heat transfer

5/19/2018 Heat Transfer

1/93

:A. A , ., ..

EIDAHA AA & AA:

KDKI

DL KLIAH


2/93

Md Kiah

PERPINDAHAN PANAS & MASSA:

KONDUKSI

Oeh:

A. Agg P Saiaa, ST., M.Tech.

Ja Tei Mei Faa Tegi Idi

INSTITUT SAINS & TEKNOLOGI AKPRIND

2011


3/93

i

DAFA II

Haaa

Haaa a

Dafa Ii i

I. 1

II. K 6

III. K 1D 17

I. 37

. K 2D 48

I. K 74

Refeece 80


4/93

(

adaah aii eegi

ecaa aai Peida

edah

ai bea

ida ejadi eida

)

Gaba 1. Tida eja

Ga

I. E

):

daa be aa aea adaa eb

a Paa/ ejadi e aah h

, ai bea aa ag diidah

a aa ada dii eeibaga e

di eidaha aa ada

a 2. Mde Peidaha Paa

DAHLA

daa h/

ag ebih

a

a (


5/93

1.K ()

Kdi adaah

eadaa dia

Paa didi

geaa ee

Pada fida age (

Gab

H F

d

dTA =

dega:

= aj e

= d

A = c e

dT = ebed

d = eba

2. K (

Kei adaah

Kei haa ej

Geaa fida ii d

Ga

afe eegi aa eai id, aa

a eh geaa aaa a(

da aeia id

ia aa diafe dega adaa )

3. Mde eidaha aa di

idaha aa/hea ae (Wa)

iia aa aeia (W/ K)

cia aea (2)

a h (K)

eia ()

fe eegi aa eh adaa geaa fi

adi ada fida, aea eibaa fida a

ieb a ei

a 4. Mde eidaha aa Radiai

2

ida daa

) da

ba aa

a

g begea


6/93

H

( )

= TTh"

dega:

= hea f

h = efiie

T = ee

T = ee

2.. K A (

Pegeaa fida

fida eeb.

Raa jei /

Tejadi iai a

Ga

2.. K (

Aia eaif fida

gaa a (

G

ei (W/2)

eidaha aa ei (W/2K)

e eaa aeia (K)

e fida (K)

/ )

i diebaba eh adaa eaia e

fida ai beag dega eaia e

aa fida ag ebih aa dega ag ebi

a 5. Viaiai aia ei aai

)

aaa fida dega eaa beda di

), iaa: fa, be

ba 6. Kei aa dega fa

3

ea ada

ea.

h digi

baba eh


7/93

4

3. ( )

Tida eea edia afe

Eegi aa diafe/dieiia eh adiai ifaed dai eaa

beda

Pagai dai gebag eeagei

Tejadi ada id, iid, da ga Meaa da

Gaba 7. : 101102 e Eecageic

H B E

4

T" = dega

= eiie e bac bd (W/2)

= aa SefaBa (5.67 108W/2K4)

T = h eaa (K)

= eiii (0 1)

:

Bac face

D/gh face

ide face aea

:

Whie/hi face

h face

a face aea


8/93

5

Waa dede eidaha aa dieajai ecaa eiah,

a daa aiaia ag eig ejadi adaah e eidaha aa

ag eibaa eigaeigaa ( )

Gaba 8.

Maa iah Peidaha Paa da Maa ( )

adaah aga eig daa , aea baa eaaaeaaa

ag eibaa egeaha aa eidaha aa da aa. Seei

iaa: Iea Cbi egie, Pe Pa, Hea Echage, Cd

Sage, Oe, ea ag aia

H F E C

Kdi

d

dT" = (W/

2) (W/.K)

Kei ( )= TTh" (W/2) h (W/2.K)

Radiai Tea

4T" = (W/

2)

dega:

= Kaa Sefa Ba

= 5,67 108W/2K4

= eiiia

(0 1)


9/93

6

II. KDKI

Gaba 1. Ch eidaha aa Kdi

Gaba 2. eidaha aa di

adaah aii eegi daa be aa aea adaa ebedaa h/

eeae gadie

ecaa aai Peidaha Paa/Hea Tafe ejadi e aah h ag ebih

edah


10/93

ai bea eea

ida ejadi eida

Eiibi)

Gaba

Gaba

H F

A =

gadie, ai bea aa ag diidah

a aa ada dii eeibaga e

3. Kdi eh

. Kdi eh

d

dT

7

a

a (Thea


11/93

L

beabah

La eaa ag

Keebaa aeia be

Kdiia aa be

dega:

= a aj

= hea f

= d

A = c e

dT = ebed

d = ajag

K (

Keaa aa ifa

Maeiaa diagga

dia

Kdiia ea S

Niai dai be

Aedi A, Icea &

:

(ebedaa eea) aaa eda

ga dega aah di beabah

ag

abah

d

dTA =

d

dT

A

=

d

dT" =

eidaha aa/hea ae (W)

eidaha aa aah (W/2)

iia aa aeia (W/ K)

cia aea (2)

a h (K)

/eba aeia ()

),

aeia didaa eghaaa aa

ii, ehigga ideede e

id > Liid > Ga.

eaa aeia ada, cai, da ga daa

De Wi (

8

eaa

hada aah

diiha ada

)


12/93

9

> L > G

Gaba 3. Kdiia aa bebeaa aeia ada eeae 250C


13/93

10

Gaba 4. Vaiai Kdiia aa ehada eea

D ( ),

Cea abaa eebaa aa di daa a aeia

ebadiga aaa diia aa dega aaia aa

c

=

dega:

= hea diffii (2/)

= hea cdcii (W/ K)

