56
KD2 Pro Operator’s Manual
8. KD2 Pro Theory
by the heat per unit length,
q
. The resulting data are fit to the
following equations using a non-linear least squares proce-
dure.
(1)
where:
(2)
Here,
Ei
is the exponential integral (Abramowitz and Stegun,
1972), and
b
o
, b
1
and
b
2
are the constants to be fit.
T
o
is the
temperature at the start of the measurement and
q
is the heat
input. The first equation applies for the first
t
h
seconds, while
the heat is on. The second equation applies when the heat is
off. The thermal conductivity is computed from
(3)
T
b
0
t
b
1
Ei
b
2
t
-----
+
=
T
b
0
t
b
1
Ei
b
2
t
-----
Ei
b
2
t
t
h
–
----------------
–
+
=
T
4
T
T
o
–
q
---------------------------
=
k
1
b
1
-----
=
