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PROBLEM 4.71
KNOWN:
Pin fin of 10 mm diameter and length 250 mm with base temperature of 100
°
C experiencing
adiation exchange with the surroundings and free convection with ambient air.
r
FIND:
Temperature distribution using finitedifference method with five nodes.
Fin heat rate and
elative contributions by convection and radiation.
r
SCHEMATIC:
ASSUMPTIONS:
(1) Steadystate conditions, (2) Onedimensional conduction in fin, (3) Constant
properties, (4) Fin approximates small object in large enclosure, (5) Fin tip experiences convection and
adiation, (6) h
r
fc
= 2.89[0.6 + 0.624(T  T
∞
)
1/6
]
2
.
ANALYSIS:
To apply the finitedifference method, define the 5node system shown above where
Δ
x =
L/5.
Perform energy balances on the nodes to obtain the finitedifference equations for the nodal
temperatures.
Interior node, n = 1, 2, 3 or 4
in
out
EE
−=
±±
0
0
(1)
abcd
qqqq
+++=
()
n1
n
n
r,n
sur
n
c
fc,n
n
c
TT
hP
x
T T k
A
h P
x
A
0
xx
+−
∞
−
−
Δ−
+
+Δ
−
+
=
Δ
Δ
(2)
where the free convection coefficient is
(3)
2
1/6
fc,n
n
h
2.89 0.6 0.624 T
T
∞
⎡
=+
−
⎢
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This note was uploaded on 12/07/2010 for the course MAE Heat Trans taught by Professor Lee,j.s. during the Spring '10 term at Seoul National.
 Spring '10
 LEE,J.S.
 Heat Transfer

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