57
KD2 Pro Operator’s Manual
8. KD2 Pro Theory
The diffusivity is
(4)
The conductivity and diffusivity are found by fitting eqs. 1 to
the transformed data. The correct values of
b
o
, b
1
and
b
2
are
the ones which minimize the sum of squares of error between
the equations and the measurements. The values are found
using the Marquardt (1963) non-linear least squares proce-
dure. This procedure is susceptible to getting stuck in local
minima and failing to find a global minimum in some prob-
lems (the single needle problem is a perfect example of a bad
non-linear least squares problem) but the dual needle problem
typically works well. Finding just three model parameters is
quick in the KD2 Pro.
Single Needle Algorithm
Heat is applied to a single needle for a time,
t
h
, and tempera-
ture is monitored in that needle during heating and for an
additional time equal to
t
h
after heating. Two needle sizes are
used. One (the KS-1) is 1.2 mm diameter and 60 mm long.
The other (the TR-1) is 2.4 mm diameter and 100 mm long.
The temperature during heating is computed from
(5)
D
r
2
4
b
2
--------
=
T
m
0
m
2
t
m
3
t
ln
+
+
=