= dei/aa jei (g/3)

c = ecific hea/aa jei (J/g K)


14/93

Maeia dega

ebaha aa ag

B/

C :

1. Jia a eaa i

adaah 10 2, eebaa

eiii diia

W/.K. Tea:

a. Teeae e

didig

b. Hea f

g ebih bea beai aa ebih ce

ejadi di eiaa

(BC)

aba 5. Tiga de aa baa

heaa

a 2.5

aa 0.2

aa a

11

ee


15/93

12

:

a. Teea eaa a didig

d

dTA =

=

L

TTA cdh

A

LTT hcd =

=

0.210

2.53000415 = 3780C:

b. Hea f

10

3

A

" == = 0.3 W/

2

D ( )

Aaia diibi eea ( ) di daa edi ebagai fgi

dia

Meda c e/ie e

Keeaa eegi c e

gi EEEE

=+

Seaja dai eeaa eegi da H Fie dia eaaa

Diffi Paa ie dia Kaei, Siide, da Shee.


16/93

K K ( C

Gaba 6.

Eeg Sce,

dddEg

=

Pebaha eeg ag ei

ddd

TcE

=

Seaja dai eai e

dd +++

Sbii E

d

d

)

e ie aei

a di daa edi

egi

d

T

cd ddd

= +++

ddd

Tcdddd

=+

13

d


17/93

dai H Fie

Tdd

=

Tdd

=

Tdd

=

Peaaa Diffi Paa

d

T

+

U ( e

d

T

T

T2

2

2

2

2

2

+

+

+

diaa:

c

=

adaah

K (

Kdia Kaei:

Tc

T

=+

+

aga ada aah , , da )

T

1

=

aeia

)

14


18/93

15

gi EEEE

=+

ddd .ddd. +++

+++ d.dd.

Tc

=

dai H Fie

Tdd

=

=

Tdd

Tdd

=

Peaaa Diffi Paa Kdia Siide:

Tc

T

d

T

1

T

12

=+

+

+

Aa jia Ii aeia

T

1

TT

1

T

1

2

2

2

2

22

2

=+

+

+


19/93

K B ( C

Gaba

dai H Fie

di =

=

=

Peaaa Diffi Paa

i

1

T

122

2

2

+

)

8. C Ve Shee

Td

Kdia Ba:

T

i

1

d

T

2 +

+

16

Tc


20/93

1.

IE KDIA KA

D

Ga

d

T

+

1D ( )

Kdi haa a a

h

haa ej

/

Tida ejadi ebaha

III.KDKI 1D

EI

3D K K

ba 1. Aaia

Tc

T

=+

+

:

ah (1D)

aa ada a aah dia

adi ada aah eeb

age eeg ehada a (

Tc

17

AD AE

0 )


21/93

/D D

Gaba 2. Kdi 1

T = f(), Teea e

Hea afe haa dii

Kei e da dai

Kdi di daa a

. K 1D

0d

dT

d

d=

Iegaa 2 ai

( ) 21 CCT +=

Baa:

= 0 = ,1

= L = ,2

Maa Diibi Teea

( ) ( ),1,2 TTL

T +=

, aa ebagia aa da baa

agai fgi dai

ja ada aah b.

ae a

e a

, ,

da ae a ead ae, aa geeai

,1

18

ei

a


22/93

Sedaga Peaaa La

ejadi

( TL

A

d

dTA ==

da Hea F

( ,2,1''

TTL

A

==

/

Peaaa ahaa

eaaa Fie dega Pe

I aag dega

V aag dega T, e

Tahaa Tea Kdi:

Tahaa Tea Kei:

Ragaia Tahaa Tea (

Sedaga bea ahaa e

eidaha Paa ( ) K

),2,1 T

)

ea daa diea dega ega

aaa A Lii

igga didaaa:

A

LRcd =

hA

1Rc =

) dai gaba diaa

a aa adaah

19

di 1 D

agiaa

ejadi


23/93

hA

L

Ah

1R

21

++=

/D D D

Gaba 3. K

Dai eaaa d

Sehigga eaaa di

0

d

Td2

2

=+

Sedaga diibi eea

1

2 C2

T ++=

A

i 1D, dega ebagia aa (

)

i dia aei

1D, degaebagia aa da ead

e ecaa daa diia ebagai

2

20

ae


24/93

D

)

( )L

1

2

LT

2

22

+

=

D

)

Bda Cdii:

L TT == da LT ==

Teeae Diibi: T

Teea Mai (ada

(

2

TT

L

2

TT ,2,1,1,2 ++

K (

T

) TL

12

L

2

22

+

=

b iei) : ( )

2

00 T2

LTT +==

=

21


25/93

D D K (

Didig/bidag daa

diia aa a

Saa daa eca

Ragaia Tahaa Teii begi a aha

eei ada ehig

Gaba 4. Mia

G

Tahaa Ta R

)

ag e dai bebeaa aeia a

g bebedabeda.

a ei aa ecaa aae.

a digabaa eei ada eggaba ea a a ei a a

ahaa ii

dai aeia A,B, da C

5.

(agaia ahaa ea)

321 RRR ++=

22

g eiii

a ahaae dihig


26/93

G

Tahaa TaR

Bei adaah ch eid

A

L

Ah

1R

A

A

1

+=

cdh

R

TT

=

5.

(Cici ahaa ea)

21 R

1

R

1+=

aha aa ada :

Ah

1

A

L

A

L

2C

C

B

B ++

23


27/93

21

21

RR

RRR

+=

1

R

TT

=

C

1. Jia jedea aca ada g

W/.K, da a eaa

a. Gaba Ragaia Tah

b. Tahaa Tea Ta

.

d.

