Materials Transactions, Vol. 50, No. 11 (2009) pp. 2623 to 2630
#2009 The Japan Institute of Metals
Measurement of Thermal Conductivity of Magnesia Brick
with Straight Brick Specimens by Hot Wire Method
Yoshitoshi Saito1 , Kinji Kanematsu2 and Taijiro Matsui1
1
Refractory Ceramics R&D Division, Environment & Process Technology Center, Technical Development Bureau,
Nippon Steel Corporation, Futtsu 293-8511, Japan
2
Nippon Steel Technoresearch, Futtsu 293-8511, Japan
As a result of a revision of the JIS system, the application of the hot wire method for determining thermal conductivity has been expanded
from heat-insulating bricks to refractories with higher heat conductivity. In this regard, focusing on magnesia bricks, which are used in the safety
lining of converters and a wide variety of other applications, the authors studied the possibility of applying the non-stationary hot wire method in
the determination of thermal conductivity up to the high-temperature range by using straight brick specimens. To perform measurements on
magnesia bricks, whose thermal conductivity is higher than that of heat-insulating bricks, a set of measurement equipment including a highcapacity electric furnace was constructed, and as a result, it was possible to confirm the linear relationship between the increase in temperature of the hot wire and the logarithm of time log t by using straight brick specimens. It is possible to determine the thermal conductivity accurately
by identifying the critical point where the log t relationship ceases to be linear and calculating the thermal conductivity of the target material
on the basis of the linear relationship. [doi:10.2320/matertrans.M2009098]
(Received March 19, 2009; Accepted August 11, 2009; Published October 25, 2009)
Keywords: straight bricks, magnesia brick, thermal conductivity, hot wire method, converters
1.
Introduction
Energy conservation is becoming increasingly important,
and as a consequence, the enhancement of the thermal
efficiency of industrial furnaces used in the production of
steel and in other industries is becoming essential. Heat loss
through furnace walls can be effectively reduced by lowering
the thermal conductivity of the refractories and the heatinsulating materials used for lining the inside of the furnaces.
While there has been an increased awareness of the
importance of accurately calculating the thermal conductivity of refractory and heat-insulating materials for furnace
design, these values fluctuate considerably depending on the
method and the measurement conditions.1–4) In this regard,
the method of stationary heat flow and the hot wire method
have been used for determining the thermal conductivity
of heat-insulating bricks under JIS R 2616. However, the
Standardization Committee of the Technical Association of
Refractories, Japan, has promoted the expansion of the
application of these methods to more heat-conductive
refractory materials, such as oxide systems. As a result, in
2007 the hot wire method was defined in the JIS system (R
2251-1) as a method for measuring the thermal conductivity
of refractories in the range of 10 Wm1 K1 and lower.
Even before the revision, Hayashi et al.5,6) pursued the
possibility of applying the hot wire method not only to
materials with low thermal conductivity, such as heatinsulating bricks, but also to refractories and ceramics with
high thermal conductivity, and studied the measurement
conditions for these materials. In performing measurements
with the hot wire method, there are certain assumptions in
using the theoretical equations related to the process of
calculating the relevant thermal conductivity.7) One of the
assumptions is that the specimen size is regarded as infinite
during the measurement. This suggests that it is necessary to
finish the measurements before the heat flow from the hot
wire reaches the outer surfaces of the specimen. The time
required for the heat flow to reach the specimen surface
depends on the thermal diffusivity, the specific heat capacity
and the thermal conductivity of the material, where the
specimen size is of particular importance in the application
of the hot wire method to materials with high thermal
conductivity.8) Aiming at expanding the field use of the hot
wire method for determining the thermal conductivity of not
only heat-insulating bricks, but also other types of refractory
materials, Haupin reported that materials with higher conductivity require proportionally larger specimens.9) Hayashi
et al.6,8) studied and defined the minimum specimen size
required for accurately determining the value of the thermal
conductivity. Moreover, according to Van der Held and Van
Drunen,10) materials with higher conductivity require proportionally larger specimens. They point out that thermal
diffusivity affects the shape of the curve in plotting the
temperature against the log of the time. More specifically, the
first part of the plot is curved and gradually becomes linear
with time until the size of the specimen becomes a factor,
which is the point where the relation ceases to be linear again.
