JPH0718826B2 - Thermal conductivity measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention directly determines the thermal conductivity by applying a steady heat flow to an object to be measured (hereinafter referred to as a sample), which is called a stationary method among the thermal conductivity measuring methods. One of the requirements is to measure the thermal conductivity of polymer materials and ceramics, which have a relatively low thermal conductivity, with a sample smaller than the conventional one and in a shorter measurement time.

[Prior Art] The flat plate method and the laser flash method have been mainly used for the measurement of the thermal conductivity of polymer materials, ceramics, etc. having relatively low thermal conductivity (eg, Magrich, Cesaryan, Perekky edition). , "Introduction to Thermophysical Properties Measurement Method, 1st
Volume, Review of Measuring Techniques ", 1984, Plenum Press,
New York; Maglic, Cezairliyan, Peletsky, `` Compend
ium of Thermophysical Property Measurement Method
s, Volume 1, Survey of Measurement Techniques '', 198
4, Prenum Press).

In the flat plate method, an electric heater is attached to one side of a disk-shaped sample with a diameter of 20 to 50 cm and a thickness of 1 to 5 cm, and a water-cooled heat sink is attached to the other side to allow heat to flow in the thickness direction of the sample, and the temperature gradient generated there. Determine the thermal conductivity from the heat generation value of the heater (for example, issued by the Japanese Standards Association, thermal conductivity measurement method for heat insulation materials (flat plate direct method), JIS A 1413, 1977). However, in this method, it is necessary to attach a protective heater around the sample in order to allow all the heat generated by the heater to flow in the thickness direction of the sample, and to control the temperature to be equal to that of the sample. Further, since the sample is large, it takes time until the temperature becomes constant, and it takes a long time of about 30 minutes to several hours to perform one measurement.

The laser flash method measures the thermal diffusivity of the sample from the time change of the temperature rise of the back side when the surface of a disk-shaped sample with a diameter of 10 mm and a thickness of 2 mm is irradiated with a pulse laser, (1)
The thermal conductivity is calculated using an equation.

λ = αCρ (1) where α is thermal diffusivity, λ is thermal conductivity, C is specific heat, and ρ is density. In this method, the sample required is small and the measurement time is short, but since the thermal conductivity is indirectly determined from the thermal diffusivity of the sample, the specific heat and density of the sample are determined in advance to measure the thermal conductivity. There is a need. Further, it is difficult to use this method for a material such as a heat insulating material having a lot of voids, for which the relation of the formula (1) is not accurately established. In addition, the laser flash method measures the thermal diffusivity by instantaneously giving a large temperature rise to the sample surface, so it is possible to measure materials that easily melt such as thermoplastics and materials that have a large temperature dependence of thermal conductivity. Not suitable for.

[Object of the Invention] An object of the present invention is to directly measure the thermal conductivity of a small sample having a low thermal conductivity by using a stationary method in a short time without depending on other physical properties such as specific heat.

[Structure and Action of the Invention] In order to accurately measure the thermal conductivity of a sample, a uniform heat flow density is applied in a certain direction of the sample, and the magnitude of the heat flow density and the temperature gradient in the heat flow direction are accurately measured. It is necessary to. In order to provide a uniform heat flow density for a small sample, the present invention utilizes radiative heat exchange between the surface of the sample being heated or cooled in a vacuum and the surroundings. That is, in the thermal conductivity measuring method according to the first invention of the present application, the heat flow density in the thickness direction of the sample is configured to be equal to the heat flow density of heat lost by radiative heat exchange between the sample surface and the surroundings. The heat flow density is expressed by the equation (2) using the hemispherical total emissivity of the surface of the sample and the temperature of the sample and the ambient, using the Stefan-Boltzmann law. Where q is the heat flow density generated by radiative heat exchange between the sample surface and the surroundings, ε _ht is the total hemispherical emissivity of the sample surface, σ is the Stefan-Boltzmann constant, T _s
Is the surface temperature of the sample, and T _e is the ambient temperature.

q = ε _ht σ (T _s ⁴ −T _e ⁴ ) (2) To measure the temperature gradient in the heat flow direction, a flat sample is embedded on the surface of a copper block and it is assumed that the temperature of the copper block is uniform. Then, the temperature gradient in the thickness direction of the sample is obtained from the temperature difference between the copper block and the sample surface. Since the sample is minute, temperature measurement is non-contact measurement using a thermal imager. The method described so far is called a passive method in the present invention, and by using this method, the thermal conductivity of a minute low thermal conductivity sample can be easily measured in a short time.

