Decagon Devices KD2 Pro Operator's Manual page 62

KD2 Pro Operator's Manual
8. KD2 Pro Theory
m is the ambient temperature during heating (which could
0
include some offset for contact resistance and the heating
element being adjacent to the temperature sensor inside the
needle), m is the rate of background temperature drift, and
2
m is the slope of a line relating temperature rise to
3
logarithm of temperature.
During cooling the model is
The thermal conductivity is computed from
Since these equations are long-time approximations to the
exponential integral equations (eq. 1), we use only the final 2/
3 of the data collected (ignore early-time data) during heating
and cooling. This approach has several advantages. One is
that effects of contact resistance appear mainly in these early-
time data, so by analyzing only the later time data the measure-
ment better represents the thermal conductivity of the sample
of interest. Another advantage is that equations 5 and 6 can be
solved by linear least squares, giving a solid and definite result.
The same data, subjected to a non-linear least squares analysis,
T = m + m t
1 2
k =
t
--------------- -
+ m ln

3
t t –
h
q
-------------
4m
3
58

(6)
(7)