3.3 Effective Thermal Diffusivity and Conductivity
151
physical properties of graphite as well as helium. The uncertainties of the average
diffusivity and conductivity are obtained from the uncertainty of vector P by the law
of propagation of uncertainty.
3.3.5.1 Error of Temperature by Thermocouples (Type B Uncertainty)
In the present test, the sheathed type K thermocouples are used in the facility to
measure temperature up to 1,200
◦ C. Recalling the inverse method, it is found that the
statistical error of measured temperature impacts the results of the effective thermal
diffusivity firstly. Then effective thermal conductivity is converted from diffusivity
by Eqs. (3.41) and (3.42). The conversion will introduce the errors of the physical
properties of graphite as well as helium, which will be discussed later. The type
K thermocouples are calibrated by the manufacturer with the grade I accuracy of
the Chinese Standard GBT 16839.2-1997. Its tolerance is 1.5
◦ C (0
◦ C ∼ 375
◦ C)
and 0.004T (375
◦ C ∼ 1000
◦ C). Moreover, the error of the NI acquisition system is
given by 0.38
◦ C (0
◦ C–300
◦ C), 0.58
◦ C (300
◦ C-900
◦ C) and 0.88
◦ C (900
◦ C–1,400
◦ C). The total error of measured temperature is calculated as the sum of these two
kinds of errors. The standard deviation of measured temperature can be obtained
by dividing total error by
√
3 since its value is assumed to be uniformly distributed.
First, this section describes the type B uncertainty of the effective thermal diffusivity.
The statistical error of measured temperature in the inverse method was studied by
[16–18] (see in Eq. (3.33))
The standard uncertainty of each parameter p j in Eq. (3.33), is the square root of
the corresponding diagonal terms of V ( P). For vacuum or helium tests, there are ten
sets of individual data from two repeated tests with five sets in the facility, namely
from C1 to C5. The standard uncertainty of p j in the different set is varying with
the different temperature and results. For instance, there exist ten p 1 parameters and
their standard deviations for ten sets of vacuum tests of shown in Fig. (3.18a). The
final diffusivity and conductivity are calculated by using the average ¯
p j with the
formula
¯
p j =
1
10
10
m = 1
p j,m .
(3.48)
Here j indicates the index of the component of vector P, and m indicates the different
sets in two repeated tests. Therefore, the uncertainty of ¯
p j should be written as
u B, ¯
p j =
10
m = 1
1
10
u p j,m
,
(3.49)
151
physical properties of graphite as well as helium. The uncertainties of the average
diffusivity and conductivity are obtained from the uncertainty of vector P by the law
of propagation of uncertainty.
3.3.5.1 Error of Temperature by Thermocouples (Type B Uncertainty)
In the present test, the sheathed type K thermocouples are used in the facility to
measure temperature up to 1,200
◦ C. Recalling the inverse method, it is found that the
statistical error of measured temperature impacts the results of the effective thermal
diffusivity firstly. Then effective thermal conductivity is converted from diffusivity
by Eqs. (3.41) and (3.42). The conversion will introduce the errors of the physical
properties of graphite as well as helium, which will be discussed later. The type
K thermocouples are calibrated by the manufacturer with the grade I accuracy of
the Chinese Standard GBT 16839.2-1997. Its tolerance is 1.5
◦ C (0
◦ C ∼ 375
◦ C)
and 0.004T (375
◦ C ∼ 1000
◦ C). Moreover, the error of the NI acquisition system is
given by 0.38
◦ C (0
◦ C–300
◦ C), 0.58
◦ C (300
◦ C-900
◦ C) and 0.88
◦ C (900
◦ C–1,400
◦ C). The total error of measured temperature is calculated as the sum of these two
kinds of errors. The standard deviation of measured temperature can be obtained
by dividing total error by
√
3 since its value is assumed to be uniformly distributed.
First, this section describes the type B uncertainty of the effective thermal diffusivity.
The statistical error of measured temperature in the inverse method was studied by
[16–18] (see in Eq. (3.33))
The standard uncertainty of each parameter p j in Eq. (3.33), is the square root of
the corresponding diagonal terms of V ( P). For vacuum or helium tests, there are ten
sets of individual data from two repeated tests with five sets in the facility, namely
from C1 to C5. The standard uncertainty of p j in the different set is varying with
the different temperature and results. For instance, there exist ten p 1 parameters and
their standard deviations for ten sets of vacuum tests of shown in Fig. (3.18a). The
final diffusivity and conductivity are calculated by using the average ¯
p j with the
formula
¯
p j =
1
10
10
m = 1
p j,m .
(3.48)
Here j indicates the index of the component of vector P, and m indicates the different
sets in two repeated tests. Therefore, the uncertainty of ¯
p j should be written as
u B, ¯
p j =
10
m = 1
1
10
u p j,m
,
(3.49)