Therefore, they limited the analysis to the linear portion of
the plot and obtained an equation for the thermal conductivity. Another necessary condition for measuring the thermal
conductivity with the hot wire method is that the temperature
of the specimen should be uniform in the material and should
be maintained at a predefined level.11) Although this is
possible when the heating furnace used for the measurement
is sufficiently larger than the specimen, if, for example, two
conventional bricks as specified in JIS R 2101 are used to
form a specimen set, a very large furnace will be required.
Otherwise, if a small furnace is used, a sophisticated
temperature control system will be required to maintain a
uniform temperature in the furnace, and the heating equipment will likely be complex and expensive.12) Using straight
bricks and other large-sized items as specimens, Hayashi
et al.12) measured the thermal conductivity of heat-insulating
bricks, chamotte bricks, silica bricks, baked and fused spinel
2624
Y. Saito, K. Kanematsu and T. Matsui
bricks, and baked and fused mullite bricks for temperatures
between room temperature and 1473 K. The thermal conductivity of these materials is around 2.0 Wm1 K1 or
lower. They have not measured the thermal conductivity of
materials with higher thermal conductivity using straight
bricks or larger specimens.
On the other hand, an advantage of the hot wire method is
that it is not necessary to form specimens into specific shapes
by preprocessing, and various materials can be measured as
industrially manufactured. When evaluating the quality of
refractory materials, straight bricks or small test pieces cut
from such bricks are usually used as specimens, and thus it is
appropriate that any quality aspects can also be evaluated
using straight bricks as specimens. In this respect, the hot
wire method can be applied by utilizing straight bricks as
specimens without the need for pre-processing. Using this
method, two straight bricks are used without pre-processing
to form a specimen set, with a heating wire and a thermocouple placed between the two bricks. The size of the set
is as large as 230 114 130 mm, and to measure the
thermal conductivity at high temperatures with this specimen
configuration, it is necessary to use the isothermal zone of a
sufficiently large furnace. In this regard, although Hayashi
et al. extensively studied the conditions and the measurement
error with simple and small furnaces, they did not examine
the conditions, the accuracy, and other parameters in the
measurement of the thermal conductivity at high temperatures with straight brick specimens.
For ease of measurement and simplicity of equipment with
regard to refractories, where measurements at high temperatures are more important than measurements at room
temperature, it is desirable to obtain reliable values for the
thermal conductivity by using the hot wire method with
straight brick specimens. Thus, it will be possible to utilize
this method for straight brick specimens without the need
to form the specimens into a specific shape or any other
preprocessing. In consideration of the above, the authors
focused their attention on magnesia bricks, which are used
for safety lining of converters and various other applications,
and studied a method for determining the value of the thermal
conductivity on the basis of measurements with the nonstationary hot wire method using straight brick specimens.
This paper reports the findings of this study.
2.
Experiment
2.1 Specimens
As the hot wire method is not applicable to electrically
conductive bricks such as carbon blocks, we chose magnesia
bricks as an example of the extension of the hot wire method
to refractory materials with high heat conductivity. Table 1
shows the chemical composition of the target bricks. The
specimens are straight bricks 230 114 65 mm in size,
in accordance with JIS R 2101 standard. To verify the
suitability and the accuracy of the equipment used for
measuring the thermal conductivity based on the hot wire
method, which the authors constructed specifically for this
study, heat-insulating bricks were used for comparison as
specimens representing the heat-insulating bricks as specified
in JIS. For the same purpose, heat-insulating brick specimens
Table 1 Chemical composition of magnesia brick and insulating bricks
(mass%).
MgO
SiO2
TiO2
Al2 O3
Fe2 O3
CaO
ZrO2
Magnesia brick
94.13
1.99
0.11
0.55
1.19
1.83
0.07
Insulating brick
—
44.4
0.8
52.2
1.03
0.3
0.02
were also measured with the stationary heat flow method in
accordance with JIS R 2616 by using HC-51 (ceramics
application type, EKO Instruments Co., Ltd).
2.2 Test equipment and measurement method
2.2.1 Hot wire method
Figure 1 shows a schematic outline of the structure of the
test equipment for the hot wire method. The measurement
equipment proper consisted of two sections of electrical
circuits, namely a power supply and a temperature measurement section. Connected to this measurement equipment
proper were a heating furnace for measurements at high
temperatures, a digital multimeter (34420A, Agilent Technologies), a DC power source unit (EX-375L2, Takasago
Ltd.), an interface unit for automatic measurement, calculation and control (Spectra Inspection Laboratory Co., Ltd.