T,i da T,

c3 RR +

ba dibaah eai efiie d

g ihea A= 1 2, aa ea:

a Teaa

24

i = 1.4


28/93

:

a. Ragaia Tahaa Te

b. Tahaa Tea Ta

h

1

A

L

Ah

1R

i

++=

++=

65

1

1.4

0.004

30

1

1

1

. /Laj

0.0

(40

R

TT

,0i,

=

=

d.

Teeae T,i

=hiA(T,i T,i)

T,i=T,i /(hiA) =

++=

i h

1

L

h

1

A

1

= 0.052 K/W

idaha aa

2

10)= 961.5 W

0 961.5/(30 1) = 7.95 0C

25


29/93

Teeae T,:

( ),i, TTL

A =

A

TT i,, = 7.95=

2.

Ua dai jedea he

aca, c= 1.4 W/.K, K

a.

Gabaa agaia

b.

Tea ahaa e

c.

Tea Hea L da

:

a.

RAgaia Tahaa Te

b. Tahaa Tea Ta:

L

A

L

Ah

1R

ai

++=

11.4

0.004961.5= 5.2 0C

ae diaa (80 50 ), Kd

iia aa daa, a= 0.0245 W/.K

ahaa eaa

a a dai cie a diaa

i jedea heae diaa

:

Ah

1

A

L

++

26

iia aa


30/93

10

1(

)(0.080.05

1+=

c.

Hea L = Hea afe

102.(20

RTT

,0i, ==

3.

Jia dieahi Kdii

Bic; bic= 0.72 W/

Pae; ee= 0.22 W

:

a.

Gaba agaiaa

b.

Tea ahaa e

:

. Gaba agaiaa aha

Mdifiai gaba

Ada bebeaa e

diaa ehada g

Wa edeaa

)80

1

1.4

0.007

0.0245

0.007

1.4

0.007+++ = 102.1 K/

ae

110) = 0.29 W

Paa:

.0C

/. 0C

ahaa eaa

a a dai cie a diaa

ea

higga ebih dah diaaia agaiaa

gia agaia eai dega d

aba

ag diaa bebeda, a haia a

27

ifiai ag

a aa


31/93

Mia difiai/eba

Ragaia Tahaa e

Diedehaaa eja

Sehigga Tahaa e

= I+ II

Diaa:

21PI R

1

R

1

R

1++=

54PII R

1

R

1

R

1+=

b. Meea ahaa h

Tea aig

A1= 4 12 =

Saai dega

gia diaa eei gaba bei

aa ejadi:

i

a a ejadi:

3R

1

ea a dai cie a diaa

aig A1, A2, A3, A4, da A5

2, d

28


32/93

A5= 3 12 =

Tea aig

11

11

A

LR =

Gaa R1, R2, R3,

21PI R

1

R

1

R

1++=

54PII R

1

R

1

R

1+=

Ahia didaaa

= I+ II

2. IE KDIA

Gaba 6. A

K

1

T

12

+

. 2

aig R1, R2, R3, R4, da R5

aai55

55

A

LR =

R4, da R5e daa eaaa RIda RPII

3R

1

ahaa hea a

ILIDE

aia c e dia iide

K

c

T

d

T =+

+

29

T


33/93

K 1D,

K

T

1=

Iegaa da ai e

( ) 1 CT =

Da Saa Baa

( ) ,1 TT 1 == d

( )

2

1

,,1

TTT

=

H

La eaag I

A = 2 L

aah eidaha

Dai H Fi

, H G

1D, , H G

0

aaa diaa:

2C

a ( ) ,2 TT 2 ==

/Diibi eea ada eebaa i

,2

2

2 T

+

hea iide = a didig iide

aaa adaah e aah adia ()

e:

30

ide


34/93

d

dTA =

=2

1

d

L2

H K

(

=

TL2

Sedaga dai H. Pe

( = TAh X

H K

= L2h

Iga: Aagia Hea

edaaa ahaa

T V

I

Sehigga:

( )d

dTL2

( ),2

,1

dTT

)

1

2

,2,1

T

digia Ne

)

( )

TT

afe Kdi da Kei dega Ta

a didig iide

31

aa Lii


35/93

Tahaa Tea Kd

Tahaa Tea Ke

C

:

H

,2,1

R

TT

=

i didig Siide(

L2

/R 12cd =

i didig SiideL2h

1Rc =

:

32


36/93

1D,

K

, H G

33


37/93

3. IE KDIA B

Gaba

K

T

12

2

2

+

A/HEE

7. Aaia c e dia ba

K B:

T

i

1

d

T

i

122 +

+

34

Tc

=


38/93

Dai H Fie

d

dTA =

=2

1

T

T

2

d

4

Dega egiegaa

H

(

=

1

,

1

T4

Dega egaagia

ahaa ii, aa;

Tahaa Tea Kdi

C :

1.

Sea dega eea

bediaee 5 c da

eebaa 3 c ( = 0.0

ei, h2= 18 W/2 0C0C,

( )d

dT4 2

( ),2

,1

dTT

eaaa diaa, aa didaaa:

)

2

,2

1

T

eaaa hea afe ae ba d

Ba

=

21

cd

1

1

4

1R

320 0C diaia daa ia ( = 8

eebaa 0.5 c. Pia diiai gea

W/ 0C). Udaa a dieahi 5 0C de

. Jia ea eai efiie ei,

Maa ea:

a.

Ragaia ahaa

b. Tea ahaa

c. Tea hea

ajag ia

d.

Tea

35

aa dega

0 W/ 0C)

dega

a efiie

1= 60 W/2

eaa

a a

a e


39/93

:

a.

Tahaa ea cici

b.

