242
F. de Monte and G. D’Alessandro
Fig. 4 + criterion for simultaneous estimation of k and C under X42B50T00 model
When a contact resistance at the heater/sample interface is considered, the optimal
experiment and heating durations (˜ t N and ˜
t h , respectively) are about 10% longer than
those obtained when the contact is perfect.
5 Standard Deviations of the Estimates
The dimensionless standard deviations of k and C under uncorrelated measurements
errors can be computed as a function of the experiment duration through the following
relations:
˜
σ
+
k =
σ k
k
(T max − T in )
√
N
σ
∼ =
˜
C
+
CC
+
(10a)
˜
σ
+
C =
σ C
C
(T max − T in )
√
N
σ
∼ =
˜
C
+
kk
+
(10b)
Results for imperfect and perfect contact are given in Figs. 5 and 6, respectively.
In these figures, the
+ determinant is also plotted. In both cases, ˜
σ
+
k reaches a
minimum for a certain ˜
t N shorter than the optimal one (maximum
+ ), while ˜
σ
+
C
continues to decrease for longer and longer experiment durations.
F. de Monte and G. D’Alessandro
Fig. 4 + criterion for simultaneous estimation of k and C under X42B50T00 model
When a contact resistance at the heater/sample interface is considered, the optimal
experiment and heating durations (˜ t N and ˜
t h , respectively) are about 10% longer than
those obtained when the contact is perfect.
5 Standard Deviations of the Estimates
The dimensionless standard deviations of k and C under uncorrelated measurements
errors can be computed as a function of the experiment duration through the following
relations:
˜
σ
+
k =
σ k
k
(T max − T in )
√
N
σ
∼ =
˜
C
+
CC
+
(10a)
˜
σ
+
C =
σ C
C
(T max − T in )
√
N
σ
∼ =
˜
C
+
kk
+
(10b)
Results for imperfect and perfect contact are given in Figs. 5 and 6, respectively.
In these figures, the
+ determinant is also plotted. In both cases, ˜
σ
+
k reaches a
minimum for a certain ˜
t N shorter than the optimal one (maximum
+ ), while ˜
σ
+
C
continues to decrease for longer and longer experiment durations.