(SPEIN Lab.)), and a PC. To measure the thermal conductivity in the temperature range between room temperature
and 1500 C (1773 K), an electric heating furnace (Taiho
Denki Seisakusho Co., Ltd.) was equipped with six silicon
carbide heating elements arranged horizontally on each side
of the furnace, for a total of twelve elements. The inner
dimensions of the furnace were 200 400 300 mm, with
an effective inner volume of 150 300 130 mm, which is
sufficiently large to accommodate a specimen with a size of
114 230 130 mm composed of two straight bricks which
have not been pre-processed in any way. The temperature in
the furnace was controlled by an automatic temperature
controller (Chino DZ1000) connected to three independent
electric circuits for the heating elements corresponding to
HIGH, MEDIUM, and LOW. The bottom-loading design of
the furnace considerably simplified the process of loading the
specimen set with the hot wire and the thermocouple.
A Pt13%Rh wire with a diameter of 0.3 mm (hereinafter
referred to as the hot wire), with a temperature measurement
junction consisting of a Pt-Pt13%Rh thermocouple with a
diameter of 0.2 mm welded onto it, was placed between the
center of the faces of two straight brick specimens, and the
bricks were tightly fastened to each other with Pt wires
with a diameter of 1 mm at two positions near the ends. The
specimen set was placed inside the furnace and was heated to
prescribed measurement temperatures. The optimal timings
for commencing the measurements are determined as
follows. After confirming that the temperature of the specimen had not fluctuated by more than 0:1 C over 5 min at
that temperature, a predefined current was passed through
the hot wire. By continuously maintaining a uniform temperature inside the furnace at a predefined level and applying
different currents to the hot wire, the increase in temperature
of the hot wire was measured three times at each current
level. The measurement results for the log t relation were
plotted, and the value of the thermal conductivity was
calculated.
Measurement of Thermal Conductivity of Magnesia Brick with Straight Brick Specimens by Hot Wire Method
Power
supply/Constant
current type
2625
Interface unit
HWM-15
EX-375L2
Electric furnace
Hot wire
Specimen
Digital multimeter
Agilent 34420A
Personal computer
PC
Thermocouple
Fig. 1
Structure and dimensions of the specimen used in hot wire method.
Heat source
Guard ring
Specimen
Water cooling plate
Heat receiving rod
Compensating heater
H
D1
D2
D3
Water
Water
Fig. 2 Structure and dimensions of the specimen used in stationary heat
flow method.
Differential thermocouple
Microvolt meter
2.2.2 Stationary heat flow method
The dimensions and the shape of the samples used in the
stationary heat flow method as provided in JIS R2616 are
shown in Fig. 2 (D1 ¼ 50 mm, D2 ¼ 54 mm, D3 ¼ 90 mm,
H ¼ 20 mm). Figure 3 shows a schematic outline of the
structure of the test equipment for the stationary heat flow
method. The heat source, which consists of Kanthal wires and
platinum wires, was placed on the test piece. The test piece
was placed on the heat receiving rod. It is most important to
avoid side-flow of the heat and to correctly measure the heat
flux Q. In this stationary heat flow method, the guard ring,
which is made of the same brick as the test piece, is placed
around the test piece. Therefore, the temperature gradient in
the test piece becomes the same as in the guard ring when
they are heated by the heat source, by which the side-flow of
the heat from the test piece is avoided. After the heater
produced by the heat source was inserted and the average
temperature between the upper and the lower surface of the
sample reached 350 C, the current was in a steady-state. This
steady-state condition was achieved when the temperature of
the upper and lower surfaces of the test piece had remained
constant for 30 min or longer. The heat transmitted through
the test piece was transferred through the heat receiving rod
which was made of copper with its high thermal conductivity.
Fig. 3 Structure of the experimental equipment in stationary heat flow
method.
The temperature of the water cooling plate equaled to that of
the heat receiving rod by controlling the amount of water
flowing in the water cooling plate. The heat transferred to
the heat receiving rod was absorbed by the flowing water
used for measurements. Denoting the heat passing through
the sample with Q, the following equation is derived for the
stationary state:
Q ¼ ð1 2 Þ
A
L
ð1Þ
Here, is the thermal conductivity of the sample, A and L
are the cross-section area and the length of the sample, 1
is the temperature at the upper surface of the sample, 2 is
the temperature at the lower surface of the sample, and the
temperature used in the stationary heat flow method is
¼ ð1 þ 2 Þ=2. Therefore, if the change in temperature for
the water between the upper and the lower surface of the
sample is measured at the steady state, it is possible to
calculate the thermal conductivity of the sample from the
above equation. The difference in temperature between
2626
Y. Saito, K. Kanematsu and T. Matsui
(b) 673K
22
20
18
16
14
12
Temperature rise of heat source, θ /K
24
25
20
15
10
5
0
10
1
10
100
25
20
15
10
5
0
1
1000
(d) 1273K
25
30
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
26
(c) 773K
Temperature rise of heat source, θ /K
(a) 623K
10
100
1000
15
10
5
0
1
10
Time, t /sec.
