
142 Heat Transfer: Thermal Management of Electronics
Therefore, n effectiveness can be dened as the ratio of the n base thermal resis-
tance to the n thermal resistance:
. (7.38)
Using Equations 7.33 through 7.35 for R
f
, and considering that for a n with
constant cross section A
b
= A
c
and therefore R
b
= 1/hA
c
, the following expressions are
obtained for n effectiveness.
Innitely long n•
(7.39)
Fin with adiabatic tip•
(7.40)
Fin with convection and radiation from its tip•
εε
f
c
kP
hA
aL
h
ak
aL
aL
h
ak
aL
=
+
+
sinh cosh
cosh sinh
or
ff
c
c
kP
hA
aL= tanh
(7.41)
Several conclusions can be drawn from Equation 7.39 ...