Tahaa ea a

Tea a ea

Tea aha e

ahaa ea a

c.

Sead Hea L dai Sea

2.

32

R

TT

21=

=

d.

Teeae d (e

Pada ia:

12C/W0.0002T =

Pada Ia

121C/W2.35T=

ag ihea

a aig ebe dijaha

e ajag ia

iaajagee(eW12161

5=

a eeae): .RT =

C0.02W1 =

C284=

36

edaaa


40/93

Meea aea e

Meecea ejadi

ebaia

Dai Ne La f Cig:

Kei

eaa ihea (A) de

aa fi (Eeded Sface)

G F

.

.

aa a aaa id da

a e eidaha aa dai id

( )

= TThAq s

daa diigaa dega eea

ga fida eia ai dega ea

37

e fid aa

aea a

baha ii


41/93

.

A H

1 D, Sead Sae da T

Thea dii,

Kefiie ei, h a

Sdig Teea

Bae Teeae ada

Tida ada bd eia

E /

Kdi eai ii/fi

d

d

d

dTA cd =+

(G)

a Hea Geeai didaa Sii

adaah a da if

aah a da if ada eaa

e adaah a

h a da if

ce aaa eaa bae da Sii

:

dd

dTAc

38

ii


42/93

39

Kei ada eaa:

Neaca Eegi ada Fi ejadi: = ++

( )

+

= TThdAd

d

dTA

d

d

d

dTA

d

dTA ccc

( ) 0TThdAdd

dTA

d

d c =+

aaaa dibagi da d

( ) 0TTd

dAh

ddTA

dd

c =

eaja dideffeeiaa:

( ) 0TTd

dA

h

d

dT

d

dA

d

dT

d

dA cc =

+

da dibagi dega Ac: edaaa be eaaa eegi 1D

eeded face

( ) 0TTd

dA

h

A

1

d

dT

d

dA

A

1

d

Td

c

c

c

2

=

+

F E,


43/93

F E,

Ch Efficiec Bebea

& )

Efiiei ii daa a

geei ii. Bei ad

a Be Sii/Fi (be ag ai daa

diea dega gafi efiiei

ah gafi efiiei ii geei e

40

diiha ada

igaig


44/93

41


45/93

42

E ,

Bia ada a eaa diaag bebeaa Fi (N),

Ta a eaa a:

Ta aj eidaha aa ecaa ei ada eaaa adaah:

Mai aj eidaha aa:

Efficiec Peaa Meeh,

Aa:


46/93

f

bf,

R =

Tahaa hea eeheaa ii

b,

hA

1

R ==

C :

1.

Tea eaia hea

diaee 4 diga

eeae 2000C. Te

ei, h = 30 W/2K.

didaaa ada jah a ii da a

afe ae jia ebah Pi Fi dega aja

a ada ebah eaa Aii

eae adjace adaah 300C deg

diia hea Aii, A = 240

43

ag ida

g 10 c da

ega bae

efiie

/.K


47/93

44


48/93

2.

Siide ebah ei e

c da diaee a 5

iide adaah 500 K da

U eaia aj e

dega fi

Higah eaia hea

a dai Aii ( = 186 W/.K) dega

c. Pada dii eeae e

dieai daa a ada h 300 K (h =

digia iide diabaha 6 bah

diaa eebaaa 6 da ajag

afe aea

45

ajag 15

aa a

50 W/2K).

a 20 .


49/93

46


50/93

3.

Pada a .2 ea b

dega eeae e

e eeae jia diaee daa Siide

aa daa Siide adaah 500 K.

47

adaah 3 c


51/93

:

Meea diibi

Meea hea a

D

d

T

T

+

U aaia 2D (b. da

Ii aeia:

ehigga

0

T

T2

2

2

2

=

+

(

Peaaa diaa ea

Pebagia Paa, Sead S

. KDKI 2D

eeae ebagai fgi dai dia ,

e ae ea hea f

:

Tc

T

=+

+

b.), Sead Sae da aa ebagia

)

be diffe aa

ae, ea diia aa ag a.

48

AD AE

T(,)

aa, ea

2D, Taa


52/93

Sebe hea afe ae

diea T(,) ai dii

eea ii daa ia e

Paia diaa. Peaaa Di

(iga) ede edeaa, ai

1.

2.

3. Sh

1.

Taf eaaa Diffee

0

T

T2

2

2

2

=

+

ejadi

0

2

2

2

2

=

+

diaa:

12

1

TT

TT

=

a hea f bia ia hig, eebih d

i eeae ebagai fgi dai da

a dega eeeaia eaaa

feeia Paia eeb daa dieeai

:

D

ed Fac

( )

ia Paia

49

ah ha

. Diibi

Diffeeia

dega 3


53/93

Da eea 2 aa baa

2 BC aigaig

(0,) = 0 (,0) = 0

(L,) = 0 (,W) =

Si Peaaa Diffeeia

( ) ( ) (Y, =

Pdc dai 2 fgi

Pe. I haa ega

Pe. II haa ega

Diffeeiaa ( ),

d

dXY

=

2

2

2

2

d

XdY

=

Da

(BC)

dia:

0

2

2

2

2

=

+

adaah:

)

ada

g ada

( ) ( )Y

50


54/93

51

d

dYX

=

2

2

2

2

d

YdX

=

bii e 0

2

2

2

2

=

+

, aa:

0d

Yd

Y

1

d

d

12

2

2

2

=+

2

2

2

2

d

Yd

Y

1

d

d

1=

Sebeah ii haa eaa fgi da ebeah aa haa fgi , aa a

aa da ii ha eai aa ag aa (aa eiah)

dega 2ebagai aa eiah;

2

2

2

2

2

d

d

1

d

d

1== , aa

2

2

2

d

d

1=

0d

d 22

2

=+ (Pe I)

da

22

2

d

d1 =

0Yd

Yd 22

2

= (Pe. II)

Saa eda eaaa diaa daa dieeaia, bia 2> 0


55/93

U 2> 0 , aa Peeeai

iCcCX 21 +=

4

3 eCeCY +=

Sbii X da Y diaa e e

( ) ( 1 cC, +=

Dega e ea BC:

(0,) = 0 (,0) = 0

(L,) = 0 (,W) =

A

( ) ( )1

2,

1

=

=

C :

1.