Time, t /sec.
20
100
1
1000
10
100
1000
100
1000
100
1000
Time, t /sec.
Time, t /sec.
30
18
16
14
12
10
10
100
20
15
10
5
0
1000
10
100
10
5
1000
22
20
18
16
14
12
10
20
15
10
5
1000
1
10
10
5
1000
1
10
Time, t /sec.
25
20
15
10
5
100
1000
20
15
10
5
0
0
0
100
100
25
25
1
10
100
1000
1
Time, t /sec.
Time, t /sec.
Time, t /sec.
15
Time, t /sec.
Temperature rise of heat source, θ /K
24
20
0
1
30
26
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
15
Time, t /sec.
28
10
20
0
1
Time, t /sec.
1
25
25
Temperature rise of heat source, θ /K
1
25
Temperature rise of heat source, θ /K
20
Temperature rise of heat source, θ /K
30
22
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
24
10
Time, t /sec.
Fig. 4 Increase in temperature of heat source wire with respect to log of time for insulating bricks.
the water inlet and the water outlet with a steady flow of
water (100 mlmin1 ) is measured with a T type differential
thermocouple. This difference in the temperature was
converted to the voltage by the microvoltmeter capable of
detecting miniscule differences in voltage. To correctly
measure the heat flux Q, Q is determined by proportional
calculation with a water calorimeter incorporating a compensating heater made of nichrome wire. The relation
between the temperature difference in water and heat Q is
calibrated with a compensating heater:
Q¼W
T1
T2 T1
ð2Þ
T1 : The difference in temperature between the water inlet
and the water outlet
T2 : The difference in temperature between the water inlet
and the water outlet when a compensating heater adds the
heat of W.
As a result, the thermal conductivity of the sample was
calculated from the following equation:
¼W
3.
3.1
L
T1
A ðT2 T1 Þð1 2 Þ
ð3Þ
Measurement Results and Discussion
Comparison of measurement results of heat-insulating bricks with hot wire and stationary heat flow
methods
First, Fig. 4 shows the changes in the temperature of the
hot wire versus the logarithm of time log t as measured at
different temperatures with the hot wire method using the
insulating brick specimens. The relation between and
log t was linear at every measurement temperature without
deviation from linearity, satisfying the following theoretical
equation for the method:7,9,10,13)
T2
log
T1
¼ 0:183I 2 R
ð4Þ
2 1
where I is the current (A) through the hot wire, R the electric
resistance (m1 ) of the hot wire at the measurement
temperature, is the increase in temperature (K) of the
hot wire from between T1 and T2 , and is the thermal
conductivity of the specimen brick (Wm1 K1 ). The values
of the thermal conductivity at different temperatures were
calculated using this equation.
Next, the values of the thermal conductivity of the heatinsulating bricks at 350 C (623 K) as obtained with the
two methods were compared. As seen in Fig. 5, the results
obtained with the hot wire method in accordance with JIS
R 2618 were higher by about 10% than those obtained
with the stationary heat flow method in accordance with JIS
R 2616. A number of researchers have reported that the
thermal conductivity as measured with the hot wire method
is often different from that measured with the stationary
heat flow method.2,14) One of the reasons for this result is
that the temperature measured with the former method does
not correspond to that measured with the latter method in
addition to that the thermal conductivity changes depending
on the temperature. Whereas the temperature measured with
the stationary heat flow method is the average of the values
-1
0.6
Thermal conductivity, λ /W m
K
0.7
-1
Measurement of Thermal Conductivity of Magnesia Brick with Straight Brick Specimens by Hot Wire Method
0.5
Stationary heat flow
method
Hot wire method
0.4
0.3
0.2
0.1
0
500
700
900
1100
1300
1500
Temperature /K
Fig. 5 Thermal conductivity of insulating bricks.
