1 –DAÃN NHIEÄT OÅN ÑÒNH
9 - 1
Maät ñoä doøng nhieät: q =
λδ
21 ww tt −
a/ Vaùch theùp: λ = 40 W/m.ñoä
→ q =
4005.0
90100 − = 8000 W/m2
b/ Vaùch beâ toâng: λ = 1.1 W/m.ñoä
→ q =
1.105.0
90100 − = 220 W/m2
c/ Gaïch diatomit: λ = 0.11 W/m.ñoä
→ q =
11.005.0
90100 − = 22 W/m2
9 - 2
1
Q = q × F = q × l ×h
2
=
λδ
21 ww tt −× l ×h
h = 4m
l = 5m
t = 40 Cw2
1w 110 C = to
o
δ = 0.25 mλ = 0.7 w/m.ñoä
=
7.025.0
40110 − 45×× = 3920 W
Giaûi gioáng trong saùch
9 – 3
Giaûi gioáng trong saùch
9 - 4
9 - 5
Cöôøng ñoä doøng nhieät truyeàn qua vaùch
q =
tb
t
λδΔ
)(21 ww
tb tt −δλ =
Trong ñoù: λtb = λo [1+ β ttb ]
= ⎥⎦
⎤⎢⎣
⎡ ++
21 21
0ww tt
βλ
(1) ( )21
21
210
wwww tt
ttq −⎥
⎦
⎤⎢⎣
⎡ ++=→ β
δλ
→ Beà daøy lôùp caùch nhieät:
( )21
21
210
wwww tt
ttq
−⎥⎦
⎤⎢⎣
⎡ ++= β
λδ (*)
a/ =λ 0.09 + 0.0000872 t W/m.ñoä 0.09(1 + 0.00097 t) W/m.ñoä
→ 2
0
/45000097.009.0
mwq ≤
==
βλ
→Ct
Ct
w
w
0
0
50
450
2
1
=
=
(*) ( )21
21
210
wwww tt
ttq
−⎥⎦
⎤⎢⎣
⎡ ++≥→ β
λδ
( )504502
5045000097.01450
09.0−⎥⎦
⎤⎢⎣⎡ +
+≥
mm100≥ b/ =λ 0.109 + 0.000146 t W/m.ñoä = 0.109(1 + 0.00134 t) W/m.ñoä
→ 00134.0109.0
==
βλo
(*)
→ ( )504502
5045000134.01450109.0
−⎥⎦⎤
⎢⎣⎡ +
+≥δ
mm130≥
3
Giaûi gioáng trong saùch 9 - 6
9 - 7
tW1 = 110 oC
4
tW3 = 25 oC q ≤ 110 W/ m2 λ1 = 0.7 W/m. ñoä
λ2 = 0.0465 W/m. ñoä δ1 = 250 mm δ2 = ? tW2 = ?
Giaûi Cöôøng ñoä doøng nhieät truyeàn qua vaùch
2
2
1
1
1
31
λδ
λδ
λδ
+
−=
Δ=
∑=
wwn
i i
i
ttt
q
δ21δ
1w t
tw3
⎥⎦
⎤⎢⎣
⎡−
−=→
1
122
31
λδ
λδq
tt ww
2/110 mwq ≤
→ ⎥⎦⎤
⎢⎣⎡ −
−≥⎟⎟
⎠
⎞⎜⎜⎝
⎛−
−≥
7.025.0
110251100465.0
1
13122 λ
δλδ
qtt ww
m019.02 ≥δ mm19≥
1
1
1
112
21
λδ
λδ
qtttt
q wwww −=→
−=
7.025.0110110 −= C07.70=
9 - 8
Ctmwq
Ct
mm
w
w
0
2
01
50/1100
800
200
3
1
≤
≤
=
=δ
δ21δ
1w t
tw3
mw /8.11 =λ .ñoä ( ) mwt /0024.01054.02 .ñoä λ = +
?2 =δ Giaûi
1
1
1
112
21
λδ
λδ qtt
ttq ww
ww −=→−
=
8.12.01100800
2−=wt
= C0678
5
⎥⎦
⎤⎢⎣
⎡ ++=
20024.01054.0 32
2
wwtb
ttλ
⎥⎦⎤
⎢⎣⎡ +
+=2
506780024.01054.0
= 0.1W/m.ñoä
( )32
2322
2
2ww
tb
tb
ww ttq
ttq −=→
−=
λδ
λδ
( ) mmm 57057.0506781100
1.02 ==−=δ
Ñeå mmCt
mwq
w
5750
/110020
2
3
≥⇒⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
≤
≤δ
9 - 9
t00023.028.01 +=λ W/m.ñoä
δ21δ
1w t
tw3
7.02 =λ W/m.ñoä
Ct
Ct
mmmm
w
w
0
02
1
50
1100
500125
3
1
=
=
==
δδ
Xaùc ñònh ??
