v .
(4.10)
gg
x
p
g
y
x
00
2
2
)(
v
. (4.14)
, (4.8), -
., ., 2009
– 37 –
2
0
2
2
1
y
g
y
wx
v
. (4.15)
(4.15) (4.11)
(4.12)
4
2
32
0
12
1
3
1
2
1
4
yyyy
g
w
x
v , (4.16)
y
y
0
. x.
, (4.16)
y0,38. (-
)
40
1
2
0
0
w
xx
g
dyvv
, (4.17)
3
1
0
w
x
dy
. (4.18)
(x)
, , ,
.
z , -
, z. -
. -
, dx
,
w
w
q
1
dx
, .
dxQ
w
. (4.19)
,
dGcQ
p
, (4.20)
dG – dx, -
., ., 2009
– 38 –
. dG
d:
d
gg
dddG
ww
x
2
2
0
2
0
00
40
3
40
)1( v . (4.21)
(4.19) (4.20) (4.21) (4.9),
d
g
cdx
w
pw
2
22
0
40
2
. (4.22)
(4.22) , x=0 =0.
:
x
gc
wp
2
0
4
320
, (4.23)
25,0
2
0
23,4
x
gc
wp
, (4.24)
25,0
2
0
23,4
22
x
gc
wp
, (4.25)
25,0
32
0
473,0Nu
xgc
x
wp
x
, (4.26)
2
3
Gr
xg
w
x
, (4.27)
Nu
x
, Gr
x
– ( )
.
//Pr
0p
ca ,
., ., 2009
– 39 –
32
0
PrGrRa
xgc
wp
xx
. (4.28)
(4.26) (4.28) , (4.26)
,
25,025,0
Pr)Gr(473,0)Ra(473,0Nu
x
x
x
. (4.29)
l-
25,0
0
4/3
0
)Ra(63,0Nu
3
4
)/(
1
NuNu
1
Nu
ll
l
l
l
x
dxlx
l
dx
l
, (4.30)
Nu
l
Ra
l
x=l.
,
, -
g
sin
g
.
, x
, . ,
.
, Ra
l
<510
2
-
Nu=1, . -
. (4.30), , -
510
2
<Ra
l
<210
7
. Ra
l
>0,710
9
-
. -
31
GrPr)(135,0Nu . (4.31)
, , (4.31),
l,
312
)Pr/(135,0/Nu Tgl .
4.3.
,
2
1
w
w
TT
(. . 4.3), -
., ., 2009
– 40 –
. -
hTT
w
w
/)(
2
1
,
h – . -
.
-
, , -
, .
, -
,
(. . 4.3,). , ,
.
h
T
w
2
T
w
1
h
T
w
2
T
w
1
. 4.3.: – -
, –
.
.
9
. -
, –
, -
. ,
. , -
5,657Ra
, (4.32)
–
8,1707Ra
. (4.33)
, -
9
.: .: . . .:
, 1958.