for the upper and the lower surface of the specimen, in the
former method it represents the temperature at a single point
of the specimen. The thermal conductivity obtained by the
stationary heat flow method will therefore correspond to that
by the hot wire method if the relation between the temperature and the thermal conductivity follows the linear
equation. However, it is difficult to decide this single point
of the temperature in the hot wire method. In this study, the
thermal conductivity of the insulating brick as obtained with
the hot wire method shows a tendency to increase as the
temperature increases. The relation between the temperature
and the thermal conductivity does not follow the linear
equation. The thermal conductivity as measured with the
stationary heat flow method, in which the average of the
temperature of the upper and the lower surface is 350 C
(623 K), is higher than that measured with the hot wire
method at room temperature. This suggests that the results
obtained with the two methods might be closer to each other
depending on the temperature at the upper and the lower
surface of the specimen in the measurement performed with
the stationary heat flow method. Furthermore, if the temperature rise changing the condition of the hot wire method,
reducing the amount of the temperature rise, it is possible to
bring it close to the average temperature in the stationary heat
flow method. In that case, the sensitivity decreases when the
temperature rise is reduced, and there is a possibility that the
accuracy of the thermal conductivity requested by the hot
wire method lowers. As mentioned above, it follows that the
absolute values of thermal conductivity and its dependence
on temperature as obtained with the two methods might not
be exactly the same even for specimens made of the same
material.
Tsukino et al.15) compared the values of the thermal
conductivity of lightweight and dense castable refractories as
obtained with the two methods, and reported that the value
obtained with the hot wire method was higher by 5 to 25%
than that obtained with the stationary heat flow method,
regardless of its absolute value. In addition, based on the
measurement results for heat-insulating bricks, Hayakawa
et al.2) reported that the values obtained with the hot wire
method tended to be approximately 30% higher than those
with the stationary heat flow method. Davis et al.16) measured
the thermal conductivity of heat-insulating bricks with the
two methods, compared the obtained results and explained
that the value of the thermal conductivity as obtained with the
hot wire method was the average of those in two directions,
2627
as well as that the difference between the results of the two
methods is attributable to the thermal anisotropy of the
specimens. A conceivable reason for the difference between
the results obtained with the two methods is the thermal
anisotropy of the specimens due to factors such as unevenness of the brick material and the direction of compression
during forming. While it is possible to clearly show the
thermal anisotropy of a specimen with the stationary heat
flow method, this is not possible in the case of the hot wire
method since the stationary heat flow method assumes
unidirectional heat flow, and the direction of measurement
can be chosen beforehand at the time of cutting the specimens
for measurement. In contrast, the hot wire method assumes
two-directional heat flow, and the obtained result is the
average of the thermal conductivity in the two directions.
Although it is difficult to perform estimation, in the present
study, to determine the factor which exerts the strongest
influence in causing the difference between the results of the
two methods, the difference was maintained well within the
range reported in past papers which compared the two
methods. Therefore, the authors believe that the values of the
thermal conductivity for heat-insulating bricks as obtained
using the new measurement equipment for the hot wire
method are reasonably reliable. However, to clarify the
differences between the methods and to use the findings as
feedback for improving the interpretation of the measurement results, it is necessary to accumulate more measurement
results with the two methods for various materials with
different thermal anisotropy and different characteristics of
dependence of the thermal conductivity on the temperature.
3.2
Measurement of thermal conductivity of magnesia
bricks
Figure 6 shows the change in temperature of the hot wire
versus the logarithm of time log t as measured at different
temperatures with the hot wire method using magnesia brick
specimens. In all graphs, the relation between and log t
became linear after approximately 10 s of the measurement
time. In the graphs for 473 and 773 K, the log t curves
deviated from linearity at about 120 s and thereafter.
Deviation from linearity was observed to a small extent at
temperatures higher than 773 K. A number of past reports
have discussed the reasons why the log t curves are not
linear at the beginning of the measurement.5,17) Apart from
the fact that the log t relationship forms a curve for small
t, the hot wire has a certain mass, and part of the energy
supplied to it is consumed for heating that mass. In addition,
the difference in heat capacity between the hot wire and the
brick specimens and the existence of layers of air between the
wire and the bricks might influence the log t relationship.
Considering the combined effects of these factors, it is not
appropriate to use the values in this region of the present
test for the calculation of the thermal conductivity.
