断熱材の熱特性～熱伝導率および比熱測定～

ニチアス㈱ 浜松研究所
大村 高弘

講演内容l 熱伝導率測定における問題点とそれに対する取り組み
l 各種熱伝導率測定方法と測定結果の比較
l 熱伝導率の推定式
l 断熱材の比熱測定

断熱材の熱伝導率測定に関する問題点
l 標準物質がない→装置間の誤差

精度確認ができない。
l 広い温度領域における断熱材の熱伝導率や比熱が正確に示されていない。
特に800℃以上の高温や真空下のデータ。

151510(λobs－λcalc)×100/λcalc(λobs－λcalc)×100/λcalc

201050-5-10-15300

400

500

600

700

800

Temperature [K]Fig. 1 Deviations of thermal conductivity
round-robin test results from values calculatedwith the corrected equation for fibrous alminasilica.

50-5-10-15-20-25300

400

500

600

700

Temperature [K]Fig. 2 Deviations of thermal conductivity
round-robin test results from values
calculated with the corrected equation forcalcium silicate.

800熱伝導率の測定精度向上にた取り組み
1. 異種測定法による結果を比較
2. 測定結果と推定式による結果との比較

1. 各種測定法が可能な装置の開発：定常法と非定常法の比較
定 常 法：保護熱板法
非定常法：非定常熱線法、周期加熱法、ホットディスク法
2. 精度の高い推定式の提案:温度と嵩密度の関数

間接加熱法定常法

軸方向定常熱流

絶対法

縦型絶対法
平板絶対法
可動間隙法

比較法

縦型比較法
平板比較法

経方向定常熱流

絶対法

同心円筒法
同心球法

比較法
非定常法

軸方向非定常熱流

同心円筒法

パルス状加熱法
ステップ状加熱法
波面分割干渉法
周期加熱法
光音響法
強制レーリー散乱法（パルス状加熱）
ラプラス変換法（平板）（任意加熱）

経方向非定常熱流

定速昇温法
熱線法（ステップ状加熱）
ラプラス変換法（円筒）

直接加熱法
定常法
非定常法

軸方向熱流（Kohlrausch法 ,積分法）

径方向熱流（Angell 法 ）軸方向熱流（物性値同時測定法）

Cooling heater

Specimen

Gap

Guard heater
Metering section
heaterQ＝

λ θ1－θ2

Specimen
Cooling heater(a) Solid figure of Double-side mode of operation
Cooling heater

Auxiliary heater
Insulation

Metering section
heaterHeat flow

Metering section
heaterHeat flow

Guard heater

Specimen
Specimen
Heat flow

Guard heater

Cooling heater(b) Single-side mode of operation

Cooling heater(c) Double-side mode of operation

Fig. 3 Schematic of the Guarded Hot Plate method(GHP method)dHot Wire

Thermocouple

λ＝SpecimenQ

ln t2/t1

4π θ2－θ1

Fig. 4 Schematic of the Hot Wire method
Specimen

NickelHeating part

Electrode

λ＝Polyimide sheet

Fig. 5 Schematic of sensor in Hot
Disk method.

QDτ

π3/2a ΔT τ

5 ～10 ℃

20

Top half of specimen

Thermal sensor2

Bottom half of specimen

Temperature( ℃)

20Thermal sensor1

Thermal sensor1

1010

3 ～6 ℃
1000

Thermal sensor2990

Thermal sensor3

Thermal sensor3

Time (hour)

Specimen cross section

φ＝arg
A＝Aj
As

＝

sinhkx 1+i
sinhkL 1+i
cosh2kx－cos2kx

ω

κ＝
ω＝2k2
2π

cosh2kL－cos2kL

φ：time lag,κ：thermal diffusivity,
λ：thermal conductivity.

T：period,ρ：density

T

Heat waves

λ＝ρcκ熱伝導率測定装置

測定装置（GHP法）
200

Guard heater

Water tank

120

Metering
sectionheater
Thermal insulation

heater

円筒
ヒ－Bell glass

タ

Cooling unit

Specimen
2 50

Cylindrical

Thermal insulation
Auxiliary heater
Thermal insulation

Vacuum pumpTemperature controller

Scanner

Water tank

Digital multimeter
Computer

測定装置（周期加熱法、非定常熱線法）
Water tank
Insulation

Cylindricalheater

円筒BellヒGlass－タ

Hot Wire

Cooling unit
Specimen
Specimen
Cyclic heater
Insulation
Auxiliary heater
Insulation