2=
=
wtq
Giaûi
2
21
32
1
21
λδ
λδ
ww
tb
ww tttt −=
−
6
( ) ( ) 12
1 322
2
1
021
21ww
wwww tt
tttt −=⎥
⎦
⎤⎢⎣
⎡ ++−⇔
δλβ
δλ ( )
t00023.028.01 +=λ )00082.01(28.0 t+=
ñoä./28.000082.0
0 mW==
→λβ
Thay vaøo (1) ta ñöôïc
( ) (21212
00082.01125.028.0
wwww tttt −⎥⎦⎤
⎢⎣⎡ ++ )
( )505.07.0
2−= wt
( )( ) 704.1110000041.0451.0124.2 222−=−++↔ www ttt
t
( ) 704.100041.0159624.222
22 −=−−↔ wtww ttt
5613
396195743957
039649573957
0364564.300092.0
000092.07064.33575
22
22
22
2
222
=Δ→
×+=Δ
=−+↔
=−+↔
=−+−↔
ww
ww
ww
tt
tt
tt
( )
⎪⎩
⎪⎨⎧
<
=⇒
−
−
teá) thöïc vôùi p phuø hôï(khoâng0
828
22
12
0
w
w
t
Ct
Ctw0828
2=→
7
2
232 δ
λww ttq −=→ ( )
5.07.050828 −= 2/1090 mw=
9 - 10
8
./5.1 mw 25mF = 46=λ 0 00014.0144.2 mwt ./+=λ ñoä 0 ./698.3 mw=λ ñoä
Giaûi Do maät ñoä doøng nhieät qua caùc lôùp vaùch laø haèng soá
( ) ( ) ( )3
3
21
143
2
3221 δλ
δλ
δλ
wwtb
wwww ttttttq −=−=−=→ (1)
( ) ( )3
3
1
14321 δ
λδλ
wwww tttt −=−→ ( )4213
3
3
1
1wwww tttt +−=→
λδ
δλ
(2)
Thay caùc trò soá ñaõ bieát vaøo (2)
( ) 50698.010
85.46250
23+−=→ ww tt
=( )
28320868
5083208185027.83250
2
2
w
w
w
tt
t
−=+−
+−=
( ) ( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡ ++−=−→
211 32
32212
0
1
1 wwwwww
tttttt β
δλ
δλ
( ) ( ) ( ) ( )
( ) ( ) ( )
( )tt
tttt
tttttt
wwww
wwwwww
001.01144.000014.0144.0
82208682
12086884
383208682
18320868
2
22
02
1
121
2
0
1
121 2222
+=+=
⎥⎦⎤
⎢⎣⎡ −+−=−⇔
⎥⎦⎤
⎢⎣⎡ −+++−=−⇔
λ
βδλ
δλ
βδλ
δλ
Thay caùc trò soá ñaõ bieát vaøo (3)
( ) ( ) ( )⎥⎦⎤
⎢⎣⎡ −+−=−
2228220868
2001.01
05.0144.02086884
008.05.46250 www ttt
02170581118
03699.10017.0
22
2
222
=+−⇔
=+−⇔
ww
ww
tt
tt
( )⎪⎩
⎪⎨⎧
=
=⇒
choïnCt
Ct
w
w
0
0
250
868
2
2
Choïn Ctw0250
2=
Do nhieät ñoä maët trong cuûa vaùch t ta choïn giaù trò
( t
→= Cw0250
1
Ctw0250
2=
21 ww t= vì do kim loaïi coù heä soá daãn nhieät lôùn maø beà daøy
laøm vaùch cuûa kim loaïi laïi beù)
mmmm
mm
1050
3
2
1
==
8=
δδδ ?,
?