The theoretical equation for the hot wire method (eq. (4))
mentioned in a number of studies is valid when the log t
relationship is linear. In the region where increases nonlinearly, it appears that the heat flow from the hot wire
reaches the surfaces of the specimen brick and subsequently
dissipates into the surrounding atmosphere. After this, the
temperature at the center of the specimen changes following
2628
Y. Saito, K. Kanematsu and T. Matsui
(a) 473K
(b) 773K
(c) 1273K
(d) 1473K
9.2
9
8.8
8.6
8.4
8.2
8
1
10
100
1000
11
10.8
10.6
10.4
10.2
10
9.8
9.6
9.4
9.2
9
Time, t /sec.
1
10
9.5
9
8.5
8
7.5
9
8.5
8
7.5
7
6.5
6
7
1000
9.5
1
10
100
1
1000
10
100
1000
100
1000
100
1000
Time, t /sec.
Time, t /sec.
10.8
10.2
10
9.8
9.6
9.4
9.2
1
10
100
1000
11
10.8
10.6
10.4
10.2
10
9.8
9.6
9.4
9.2
9
Time, t /sec.
1
10
100
10.5
Temperature rise of heat source, θ /K
10.4
Temperature rise of heat source, θ /K
10.6
9
10
9.5
9
8.5
8
7.5
1
10
10.4
10.2
10
9.8
9.6
9.4
9.2
9
1
10
100
1000
Time, t /sec.
11
10.8
10.6
10.4
10.2
10
9.8
9.6
9.4
9.2
9
10
8
7.5
7
6.5
1000
1
10
Time, t /sec.
10.5
10
9.5
9
8.5
8
7.5
7
1
100
1000
Time, t /sec.
Fig. 6
100
Temperature rise of heat source, θ /K
10.6
9
8.5
Time, t /sec.
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
10.8
9.5
6
7
1000
Time, t /sec.
11
Temperature rise of heat source, θ /K
100
10
Time, t /sec.
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
11
10.5
Temperature rise of heat source, θ /K
9.4
Temperature rise of heat source, θ /K
9.6
Temperature rise of heat source, θ /K
Temperature rise of heat source, θ /K
10
9.8
1
10
100
1000
9.5
9
8.5
8
7.5
7
6.5
6
1
10
Time, t /sec.
Time, t /sec.
Increase in temperature of heat source wire with respect to log of time for magnesia bricks.
the changes in the temperature distribution inside the
specimen. Therefore, it is not appropriate to use the values
in this non-linear region for the calculation of the thermal
conductivity. The usable values of are only those in the
linear portion.
When the thermal conductivity of a specimen is high and
its size is small, the heat flow from the hot wire reaches the
surfaces quickly, and for this reason the heat either dissipates
into the environment through the surfaces or accumulates
near the surfaces, thus notably affecting the changes in
temperature distribution with time inside the specimen. Since
this also influences the rate of increase in temperature of the
hot wire, the value of the thermal conductivity as calculated
from the values obtained in this way will inevitably include
an error. For this reason, the hot wire method is not suitable
for determining the thermal conductivity of materials with
high thermal conductivity where the heat can quickly reach
the outer surfaces. In this regard, Hayashi et al.8) pointed out
that the most important factor for expanding the applicability
of the hot wire method to such materials is the size of the
specimens. In other words, the specimens should be as large
as possible to increase the time necessary for the heat to flow
from the hot wire to the outer surfaces of the specimens.
Based on this, Hayashi et al. proposed suitable specimen
sizes for different target materials which take into account the
level of thermal conductivity. In addition, using specimens of
various materials with different levels of thermal conductivity, such as polyester resins, gypsum, graphite-clay and
SiC-clay composites, heat-insulating and chamotte bricks,
they examined the relationship between the point where the
curve deviated from linearity and the value of the thermal
conductivity. As a result, they derived the following
empirical equation governing the relation between the point
Td (s) at which begins to deviate from the linear relation,
the radius r (cm) of the specimen and its thermal conductivity
(calcm1 s1 C1 ):
Td ¼
r2
:
10
ð5Þ
In SI units, this equation is as follows:
Td ¼ 4:18 106
r 02
;
10 0
ð6Þ
where r 0 is in units of m and 0 is in units of Wm1 K1 .
In actual measurements with the hot wire method, the size
of the sample is not infinite. In this regard, Horrocks et al.18)
theoretically considered the effect of the diameter of the
sample and reported that the error margin decreases as t=r 2
decreases (radius r, thermal diffusivity ). The thermal
conductivity is proportional to the thermal diffusivity if it
is assumed that the changes in specific heat and density at
high temperatures are not substantial since ¼ Cp , which
becomes t ¼ Cr 2 = if t=r 2 ¼ C is taken as an index (C is a
constant). This relation between the radius r of the sample
and the thermal conductivity at time t is similar to the
empirical eq. (5). Hayashi et al.8) reported that a minimum
radius obtained from the empirical eq. (5) corresponds to that
from the findings obtained by Horrocks.