On the other hand, in the passive method, when the thermal conductivity of the sample is relatively high or the temperature difference between the sample and the surroundings is small, the temperature difference in the sample thickness direction is small and measurement is difficult. In such a case, apply a metal foil to the surface of the sample and heat it electrically, or irradiate the sample surface with light to uniformly heat the sample surface and forcibly apply a large temperature gradient to the sample. . This method is called an active method in the present invention. In the active method, the heating amount is adjusted so that the temperature of the copper block and the sample surface become equal, and the hemispherical total emissivity of the black paint on the sample surface can be measured simultaneously from the heat generation amount per unit area on the sample surface at this time. Is.

Further, the active method can measure the thermal conductivity in the atmosphere or an inert gas although the measurement accuracy is lowered.
In this case, the estimation of heat loss due to convection from the sample surface becomes a problem, but the amount of heat generated per unit sample surface area when the temperature of the copper block and the sample surface are equal is applied by applying the above-mentioned method of measuring the total hemispherical emissivity. Measure the convection heat transfer coefficient from
The heat loss due to convection can be estimated.

[Example] FIGS. 1A and 1B show structures of a sample and a copper block in the passive method. First, prepare a rectangular parallelepiped copper block 2 with a size of 10 × 35 × 60 mm, and insert 3 in the center of the surface.
Make a dimple of size 25 x 25 mm. The back side of this copper block has a thickness of 0.1 mm to heat the block uniformly.
The stainless steel heater 5 of the epoxy resin insulation layer 4
Stick through. A pair of electrodes 7 for supplying an electric current to the heater is attached to both ends of the heater. Further, a thermocouple 6 for temperature measurement is screwed to the center of the copper block.

Next, sample 1 of a size that fits exactly into the depression on the surface of the copper block.
Prepare and embed in this part. In order to improve heat conduction, the bonding surface between the sample and the copper block is bonded with an epoxy adhesive in a thin layer as much as possible so that gaps and bubbles are not generated. When the sample is a thermoplastic resin, the copper block may be heated in a vacuum to melt and degas the sample, and then the sample may be poured into the recess. Make sure that the thickness of the sample is as uniform as possible and that the surface of the sample and the copper block are on the same plane. In order to realize more accurate and uniform radiant heat exchange and temperature measurement by a thermal imager, heat-resistant black paint 3 having a constant emissivity is applied to the surface of the sample and the copper block.

FIG. 2 shows a block diagram of an apparatus in the present thermal conductivity measuring method. First, sample 1 and copper block 2 are water-cooled vacuum container 12
The sample surface is held vertically in the center of, and the inside of the vacuum vessel is evacuated to a vacuum degree of 1 × 10 ⁻⁴ Torr or less. Next, a constant current is applied to the heater on the back surface of this copper block by a direct-current stabilizing power source to heat it, the copper block is kept at a constant temperature of about 50 ° C., and sample 1 is heated from the back surface side. At this time, the sample surface is cooled by radiative heat exchange with the surroundings, so heat flows from the copper block toward the sample surface, and the sample surface temperature is lower than that of copper because the thermal conductivity of the sample is smaller than that of copper. It will be lower than the surface temperature. In this case, the heat flow density in the thickness direction of the sample becomes equal to the heat flow density of heat lost by radiative heat exchange between the sample surface and the surroundings.

FIG. 3 shows one example of the temperature distribution on the sample and the copper block surface. In measuring the thermal conductivity, the temperature difference ΔT between the surfaces of the sample 1 and the copper block 2 is measured from the outside of the vacuum container through the optical window 13 by the thermal imager 14 as shown in FIG. Assuming that the thermal conductivity of copper is sufficiently larger than that of the sample and the temperature of the entire copper block is uniform, and the temperature of the boundary surface between the sample back surface and the copper block is equal to the temperature of the copper block surface, The temperature difference ΔT on the sample surface becomes equal to the temperature difference between the sample front surface and the back surface, that is, the temperature difference in the heat flow direction. Therefore, assuming that the heat conduction in the width direction of the sample can be ignored, the heat conductivity λ of the sample is expressed by the equation (3).
Here, ε _ht is the hemispherical total emissivity of the black paint, d is the thickness of the sample, and ΔT is the temperature difference between the front surface and the back surface of the sample.

