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××= =