We applied the above eq. (5) to the three measurement
results for magnesia bricks at different temperatures. Here,
Measurement of Thermal Conductivity of Magnesia Brick with Straight Brick Specimens by Hot Wire Method
Table 2 Deviation point Td0 as observed in Figs. 4 and 6, and Td as
calculated from eq. (5).
Temperature
/K
Thermal
conductivity
/Wm1 K1
Distance from
heat source
/mm
Observed
value Td0
/s
Calculated
value Td
/s
473
10.1
57
141
135
473
9.4
57
111
145
473
9.7
57
126
141
773
9.6
57
112
141
773
9.2
57
127
148
773
9.8
57
127
139
1273
6.3
57
—
216
1273
6.3
57
—
218
1273
6.5
57
—
208
1473
5.4
57
—
250
1473
5.6
57
—
243
1473
5.6
57
—
242
Thermal Conductivity, λ /W m
-1
K
-1
—: Td0 was not observed as shown in Figs. 1–3.
20
18
16
14
12
Ref.(5)
Ref.(19)
Measured
10
8
6
4
2
0
0
200
400
600
800
1000
1200
1400
1600
Temperature, T/K
Fig. 7
Thermal conductivity of magnesia bricks.
the thermal conductivity was calculated based on the portion
of the curves describing the increase in temperature between
18 and 90 s, where all of them were clearly linear at any of the
measurement temperatures. The position of Td was calculated by substituting r with the shortest distance from the heat
source (hot wire) to the outer surface. Table 2 compares the
calculated values of Td calculated with those of Td0 as
obtained from Fig. 6. All measurements at 473 K deviated
from linearity at about 120 s, while the measurement results
agreed well with the calculations performed in accordance
with the empirical eq. (5). Furthermore, as seen in Fig. 6,
regarding the conditions of the present study, the changes in did not deviate from linearity at 1273 and 1473 K. Some
researchers have reported that the thermal conductivity of
magnesia bricks fell drastically as the temperature increased5,19) due to an increase in phonon scattering. As seen in
Fig. 7, the value of thermal conductivity for the magnesia
bricks used in the present study tended to decrease from that
at 473 K as the temperature increased. For this reason, the
position of Td as calculated from the equation exceeded
180 s at 1273 and 1473 K. This indicates that the curves do
not deviate from linearity, at least for the conditions of the
present study, and thus the calculated result and the test result
are in agreement. For reference purposes, we also measured
and studied in the same manner the changes in temperature
with time at different temperatures by using heat insulation
2629
brick specimens with a thermal conductivity within the range
specified in JIS R 2616. The result was that none of the
log t curves deviated from linearity in the test conditions
for the present study. In fact, the heating curves of the hot
wire obtained through actual measurements did not deviate
from linearity, thus agreeing with the estimation based on
eq. (5).
Next, we measured the thermal conductivity as obtained
from analysis of the linear portions of the curves, as well as
the dependence of the thermal conductivity on the temperature. The obtained values of the thermal conductivity were
equal to or lower than 10 Wm1 K1 , which is within the
applicable range of the recently established JIS R 2251-1.
The analysis is fundamentally the same as the determination
of the thermal conductivity of heat-insulating bricks mentioned in the previous subsection 3.1. Our aim was to
compare the results of measuring the thermal conductivity of
magnesia bricks with the hot wire method to the results
obtained with the stationary heat flow method. However, it is
not straightforward to obtain reliable values for the thermal
conductivity of magnesia brick with the stationary heat flow
method, especially in the temperature range of its use in
converters, that is, between room temperature and 1273 K. In
addition, there are different views regarding the interpretation of the measurement results of the thermal conductivity of
magnesia bricks obtained with the hot wire method, and as
a result there are ambiguities in the results. For instance,
Mittenbühler20) found two linear portions with different
slopes in a log t curve for magnesia bricks. He attributed
the existence of the region with the smaller slope in the first
4 min to the poor contact between the hot wire and the
specimen bricks, and more specifically to the specimen
configuration, whereby the hot wire is placed in a groove cut
into the brick surface and the gap is filled with magnesia
brick powder, which produces a difference in porosity
between the bricks and the packed layer around the hot wire.