50
250
32
4
1
0
0
==
=
=
ww
w
w
ttQ
Ct
Ct
4w t
tw1
1 2 3δ δ δ
2508320868832086823
×−=−=→ ww tt C0118=
∗ Maät ñoä doøng nhieät truyeàn qua vaùch
( ) ( )01.0
698.0501183
343
−=−=δλ
ww ttq 2/4746 mw=
→ Q = q × F = 4746 × 5 = 23730 W
9 - 11
mmd 321 =mmd 422 =
mw /14=d1
t w2
2d
o= 580 C
= 450 C o
1w t
.ñoä λ
Xaùc ñònh maät ñoä doøng nhieät treân 1 ñôn vò chieàu daøi oáng ?=lq
Giaûi
( )
1
2ln12
12
dd
ttq ww
l
λ
−π= W/m
( )
3242ln
141
4505802 −=
π
= 42031 W/m
9 - 12
9
mmdmmd
110100
2
1
==
d3
3w t
1d 2d t w1
./551 mw=λ ñoä ./09.02 mw=λ ñoä
mwq
Ct
Ct
l
w
w
/300
50
2000
0
2
1
≤
=
=
?=cnδ Giaûi
( )
∑=
+
−= 2
1
1ln12
31
i i
i
i
wwl
ddtt
q
λ
π W/m ( )
2
3
21
2
1
31
ln1ln12
dd
dd
ttq wwl
λλ
π
+
−=⇔
300 = ( )
2
3
2
ln1100110ln
551
502002
dd
λ
π
+
−
2
3
2
ln10017329.0
5.942300
dd
λ+
=⇔
1417.30017329.0300
5.942ln1
2
3
2
=−=→dd
λ
1417.309.01417.3ln 22
3 ×=×=→ λdd = 0.28275
3268.128275.0
2
3 ==→ edd
3268.12
2
2 =+
→d
d cnδ
→ mmddcn 97.17
23268.1 22 =
−×=δ
9 - 13
10
d1 = 100mm d2 = 110mm
11
mm5032 == δδ
⎩⎨⎧
==
→mmdmmd
310210
4
3
501 =λ W/m.ñoä 06.02 =λ W/m.ñoä 12.03 =λ W/m.ñoä
Ct
Ct
w
w
0
0
50
250
4
1
=
=
a/ Xaùc ñònh vaø lq3wt
b/ Xaùc ñònh vaø khi ñoåi vò trí 2 lôùp
tw4
ot C
d2
1d3δδ2
1w t
tw3
λ1 λ2 λ3
l 3q wt
Giaûi a/ q ?,
3=wl t
( )∑
=
=
−= n
i i
i
i
wwl
ddtt
q
1
1ln12
41
λ
π
( )
210310ln
12.01
110210ln
06.01
100110ln
501
502502
++
−=
πlq
= 90W/m
( )
3
4
3
ln12
43
ddtt
q wwl
λ
−π=
433
4
3
ln2
1wlw t
ddqt +×=→
πλ
Ctw06.96
3=→
b/ Khi ñoåi vò trí 2 lôùp caùch nhieät
( )
210310ln
06.01
110210ln
12.01
100110ln
501
502502
++
−=
πlq = 105.7 W/m
433
4
3
ln2
1wlw t
ddqt +×=
πλ = 105.7 50
210310ln
06.021
+×
×π
= 159 0C ∗ Keát luaän : Lôùp caùch nhieät coù λ beù ñaët ôû trong (ñoái vôùi vaùch truï) thì hieäu quaû caùch nhieät seõ cao hôn.
