
Fins and Heat Sinks 147
Two common examples of ns with nonuniform cross sections are triangular and
circular ns shown in Figure 7.10. The solutions of Equation 7.51 can be used to
show that efciency of a triangular n is
η
f
aL
IaL
IaL
a
h
kt
==
12
2
2
1
0
()
()
,with
(7.52)
where t is the n thickness at the base, and the efciency of a circular n is
η
f
i
oc i
ioci
r
ar r
KarI ar IarK
=
−
(
)
−2
22
11 11
()()()(aar
KarI ar IarK ar
a
oc
iocioc
)
()() ()()
01 01
+
=with
22h
kt
,
(7.53)
where t is the n thickness and r
oc
= r
o
+ t/2 is the correct outer radius of the n [1,2].
Here I
0
and K
0
are modied, zero-order Bessel functions of the rst and second
kinds, respectivel