Vacuum pump
Temperature Controller
Function Generator

Scanner
Digital Multimeter
ComputerTable 2-3
Property

Developped measuring apparatus.
Principle of measurement
Temperature
Apparatus
range [℃]C 170
Thermal conductivity
Transient hot-wire method-170～40
Thermal diffusivity
Cyclic heat method
Specific heat
Hot Disk method
H1000
Thermal conductivity
Transient hot-wire method
100～1000
Thermal diffusivity
Cyclic heat method
HV1000 Thermal conductivity
Transient hot-wire method
100～1000
Thermal diffusivity
Cyclic heat method
H1300
Thermal conductivity
Guarded hot plate method
100～1300
Thermal diffusivity
Cyclic heat method
S1000
Specific heat
Drop caloriemeter method
100～1000
Table 2-4 Measurment error of each method
Method ofmeasurement
Guarded hot platemethod
Transient hot-wiremethod
Cyclic heat method
Hot Disk method
Drop caloriemeter
methodError [%]
65Under 10 (depending onspecimen)
Thermal conductivity ：3
Thermal diffusivity ：7：3
Specific heat8

：Transient hot-wire method：Cyclic heat method

・ρ=393 kg/m+10%

0.3-10%0.2

Least squares approximation
by a quadratic equation

0.1
003200400600Temperature [℃]800Fig. 6 Thermal conductivity oflightweight insulation with bulk
density ρ=393 kg/m3.

1000

Thermal conductivity [W/(m K)]

Thermal conductivity [W/(m K)]

0.40.4・：Transient hot-wire method：Cyclic heat method

ρ=458 kg/m 3+10%

0.3-10%0.2
Least squares approximation
by a quadratic equation0.100200400600

Temperature [℃]800Fig. 7 Thermal conductivity oflightweight insulation with bulkdensity ρ=458 kg/m3.

Al2O3:SiO2:Fe2O3=27:32:6

1000

0.4・

0.3
0.2
0.1

：GHP method under atmosferic pressure：Cyclic heat method underatmosferic pressure：GHP method under 1.3 Pa：Cyclic heat method under 1.3 Pa+10%+10%

Atmosphericpressure-10%
1.3 Pa

00500

0.4・

-10%

Least squares approximation
by a quadratic equation

Thermal conductivity [W/(m K)]

Thermal conductivity [W/(m K)]

H1300を使った測定比較

1000

Temperature [℃]Fig. 8 Thermal conductivity of alumina
fiber insulation with bulk density ρ= 205kg/m3.

0.3+10%：H1000(Atmospheric pressure)：H1300(Atmospheric pressure)：H1000(1.3Pa)：H1300(1.3Pa)

-10%

0.2

+10%

Atmosphericpressure

-10%

0.1
1.3 Pa

00500

1000

Temperature [℃]Fig. 9 Comparison thermal conductivity ofalumina fiber insulation (ρ= 205 kg/m3) by
H1000 with H1300 using cyclic heat method.

異種測定法間の差
l 保護熱板法、非定常熱線法、周期加熱法、ホットディスク法に関して、同一試験体であれば、測定結果は±10%以内で一致する。

未知の材料に適用可能

推定式の結果と測定結果の比較による精度向上
なぜ推定式が必要か？
低嵩密度（20kg/m3以下）断熱材は、ふく射エネルギーを透過させてしまうため、測定誤差が大きい。装置に依存してしまう。

測定精度の高い高嵩密度断熱材のデータから推定式を作成

測定結果と推定結果を比較

異種測定法によるチェックが難しい

精度向上

従来の推定式と問題点
最も実用的な式

bl = ar + + c
ra, b, cは係数
ρは嵩密度

＊その他の数多くの推定式
箇々の素材の熱物性値や素材同士の接触熱抵抗を必要としている

開発スピードについて行けず、実用性に欠ける

従来の推定式の問題点
1. 温度の関数になっていない
2. 嵩密度のみの関数：他の情報（固体、ふく射、気体による伝熱効果）が得られない
3. 高嵩密度試験体で推定式を作成すると、低嵩密度側は外挿になるため、推定精度が悪い

根本的な原因試験体ごとに、最小自乗法を使って係数a, b, c を導出しているため

Thermal conductivity [W/(m K)]

0.30:Measured values at 200℃
:Measured values at 300℃
:Measured values at 400℃
:Calculated line using all data at 200℃
:Calculated line using all data at 300℃
:Calculated line using all data at 400℃
:Calculated line using 5 data at 200℃
:Calculated line using 5 data at 300℃
:Calculated line using 5 data at 400℃

・ 0.25

0.20
0.15
0.10
0.05
0050

100

150

200

Bulk density [kg/m3]

250

Fig. 10 Calculated results by least square method.

300

係数UおよびV0の決定真空下の熱伝導率λv：

B 3lv = Ar + Trλv
B /ρAρ

切片=Aρ

傾き=B/ρ

T3切片

傾きABρ

1/ρ

Thermal conductivity [W/(m K)]

・0.05
0.04
0.03
0.02

：166kg/m3：293kg/m3：288kg/m33：227kg/m

0.01
00

100

200

300

400

500

600

6

[×10 ]
3
Third power of absolute temperature [K ]Fig. 11 Thermal conductivity of rock wool with four kinds ofbulk density under evacuated condition (2 Pa).

140.015

・ 0.010

Gradient of solid line in4 Fig. 5-8[W/(m・K ]Intercept of solid line in Fig. 5-8[W/(m K)]

[×105]

Least squares approximation
by a linear equation

0.005

00100

2003003

Bulk density [kg/m ]Fig. 12 Intercepts of each line in Fig. 11vs. bulk density.