λ = ε _ht σd (T _s ⁴ −T _e ⁴ ) / ΔT (3) When actually measuring by this method, heat conductivity in the sample width direction and thermal conductivity due to uneven temperature of the copper block Measurement error occurs. Therefore, as a result of numerical analysis of heat conduction around the sample using the finite element method, the measurement error due to the heat conduction in the width direction of the sample is within 1% under the present measurement conditions, and the temperature of the copper block is non-uniform. It was also confirmed that the modality is at most a few mK and does not pose a problem.

The method described above is called the passive method. However, in this method, when the temperature difference between the sample and the surroundings is small or the thermal conductivity of the sample is large, ΔT becomes small and measurement becomes difficult. It is also necessary to measure the hemispherical total emissivity of black paint by another method. Therefore, in such a case, the active method described below is used. In this method, contrary to the passive method, the temperature of the sample surface becomes higher than that of the copper block, and heat flows from the sample surface toward the copper block.

FIGS. 4 (a) and 4 (b) show the structure of the sample, the copper block, the stainless steel foil on the surface of the sample and the current heating electrode for the stainless steel foil in the active method. As shown in these figures, a stainless foil 8 having a thickness of 10 to 30 μm is adhered to the surface of the sample 1, and the black paint 3 is applied thereon. An insulating material 11 is attached to a portion where the stainless foil contacts the copper block 2. Then, a pair of copper current-carrying electrodes 9 are pressed against the stainless foil from both sides, and a uniform DC current is passed in the sample width direction. A heater 5 is attached to the back surface of the copper block as in the case of the passive method, but this heater is used as an auxiliary to keep the temperature of the copper block constant.

In the measurement by the active method, the thermal conductivity is expressed by equation (4).
Here, H is the amount of heat generated per unit surface area of the sample due to energization heating, and is obtained from the energization current I, the voltage drop V on the surface of the stainless steel foil, and the surface area A of the stainless steel foil by the equation (5). Among these, the energizing current is measured by the potential difference generated in the standard resistance inserted in series in the circuit, and the voltage drop is measured by the pair of voltage probes 10 pressed against the stainless steel foil together with the energizing heating electrode.

λ = d {H−ε _ht σ (T _s ⁴ −T _e ⁴ )} / ΔT (4) H = VI / A (5) In the active method, the temperature of the sample surface and the copper block can be When they are kept equal, that is, when the temperatures of the sample front surface and the sample back surface are kept equal, the heat conduction in the sample thickness direction becomes zero. Therefore since be lost by radiation heat exchange with all heat ambient occurring at the sample surface by electrical heating at this time, the electrical heating amount at the H ', the surface temperature T _s of the sample', the ambient temperature Let T _e ′ be the in-situ measurement of the total hemispherical emissivity of the black paint on the sample surface using equation (6).

ε _ht = H ′ / σ (T _s ′ ⁴ −T _e ′ ⁴ ) (6) By using the active method in this way, it becomes possible to measure at room temperature and samples with relatively high thermal conductivity. Instead, since the total hemispherical emissivity of the black paint can be measured on the spot, the error caused by the variation in the total hemispherical emissivity of the black paint can be reduced. Also, as can be seen from equation (4), even if there is an error in the measurement value of the hemispherical total emissivity, it is 100
It also has the advantage that it does not affect the measured% thermal conductivity.

The thermal conductivity of the sample when the thermal conductivity is measured in the atmosphere or the inert gas using the active method is expressed by the equation (7). Where h is the convection heat transfer coefficient.

λ = d {H−ε _ht σ (T _s ⁴ −T _e ⁴ ) −h (T _s −T _e )} / ΔT (7) The convection heat transfer coefficient is the same as the hemispherical total emissivity measurement method described above. , The temperature of the sample surface and that of the copper block in the atmosphere, that is, the temperature of the sample surface and the sample back surface are equal, and the heat conduction amount H ″ per unit sample surface area so that the heat conduction in the sample thickness direction is 0, The surface temperature of T _s ″ and the ambient temperature
Since T _e ″ and the heat loss due to radiative heat exchange can be ignored as compared with the heat loss due to heat convection transfer, they can be measured in-situ using Equation (8).

h = H ″ / (T _s ″ −T _e ″) (8) If the convection heat transfer coefficient is obtained, it is possible to measure the thermal conductivity in the atmosphere using the passive method. In this case, the thermal conductivity of the sample Is expressed by equation (9).