Mia ebah a eegi

a.

Tea eeae

eggaa 3 dee g

b.

Tea aj ei

diia aaa

a Pe. II da Pe. II diaa adaah:

aaa ( ) ( ) ( ), = , ehigga:

)( )4

32 eCeCiC +

D 0

2

2

2

2=

+

( )

( )LW/ih

/Lih

L

i

11++

ajag dega BC ebagai bei

ag ejadi di egahegah a e

ji eaa.

aha aa eai eaa baah

= 50 W/.K

52

b dega

ae jia


56/93

53

:

L = 2 , W = 1

a. Teeae di egahegah a

Kdia ii egah ae : (,) = (1 , 0.5)

dai:

( ) ( ) ( )

( )LW/ih

/Lih

L

i

11

2,

1

1

=

++

=

Da 3 dee gaji eaa: = 1, 3, 5

( )

( ) ( )

( )

( ) ( )

( )

( ) ( )

( )

+

+

++

+

=

1/25ih

0.5/25ih

2

15i

5

11

1/23ih

0.5/23ih

2

13i

3

11

1/21ih

0.5/21ih

2

11i

1

11

21,0.5

6

42

( )

( )

( )

( )

( )

( )

( )

+

+

=

/25ih

/45ih

2

5i

5

2

/23ih

/43ih

2

3i

3

2

/2ih

/4ih

2

2i

21,0.5

( ) { } 0.460.0080.0630.755

21,0.5 =+=

edaga:

12

1

TT

TT

=

aa:

50150

50T(1,0.5)

0.46

=

(1, 0.5) = 960C


57/93

b.

Laj eidaha aa

dega:

eai eaa baah a

54


58/93

= 3.183 W/ [1.738+0.

2. F D

Mebagi bje eja

, eaii ,

Nda , eaii d

24+0.00062] = 5.610 /

)

i bebeaa egi

aeah didaa gai

55


59/93

56

T

T

T 1/2,1/2,

,

2

2+

TT

TT 1,,,1,

=

+

2

,1,1,

)(

2TTT +=

+

T

T

T 1/2,1/2,

,

2

2+

TT

TT 1,,,1,

=

+

2,1,1,

)(

2TTT += +

daiBe FiieDiffeece Hea Eai 0

T

T2

2

2

2

=

+

2

,1,1,

)(

2TTT +=

+

+ 2,1,1,

)(

2TTT + +

U =

Peaaa Fiie Diffeece (FDE) Iei de N Hea Geeai

04TTTTT ,1,1,1,1, =+++ ++


60/93

Seaja Hea Tafe dih

T=

K E

( ) ( ) (

+

4

1i

,i

Hea ae dai ia de i e a

( ) ( ) ( ,1, =

( ) ( ) ( ,1, =+

( ) ( ) ( 1 ,1, =+

( ) ( ) ( ,1, =

TTT 1,1,1, ++ ++

g dega:

)= 01

h iei de ,

)

TT ,1,

)

TT ,1, +

)

TT ,1, +

)

TT

1 ,1,

+

( )04T

T ,1, =

+

57


61/93

Taa Pabagia Paa

TTT 1,1,1, ++ ++

B K

1.

I

TTT 1,1, ++ ++

2. D

( ) (TT2 1,1, ++ +

04TT ,1, =+

FDE =

04TT ,1,, =+

K

)

h32T

h2T 1,1,

+

++

+

58

0T

, =


62/93

3.

( TT2T ,1,1, ++ +

U Adiabaic Sface: S

4. L

( ) h2TT 1,1,

++

K

) 0T

h22T

h2 ,1 =

+

+

e h = 0

K

0T

h12T

, =

+

59


63/93

5.

( TT2T ,1,1, ++ +

U Se Sface:

F

Mia ia eiii N de (N

Nda 1: a11T1+ a1

Nda 2: a21T1+ a2

Nda 3: a31T1+ a3

d aai

Nda N: aN1T1+ a

Diaa

T = eea

a, C = a biaga

Peaaa Fiie Diffeece (

1. I G

2. I

) 04T

2",1 =+

e = 0

D (FDE)

e. FDE)

2T2+a13T3++a1NTN= C1



2T2+aN3T3++aNNTN= CN

DE) diaa daa dieeeaia dega:

60


64/93

61

1. FDE I G

Lagahagah:

a.

Seia eaaa dia aa ehigga edaaa eee diaga dega

iai ebea

1N131211 a,.....a,aa >

2N232122 a,.....a,aa > d

b. Maigaig eaaa diia daa be eici; eeae ag

beeaia dega eee diaga

= +=

=

1i

1j

N

1ij

1)(

j

ii

ij()

j

ii

ij

ii

i()

i Ta

a

Ta

a

a

C

T

i = 1,2,3,..N

= jah ieai

c. Iiia ieai (=0), iih iai ag aia ia Ti

d.

Seaja hig Ti () dai iai Tj () ,dega 1 j i1, da Tj (1) dai ieai

ebea (i+1) j N

e.