Baøi 9-15: d=600 mm δ1=15 mm
δ2=150 mm λ1=50 W/mñoä λ2=0,1 W/mñoä t1= 2000C t3=500C ql=?
Giaûi: Toån thaát nhieät treân 1m chieàu daøi cuûa bao hôi:
( ) ( )
( ) ( )m/Wln
,ln
ddln
ddln
ttn
iid
idlni
nttlq
242
1526001502152600
101
600152600
501
502002
23
21
12
11
312
1 11
112
=⎟⎠⎞
⎜⎝⎛
×+×+×+
+⎟⎠⎞
⎜⎝⎛ ×+
−×π×=
λ+
λ
−π=
= +λ
+−π=
∑
12
9 – 16
13
=1θ 600
λ = 58 W/m.ñoä 1α = 7 W/m2.ñoä
Xaùc ñònh: - Phaân boá nhieät ñoä doïc theo truïc - Nhieät löôïng Q = ?
iaûi Xem truïc nhö thanh daøi voâ haïn Phaân boá nhieät ñoä doïc theo truïc
Vôùi m =
θ = 60o
1
t
t
1
f
t
x0
d = 60 mm G
→laø mxe−= 1θθ
FU1
λα (1)
d = 60mm = 60 m
m = 2.84 (Ñôn vò laø
310−×⎩⎨⎧
×=
=→
− 231083.219.0
mFmU
→m1 )
θ = 60 xe 84.2− →Nh ät oaû raie löôïng t Q = 1θλFm = 83 .258 3 ×××× −
W 6084.210
= 28
14
mmmmlCt
Ct f
8.0160
70
1000
0
0
===
=
δ
3.23
9 – 18
=λ W/m.ñoä 3.23=α W/m2.ñoä
Giaûi
Sai soá cuûa pheùp ño laø do coù hieän töôïng daãn nhieät doïc theo oáng. Neáu coi oáng nhö
l
d
1 thanh troøn höõu haïn vaø boû qua toaû nhieät ôû ñaàu thanh ta coù:
)()(00 tt
tt f
mlchmlchllf
−===−
θθ
)(1
00 mlchtttt
f
lfl =−−
=θθHay (1)
Ta coù: ml = λδα
δλπαπ
λα l
ddl
fUl ==
3108.03.233.2316.0 −××
=
= 5.66 = )66.5()( =→ chmlch 5.143
3−
0
1096.65.143
1×==
−
−→
tttt
f
lf
= 99.8 0C Sai soá t f
02.0=
100)70100(1096.6 3 +−×−=→ −lt
→ Ctl 8.99100 −=−
Ba
th=100 C
m
ñoä
Giaûi
øi 9-19: 0
t0=500C h=140 m δ= 1 mm λ=58 W/m
α=29 W/m2ñoä tf= ? %saiso á= ?
