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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.
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