Laa ieai ii aai ecaai ieia ag diea (Ieai

dega , )

TT 1)(i()

i

Meiiaa jah ieai edaaa ieia ege, aga e

diehaia eiiha Ti =0 ( )

:


65/93

Tea eeae T1, T2,

iiiia eei ada gab

:

Piih Peaaa Fiie Di

Nde 1, 2, 3 da 4 adaah I

TTT 1,1,1, ++ ++

Tea Peaaa

1: 500+ T3+

4T1 + T2

2: 500 + T4

T1 4T2

3: T1+ 100

T1 4T3 +

4: T2+ 100T2+ + T3

Taf (1), (2), (3), da

T3, da T4ebah ab dega dii e

feece (FDE) aigaig de,

ei Nde

04TT ,1, =+

aigaig Nde

T2+ 150 4T1= 0

+ T3 = 650 (1)

100 + T1 4T2= 0

+ T4=600 (2)

T4+150 4T3= 0

T4 = 250 (3)

100 + T3 4T4= 0 4T4= 200 (4)

(4) e be

62

ae ada

a


66/93

4T1 + T2 + T3 + 0

T1 4T2 + 0 + T

T1 + 0 4T3 + T4

0 + T2+ + T3 4T4

S daa be Mai

Dai ai diaa, bah

=

=

1i

1j

(

j

ii

ij

ii

i()

i Ta

a

a

CT

Sehigga didaaa be

= 650 (N1)

=600 (N2)

250 (N3)

= 200 (N4)

Diaga

be

+=

N

1ij

1)(

j

ii

ij) Ta

a

aigaig Nde:

63


67/93

64

162.50.25T0.25TT 1)(31)(

2

()

1 ++=

1500.25T0.25TT 1)(4()

1

()

2 ++=

62.50.25T0.25TT 1)(

4

()

1

()

3 ++=

500.25T0.25TT ()3()

2

()

4 ++=

U edaaa T1, T2, T3, da T4, eaja aa Ieai ada eea

be diaa ea iih (ia =0; T1= 250, T2=

250, T3= 120, da T4= 150)

Ieai T1 T2 T3T4

=0 250 250 150 150

=1

=2

=

Laa N Ieai aai TT

1)(

i

()

i

(ia aai /gaa, 0.1)

2. ALAB


68/93

65

Lagaagah:

a. Tia FDE aigaig Nde

1N131211 a,.....a,aa >

2N232122 a,.....a,aa > d

b. Ubah daa ai ai [A] [T] = [C]

NNN2N1

2N2221

1N1211

a...aa

............

a...aa

a...aa

+

N

2

1

T

...

T

T

=

N

2

1

C

...

C

C

c.

Tea eeae ia da dg ede Iei Mai [T] = [A]1[C]

Diaa ai [A]1adaah Ie dai ai [A]

N

2

1

T

...

T

T

=

1

NNN2N1

2N2221

1N1211

a...aa

............

a...aa

a...aa

N

2

1

C

...

C

C

ALAB:

>> A=[a11 a12 a13; a21 a22 a23; a31 a32 a33];

>> C=[C1 ; C2 ; C3];

>> T=i(A) * C

:


69/93

Sebah ab dieahi dii

a. Tea eeae T1,

b.

Tea hea afe a

:

a.

Teeae T1, T2, T3, da

Piih Peaaa Fiie Dif

gaa FDE Iei

TTT 1,1,1, ++ ++

Tea Peaaa

1: 500+ T3+

4T1 + T2

2: 500 + T4

T1 4T2

3: T1+ 100

T1 4T3 +

4: T2+ 100

T2+ + T3

Taf (1), (2), (3), da

eeae ada iiiia eei ada g

T2, T3, da T4dai ab eeb

e

T4

eece (FDE) ag digaa, a d

Nde

04TT ,1, =

aigaig Nde

T2+ 150 4T1= 0

+ T3 = 650 (1)

100 + T1 4T2= 0

+ T4=600 (2)

T4+150 4T3= 0

T4 = 250 (3)

100 + T3 4T4= 0

4T4= 200 (4)

(4) e be

66

ba

iaa


70/93

4T1 + T2 + T3 + 0

T1 4T2 + 0 + T4

T1 + 0 4T3 + T4 =

0 + T2+ + T3 4T4=

S daa be Mai

4110

1401

1041

0114

Jadia e be

N

2

1

T

...

T

T

=

10

01

41

14

Dega eggaa MA

>> A=[4 1 1 0 ; 1 4

>> C=[650 ; 600 ; 25

>> T=i(A) * C

T=

268.7500

256.2500

168.7500

156.2500

Maa Teeae T1, T2,

4

3

2

1

=

156.25

168.75

256.25

268.75

b. Laj Hea Tafe:

= 650 (N1)

600 (N2)

250 (N3)

200 (N3)

Diaga

+

4

3

2

1

=

200

250

600

650

1

41

14

10

01

200

250

600

650

LAB aa T1, T2, T3, da T4didaaa

0 1 ; 1 0 4 1 ; 0 1 1 4];

; 200];

3, da T4adaah

67


71/93

T ==

Dihig dai face 5000

(268.75 =

Aa:

Dai face 1500C i

26(150 =

Dai face 1000C ba

1(100 =

Dai face 1000C a

25(100 =

Laj Hea Tafe:

Tedaa ebedaa 0.5

C:

Mai eci diei e

C (D F

4

3

2

1

=

156.25168.75

256.25

268.75

)T(T)T(T

21 +

C:

475500)(256.2500) =+

:

137168.75)(150.25) =+

ah:

125156.25)(1008.75) =+

a:

212.5156.25)(1006.25) =+

137 + 125 + 212.5 = 474.5

ega jia dihig dai face 5000C

h (fie eh) eai aa hai ag did

)

68

aaa.


72/93

1. C ebah face

eadaa ead eiga e

ii die e daa

aa aaaa e aja

:

Bagi bjec dega a

Nde 1, 3, da 5 : Iei

TT 1,1, ++ +

1: 500 + T3+ T2+ 5

4T1+ T2+ T3=

eba dai fieca bic dega ii 1

aa c dijaga eeaea, e

a. Tea diibi eeae 2D da

g c.Gaa gid dega a 0.25

Kbic@478 K = 1

W/.K

T = 300 K

h = 10 W/2.K

gid ag aa, ai 0.25 0.25

de

04TTT ,1,1, =+ +

00 4T1= 0

1000 (1)

69

1 . Pada

aga a

aj aia

0.25


73/93

3: T1+ T5+ T4+ 50

T14T3+ T4+ T5

5: T3+ T7+ T6+ 500

T34T5+ T6+ T7

Nde 2,4 da 6 : e

2: 2T1+ 500 + T4

2T14T2+ T4=

4: 2T3+ T2+ T6 4

T2+ 2T3 4T4+

6: 2T5+ T4+ T8 4

T4+ 2T5 4T6+

Nde 7 da 8 : Nde ih

( )TT2T 1,1,1, ++ +

dega

2.51

0.2510

h==

7: 2T5+ T8+ 500 +2

2T5 9T7+ T8=

8: 2T6+ T7+ T7+2

2T6+ 2T7 9T8=

Seaja 8 FDE eeb

4T3= 0

500 (3)

4T5= 0

500 (5)

adiaba (e h = O)

T2= 0

00 (2)

4= 0

6= 0 (4)

6= 0

8= 0 (6)

face ceci

0T

h22T

h2 , =

+

2.5300 (24.5)T7= 0

2000 (7)

2.5300 (24.5)T8 = 0

1500 (8)

diia daa

70


74/93

71

4T1+ T2+ T3+0 + 0 + 0 + 0 + 0 = 1000 (N1)

2T1 4T2+ 0 + T4+ 0 + 0 + 0 + 0 = 500 (N2)

T1+ 0 4T3+ T4+ T5+ 0 + 0 + 0 = 500 (N3)

0 + T2+ 2T3 4T4+ 0 +T6+ 0 + 0 = 0 (N4)

0 + 0 + T3+ 0 4T5+ T6+ T7+ 0 = 500 (N5)

0 + 0 + 0 +T4+ 2T5 4T6+ 0 + T8= 0 (N6)

0 + 0 + 0 + 0 + 2T5+ 0 9T7+ T8= 2000 (N7)

0 + 0 + 0 + 0 + 0 + 2T6+ 2T7 9T8= 1500 (N8)

Tia daa ai ai [A] [T] = [C]

92200000

19020000

10421000

01140100

00104210

00011401

00001042

00000114

+

=

1500

2000

0

500

0

500

500

1000

T

T

T

T

T

T

T

T

8

7

6

5

4

3

2

1

Gaa Ie Mai [A] eea [T]

=

8

7

6

5

4

3

2

1

T

T

T

T

T

T

T

T 1

92200000

19020000

10421000

01140100

00104210

00011401

00001042

00000114

1500

2000

0

500

0

500

500

1000

Maa Mai diaa e ci MATLAB


75/93

>> A=[4,1,1,0,0,0,0,0;2,4,

0,0,0,1,2,4,0,1;0,0,0,0,2

>> C =[1000;500;500;0;

>> T = i(A)*C

T =

489.30

485.15

472.07

462.01

436.95

418.74

356.99

339.05

Ahia eeae aig

=

=

=

=

=

=

=

=

339.05T

356.99T

418.74T

436.95T

462.01T

472.07T

485.15T

489.30T

8

7

6

5

4

3

2

1

0C

Meea hea afe

,1,0,0,0,0;1,0,4,1,1,0,0,0;0,1,2,4,0,1,0,0;0,0,

0,9,1;0,0,0,0,0,2,2,9];

500;0;2000;1500];

aig Nde adaah:

ae e ajag c

72

1,0,4,1,1,0;


76/93

= 2(a + b + c)

= 2[h(/2)(T8T) +

(

=

TT2

2h

L

8

Hea ae dai c e ai

(

=

T

2

2h

L

8

(

= 3

20.25210

= 883 /

h() (T7T)+ h(/2)(TT)]

) ( ) ( )

++

TT

2

TT 7

ea

) ( ) ( )

++

TT

2

TT 7

) ( ) (

++ 5

20.25300356.990.253009.05

I.KDKI

73

)3000

AIE


77/93

K (

Teeae beaia

digaa

aeia ecaai e

EE

=

( )(ThAdTC =

( )(= ThAd

dTVC

diaa:

= V (aa aei

= aa jei aeia

= e aeia (3

):

ehada a

eea a ag die

eae ee T()

)dT

)

T

)

(g/3)

)

74

eh id


78/93

75

Seaja dega eeae diffeece,

( ) = TT da

=

d

dT

d

d

dd

hAVC

=

Kea Vaiabe da Iegaa

=

0

d

d

hA

VC

i

hA

VC

i

=

i

hA

VC

=

( )

VC

hA

i

i

eTT

TT

=

= (. L C)

dega

( )

CRVChA

1

hA

VC =

==

diaa:

R= Ceci Reiace

C = Led Thea Caaciace f Sid

Sehigga . L C jga diia ebagai

( )

i

i

eTT

TT

=

=

ie

=


79/93

R aa C ai be

ee ebaha

R aa C ai be

ecaai eeibag

L

==

0

0

dhAd

i e

hA

=

=

i e

hA

=

i e1VC

abah, aa aeia id aa e

eeae eiaa

bah, aa aa eai aa aeia

hea ( = 0)

0

ie

hA

=

0

i e

hA

i

hA

76

ai aba

id


80/93

L C

Keeagaa diibi

Nbe, Bi

Led Caaciace M

Hig Bi Nbe, Bi

B , B

Kefiie eidaha

Teeae D di

eaa id dega

Pebadiga PP

di di daa id

Dai Eegi Peaa

( )= hATTL

A,2,1

( )

( )hA1A

L

TT

TT

,2

,2,1=

hLBi =

(B

aa, 0.1

hLB

c

i


81/93

78

diaa:

Lc = Chaaceiic Legh,

c

A

V

AeaSface

VeL ==

c

A

VL =

Seaja dai Eeia L Caaciace

VC

hA

c

LC

h

CV

Ah

=

2

c

c

L

C

Lh

=

2

c

c

L

Lh =

Didaaa efiie Ta Bediei (N Deia)

LhB ci

= B

2c

L

F

=

F :

Sehigga L Caaciae daa a dii ebagai:

( ) ( )i FB

i

i

eTT

TT

=

=

( . L C)

:

1. Teeae dai aia daa aa di dega ece ag eiii

jci bebe hee eei gaba.


82/93

Tea a ag die

diffeece

:

Jci :

6

1

D

D

A

VL

2

3

61

c ===

Bi Nbe:

35

2101.67

LhB ci =

=

L Caaciace aid dig

( )

i

i

eTT

TT

=

=

c

LC

h

CV

Ah=

=

( ) VC

hA

i

eTT

TT

=

( ) 0.462e0.01 =

( ) 0.4620.01 =

= 10

a ece ebaca 99% iiia

( ) 1.67100.0016

1 4==

0.00101 4

=

a, ehigga

VC

hA

1

4 0.462

.671085003201

210 =

79

eeae


83/93

80

Led Caaciace Mehd eai bd ag eaif eci dega diia

hea ag iggi. Jia bd eaif bea dega diia hea ag edah,

aa ed caaciace ag aa (Teeae gadie ag ejadi di daa

bd beaiai ehada ii da a). Sehigga bd ag bea Kdi

Taie daa diea dega (Hiee, M.P., 1947)

K 1D : G

Peeeaia dega

Bebeaa N Dieia Paaee ag diea daa eggaa Heie

Cha:

Dieie Teeae: ( ) ( )

=

TT

T,T,

i

Dieie Diace f Cee:L

X =

Dieie hea afe Cefficie:

hLBi=

Dieie ie: 2L

=

Maigaig geei eiii 3 aca gafi ():

1.

Teeae a Mid ae (1C)

2. Seica Teeae Diibi (2)

3. Hea Tafe ae (3)


84/93

81

H C

1Cha.

2dCha.


85/93

H C

1C

dCha.

ha.

82


86/93

2dCha.

dCha.

83


87/93

:

Pa Tebaga ebaa 4 c

e ada eeae 5000C

ea eeae e

:

Peggaa 1Cha:

( W/120W/100

hL

Bi

102

==.

(

( 0.02

33.910

L

26

2 ==

Gaa eda iai diaa a

Liha aah gai bi ada ga

Dai 1Cha, 45.8Bi

1=

dega iiia eeae 200C dia

eaa 7 ei. Jia efiie di h =

aa a eia dieaa dai e

)( ) 45.8

0.02

C.0=

)( )

)

35.6607

2 =

a 1Cha edaaa

=

TT

TT

i

00

a (caa eggaa 1Cha)

da 35.6 = aa 0.46TT

TT

i

00

=

84

a e daa

20 W/2.0C,


88/93

1C

Peggaa 1Cha:

45.8Bi

1=

1L

L

L

==

Liha aah gai eba ada ga

Maa: 0.99TT

TT

0

ha.

ba (caa eggaa 2Cha)

85


89/93

2dCha.

Seaja dega

T

T

TT

TT

TT

TT

i

0

0i

=

Ahia didaaa eea

( )TT0.455TT i +=

Aca hea afe diea

Bi = 1/1/Bi = 1/45.8 =

Bi2 = (0.02)2 35.6 = 0

0.4550.990.46 ==

e eaa ae aa ea e:

( ) C282500200.455500 0=+

dai 3dCha

.02

.014

86


90/93

Qa= C(T Ti)

Qa = C(T Ti)

= 8530 g/3 3

= 1555.8 MJ/3

Dai 3dCha Q/Qa = 0.

Maa:

Q = 0.4 Qa

Q = 0.4 1555.8 = 622.

dCha.

80 J/g.0C (500 20)0C

5 J/3

87


91/93

L

1. Sebah ST304 dia

6000C. P didigia

Tea:

a.

Cee ie eea

b. Hea afe ae e

ee 20 c dieaa dai e ada

didaa ebah chabe beeea

e eeah 45 ei edigia

i egh

88

eeae

e 2000C.


92/93

89

DAFA AKA:

1. Cege, Y.A., Te, R.H, , Eb

2.

Ha, J.P., 1986, , 6hEd., McGaHi, Sigae

3. Ha, J.P., 2005, , 7hEd. Taa McGaHi,

Ne Dehi.

4. Lg, C., Saa, N., 2009, , Ve Pbihig AS, Fee eb a

.bb.c

5.

Icea, F.P., DeWi, D.P, 1981, , Jh

Wie ad S, Ne Y.

6.

Iee, S., PhD., ( ), df fie.


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90

. , ., ..

.

: +62 8179400013

: .

heat transfer

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