Assuming, as above, that Mittenbühler ignored the first
linear portion of the curve and based his measurements on the
later linear portion, he determined the value of the thermal
conductivity to be 5.93 kcalm1 h1 C1 . On the other
hand, Hayashi et al.8) questioned this interpretation, maintaining that it is unlikely for a small gap between the hot
wire and the bricks to exert an effect on the measurement
for a period of time as long as 4 min. In fact, the heating
curves of hot wires which they obtained with other types
of bricks in the same packing conditions began to behave
linearly after about 12 s, which indicates that differences in
packing condition do not affect the heating curve for as
long as 4 min. Therefore, with respect to the interpretation
provided by Mittenbühler, Hayashi et al. considered that the
point where the slope changes is the point of deviation from
linearity Td, and therefore, based on the linear portion in
the first 4 min, determined the thermal conductivity to be
13.5 kcalm1 h1 C1 . In all curves at different temperatures obtained in the present study, we confirmed linear
regions 18 s after the beginning of the measurement, which
is considerably shorter than the 4 min that Mittenbühler
reported and closer to the value reported by Hayashi et al.
Figure 7 presents a comparison between the thermal conductivity of magnesia bricks as calculated by the authors
2630
Y. Saito, K. Kanematsu and T. Matsui
from the linear portions and those obtained by Hayashi
et al. with the hot wire method by using small specimens
of cylindrical and other shapes. The results are close to
each other in terms of absolute value and show a similar
dependence on temperature, namely decrease at higher
temperatures.
As stated above, the thermal conductivity of magnesia
bricks tends to decrease as the temperature increases, and as a
result the point of deviation from linearity Td shifts away
from the zero point, thus making the linear portion longer and
the hot wire method more suitable at higher temperatures. In
industrial applications, magnesia bricks are used mainly as
safety lining of converters, and since the brick temperature is
lower during the initial stage of heating the converter and
after tapping than during the stage of oxygen blowing, the
most important property of magnesia bricks in actual use is
their thermal conductivity over a wide temperature range.
However, the thermal conductivity of magnesia bricks might
fluctuate depending on the type and the distribution of
impurities, the difference in porosity, the existence of glassy
phases, and so on, even when the purity of its constituent
MgO is essentially the same. For this reason, to measure the
thermal conductivity of magnesia bricks accurately in the
temperature range of their industrial use with the hot wire
method, it is important to be able to predict and examine the
point where the log t curve deviates from linearity, and it
is necessary to closely examine the measurement readings in
order to identify the point of deviation correctly and avoid
erroneous final results.
4.
Conclusion
In view of the revision of the JIS system regarding the
thermal conductivity of refractory materials and its incorporation into the ISO system, the application of the hot wire
method in the measurement of the thermal conductivity of a
wide variety of materials is under evaluation. In this regard,
the authors have studied the conditions for measurement
of the thermal conductivity by focusing on bricks made of
magnesia, which is a commonly used material with high
thermal conductivity among non-carbon materials.
To measure the thermal conductivity of refractory bricks at
high temperatures, the authors constructed a high-capacity
electric furnace capable of accommodating a specimen set
composed of straight bricks without preprocessing. Subsequently, the increase in temperature of the hot wire was
measured and the linear relationship between the increase in
temperature and the logarithm of time log t was investigated
together with the relationship between the time Td at which
the log t curve ceases to behave linearly and the shortest
distance between the hot wire and the outer surface of the
specimen. Consequently, as reported previously, Td was
found to be proportional to the square of the shortest distance.
In actual measurements of the thermal conductivity of the
refractory material, if its approximate value is known, these
relationships provide guidelines for the time range on which
the analysis should focus and a criterion for estimating the
adequacy of the measurement results. The present study
indicates that the thermal conductivity of bricks with high
heat conductivity, such as magnesia bricks, can be determined accurately even when using straight brick specimens
if the point where the log t curve ceases to behave
linearly is identified and the value of the thermal conductivity
is calculated only on the basis of the linear relationship.
Acknowledgement
The authors would like to express their gratitude to
Dr. Kunio Hayashi, former professor at Kyoto Institute of
Technology, and Mr. Naoki Inamoto, Director of Spectra
Inspection Laboratory Co., Ltd., for their guidance and
assistance in the construction and automation design of the
equipment for measuring the thermal conductivity with the
hot wire method. The authors would also like to thank
Kurosaki Harima Corporation for supplying brick specimens
for the present study.
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