15
:ai soá cuûa pheùp ño laø do coù hieän töôïng daãn nhieät doïc theo voû boïc neân nhieät ñoä cuûa
Snhieät keá khoâng phaûi laø nhieät ñoä cuûa khí trong bình tf maø laø nhieät ñoä cuûa ñaàu voû boïc th
Xem thanh daøi höõu haïn, boû qua toûa nhieät ñaàu thanh, ta coù:
)mh(chh
0θθ =
f
fhh
tttt
)mh(ch −−
==→00
1θθ
1331058
29140 3 ,,hdd vôùi h
fUhmh =
×==== −λδ
αλδπαπ
λα
46112
133133133
,ee),(ch)mh(ch,,
=+
==→−
C,t,t
tf
f
f 081044611
150
100=⇒=
−−
→
Sai soá cuûa pheùp ño: 841008104 ,,tt hft =−=−=δ
%,,th
t 84100
84==
δ
16
mm5
9 – 21
=δ = 50 mm
l = 1 m h
=λ 58 W/m.ñoä =α 11.65 W/m2.ñoä =1θ 80 0C
Xaùc ñònh: Nhieät ñoä ñænh caùnh Nhieät löôïng truyeàn qua caùnh
o+ Nhieät ñoä ñænh caùnh
δ
h
l
Giaûi a/ Khoâng keå ñeán söï t aû nhieät ôû ñænh caùnh
)(mhchh1θθ = [ ]C0
( )005.0158
005.01265.11××
+×==
UαTrong ñoù: f
mλ
= 8.986
Cchh )05.0986.8(
=×
=θ 06.7280
+ Nhieät löôïng truyeàn qua caùnh [W] (1) )(.... 1 mhthfmQ θλ=
Ta co:ù 44.005.0986.8 =×=mh 93 4213. 0)( =mhTh(1) 4213.080005.01986.858 × × × ××= = 87.83 W
hôïp coù keå ñeán ieät ñænh caùnh. Ñeå tính ñ öï toaû nhieät ôû ñænh caùnh ta taêng chieàu ca
→ Qb/ Tröôøng toaû nh
2δeán s o caùnh leân 1 ñoaïn =
2
' δ+=→ hh
17
m.522550 =+= m2
+ Nhieät ñoä ñænh caùnh
h
δ/2
)0525.098.8()( ' chmhchh 6801
×==
θθ
= 72 0C + Nhieät löôïng truyeàn qua caùnh
'mhth (2) =
)(.... 1fmQ θλ=Trong ñoù: 0525.0986.8' ×=mh 471765.0 4396.0)( ' =mhTh (2) =→ Q 4389.080005.01986.858 ×××××
= 91.6 W
9 – 23
2./35 mw=α ñoä ./35 mw=λ ñoä
C01 80=θ
Xaùc ñònh nhieät löôïng truyeàn qua caùnh Q = ?
δ
rr
1
2
mmrmm0rmm
12063
2
1
==
6.=δ
18
iaûi Giaûi baèng phöông phaùp duøng caùnh thaúng töông ñöông G ∗
260120
212 +−=+−=6.3δrr h
= 61.8mm Caùnh thaúng töông ñöông coù beà daøy δ, chieàu cao h, chieàu daøi L = 1 m
( )δλλ ×
==1.. f
m α.U δα +12.
6.23106.335
)0036.01(3523 =
××+××
= −m
46.1108.6157.23 3 =××= −mh Ch(mh) = 2.27
44.027.21
)(1
==mhChθ12 =
θ
260
120
1
2 ==rr
,;1
2
1
2
rr
θθCaên cöù vaøo tra ñoà thò (hình 9-2) saùch baøi taäp
.0'' =Nhieät löôïng truyeàn qua caùnh xaùc ñònh baèng coâng thöùc
.. ""ε=
Ta ñöïôc 6ε 8
qFQ" (*)
Trong ñoù q = FQ
Q: Nhieät löôï truyeànng cho caùnh phaúng coù chieàu cao, beà daøy baèng chieàu cao, beà daøy cuûa caùnh troøn, chieàu roäng 1m
Dieän tích F: Dieän tích toaøn boä beà maët toaû nhieät cuûa caùnh thaúng töông ñöông
toaøn boä beà maët caùnh troøn "F : )(.... 1 mhthfmQ θλ= (1)
Vôùi (1) 0157.2335
Th(mh) = 0.9 0036. 9.080× × ×××=→ = 213.8W
3 ×××= − Q
F = 2 ×× lh 1108.612 21236.0 m=
2/17301236.0
8.213 mwF
q =→Q
==
än tích beà maët toaû nhieät cuûa caùnh troøn Die ( )2
12
2 ( ) 2622 067824.01060120.2 m=×−= −π " .2 rrF −= πNhieät löôïng truyeàn qua caùnh troøn
qFQ .. """ ε= 1730067824.086.0 W101××= =
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