12

Least squares approximation
by a linear equation

1086
4
2
0
00.002

0.004

0.006

0.008

3

Reciprocal of bulk density [m /kg]

Fig. 13 Gradients of each line in Fig.
11 vs. reciprocal of bulk density.

：Measured values at 20℃：Measured values at 60℃：Measured values at 100℃
：Calculated line by Eq.(5-36) at 20℃：Calculated line by Eq.(5-36) at 60℃：Calculated line by Eq.(5-36) at 100℃

・ 0.070.06
0.05
0.040.030.02
0501001502002503

Bulk density [kg/m ]Fig. 14 Thermal conductivity ofrock wool.

300

Thermal conductivity [W/(m K)]

Thermal conductivity [W/(m K)]

0.08

0.3
：Measured values at 200℃
：Measured values at 300℃
：Measured values at 400℃
：Calculated line by Eq.(5-36) at 200℃
：Calculated line by Eq.(5-36) at 300℃
：Calculated line by Eq.(5-36) at 400℃

・0.25

0.2
0.15
0.1
0.05
0050100150200250300

Bulk density [kg/m 3]

Fig. 15 Thermal conductivity of rockwool.

Thermal conductivity [W/(m K)]

0.30

・ 0.25

600℃

0.20

500℃

0.15

400℃

0.10

300℃

0.05

100℃

00200℃

50100150

3200

Bulk density [kg/m ]Fig. 16 Comparison of reference data with calculated results.

250

真比熱と平均比熱

真比熱

1 d(H s1 - H base )cst =m s dq s1

平均比熱

1 H s1 - H s 2csm =ms q s1 - q s 2②⑤ －1275

φ89⑥152φ 191⑤ －2①140⑦⑧③600⑨④250
700① Cylindrical heater⑤-2 Thermocouple② Specimen⑥ Measuring water tank

③ Digital multimeter⑦ Monitoring water tank

④ Temperature controller⑧ Support plate⑨ Personal computer⑤-1 Thermocouple

Fig. 17 Schematic of specific heat measuring apparatus(Type: S1000)

Enthalpy [kJ/kg]

1200:Measured values:Eq.(2-90)+10%-10%

1000
800
600
400
200
00200

400 600 800 1000 1200
Temperature [℃]Fig. 18 Enthalpy of the standard
specimen SRM720 Synthetic
Sapphire (α-Al2O3)

Mean specific heat [kJ/kg/K]

1400

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
00+10%-10%:Measured values:Eqs.(2-15) and (2-90)

200400600

800 1000 1200

Temperature [℃]Fig. 19 Mean specific heat of thestandard specimen SRM720
Synthetic Sapphire (α-Al2O3)

Specific heat [kJ/kg/K]：Measured values (Mean specific heat)：Mean specific heat by Eq. (6-9)：True specific heat

+5%
-5%

SiC refractory material
ρ=2800kg/m3
Ts1=290～1000℃

200400 600 800 1000 1200
Temperature [℃]Fig. 20 Mean and true specific heats of
SiC refractory.
Specific heat [kJ/kg/K]

Specific heat [kJ/kg/K]

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
00

1.6
1.4
1.2
10.8
0.6
0.4
0.2
00

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

：Measured values (Mean specific heat)：Mean specific heat Eq. (6-9)：True specific heat

+5%-5%

Rockwool
ρ=100kg/m3
Ts1=100～700℃

200

400 600 800 1000 1200
Temperature [℃]Fig. 21 Mean and true specific heats ofrock wool.

：Measured values (Mean specific heat)：Mean specific heat by Eq. (6-9)：True specific heat

+5%-5%

Alumina silica fiber insulation
ρ=130kg/m3
Ts1=100～1000℃

200

400 600 800 1000 1200
Temperature [℃]Fig. 22 Mean and true specific heats of alumina silica fiber.

+5%-5%

Calcium-silicate insulation3
ρ=130kg/m
Ts1=120～1000℃

200

400 600 800 1000 1200
Temperature [℃]Fig. 23 Mean and true specific heats ofcalcium-silicate insulation.
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
00Specific heat [kJ/kg/K]：Measured values (Mean specific heat)：Mean specific heat by Eq. (6-9)：True specific heatSpecific heat [kJ/kg/K]

Specific heat [kJ/kg/K]

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
00

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
00

：Measured values (Mean specific heat)：Mean specific heat by Eq. (6-9)：True specific heat

+5%-5%

SiO2-glass 3
ρ=2465kg/m
Ts1=200～600℃

200

400 600 800 1000 1200
Temperature [℃]Fig. 24 Mean and true specific heats of
SiO2-glass.

+5%-5%
Fluoro rubber
ρ=1858kg/m 3
Ts1=100～200℃：Measured value (Mean specific heat)：Mean specific heat by Eq. (6-9)：True specific heat

50100 150 200
Temperature [℃]250300Fig. 25 Mean and true specific heats of Fluoro rubber.