λ = d {ε _ht σ (T _s ⁴ −T _e ⁴ ) + h (T _s −T _e )} / ΔT (9) When the thermal conductivity is measured using the active method at room temperature, stainless steel on the surface is used. The heat generated by the foil heater raises the temperature of the copper block, making it difficult to maintain the temperature of the copper block at room temperature. In such a case, the temperature of the copper block is kept at room temperature by water cooling the copper block or the supporting portion supporting it.

In order to perform the measurement at a low temperature using this thermal conductivity measuring method, the copper block is electronically cooled or liquid nitrogen cooled.
In this case, in the active method, the amount of radiant heat exchange with the surroundings is smaller than the amount of heat generated on the surface of the sample, so the measurement accuracy is improved. In the passive method, the surface of the sample is heated by heat radiation from the surroundings to generate a heat flow, and the thermal conductivity is measured.

In principle, the measurement temperature range in the present thermal conductivity measurement method is from extremely low temperature to the melting point of the sample. However, in practice, the adhesive between the copper block and the sample becomes brittle at low temperatures, so
The lower limit of the measurement temperature is about the liquid nitrogen temperature. Even at high temperatures, the maximum temperature is limited mainly by the heat resistance of the adhesive,
The temperature is about 150 ℃ for polymer adhesives and about 700 ℃ for ceramic adhesives and silver paste. If you want to make measurements at temperatures above 800 ° C, it is necessary to make blocks of refractory metal such as molybdenum instead of copper blocks.

Fig. 5 shows the hemispherical total emissivity of the black paint on the sample surface measured by the active method. From this result, the variation in the measured value of the hemispherical total emissivity is 2-3%. In measuring the thermal conductivity, the value obtained by approximating the temperature dependence of the total emissivity of the hemisphere by the curve in the figure was used.

FIG. 6 shows an example of measuring the thermal conductivity of a silicon rubber standard sample by the active method and the passive method. The solid line in the figure is the standard value of the thermal conductivity of the silicone rubber standard sample, and the maximum difference between the measured value and the standard value is about ± 8%. The error bar in the figure is the variation in thermal conductivity corresponding to the temperature resolution (0.1 ° C) of the thermal imager, and the difference between the measured value and the standard value is within this range. Also, the measurement time is short, which is 1 under the current measurement conditions.
The time required to measure the points was about 5 minutes.

[Advantages of the Invention] As described above, by using the present thermal conductivity measuring method, the thermal conductivity of a material having a relatively low thermal conductivity such as a polymer material is about 3 × 25 × 25 mm. It becomes possible to measure in a short time by using a sample much smaller than the above, without depending on other physical properties such as specific heat. In addition, by using the active method that also uses current heating of the sample surface, it is possible to measure at room temperature, increase the temperature difference in the sample thickness direction and improve the measurement accuracy by simultaneous measurement of the hemispherical total emissivity, and simultaneously measure the convection heat transfer coefficient. It is also possible to measure thermal conductivity in the atmosphere. If it is possible to measure in the atmosphere, not only will a vacuum device be unnecessary, but it will also be possible to measure the thermal conductivity of a porous heat insulating material or a liquid enclosed in a small container. The range of application of the measurement method is dramatically expanded. Furthermore, the measurement temperature can be increased from liquid nitrogen temperature to 700 ℃ by cooling the copper block with liquid nitrogen and improving the heat resistance of the adhesive.
It can be applied to a temperature range of a certain degree.

[Brief description of drawings]

FIG. 1 (a) is a diagram for explaining the structure of a measuring apparatus in an embodiment using the passive method of the present invention. FIG. 1 (b) is a sectional view taken along the center line AA ′ of FIG. 1 (a). FIG. 2 is a block diagram of the apparatus in the embodiment of the present invention. FIG. 3 is a diagram showing an example of the temperature distribution on the sample surface in the passive method of the present invention. FIG. 4 (a) is a view for explaining the structure of the measuring apparatus in the embodiment using the active method of the present invention. FIG. 4 (b) is a sectional view taken along the center line BB 'in FIG. 4 (a). FIG. 5 is a graph showing an example of hemispherical total emissivity measured using the present invention. FIG. 6 is a graph showing an example of thermal conductivity measured using the present invention. 1 …… Sample 2 …… Copper block 3 …… Black paint 4 …… Insulating layer 5 …… Heater 6 …… