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Case I

Fin is very long, and the temperature at the end

of the fin is essentially that of the surrounding

fluid.

Case IIEnd of the fin is insulated

Case III

Fin is of finite length and loses heat byconvention from its end.

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The number of fins, finned and unfinned surface areas,

and heat transfer rates from those areas are

unfinnedfinnedfintotal,QQQ

)(finfinmaxfin,finfinned TThAQQb

3 cm

0.6cm D=0.25 cm

)(unfinnedunfinned TThAQb

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n 1

0 006 0 00627777

m

m) m)

2

( . ( .

427777

2

fin

DDLA

2D

4unfinned

222

unfinned

2

22

fin

m86.04

)0025.0(277771

4277771

m68.64

)0025.0(

)03.0)(0025.0(27777427777

DA

D

DLA

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ahp

kA

h D

k D

h

kDc

24

4 4 35

237 0 00251537

/

( )

( )( . ).

W / m . C

W / m. C mm

2-1

aL

aLtanhfin

fin

-1

-1

m m

m m

tanh tanh( . . )

. .

.aL

aL

1537 0 03

1537 0 03

0935

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C)30100)(m68.6)(C.W/m35(935.0

)(

22

finfinmaxfin,finfinned

TThAQQ b

W2107

C)30100)(m86.0)(C.W/m35()(22

unfinnedunfinned

TThAQ b

W300,15

kW17.4 W1074.12107300,15 4unfinnedfinnedfintotal,

QQQ

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A

Q hA T T b

no fin2

no fin no fin2 2

m m m

W / m C m C W

( )( )

( ) ( . )( )( )

1 1 1

35 1 100 30 2450

The rate of heat transfer if there were no fin

attached to the plate would be

Then the fin effectiveness becomes

7.102450

400,17

finno

finfin

Q

Q

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Repeat Problem using copper fins (k = 386 W/m C)

instead of aluminum ones.

Vary the center-to-center distance from 0.4 cm to 2.0

cm. Plot the rate ofheat transfer and the overall

effectiveness as a function of the center-to-centerdistance, and discuss the results.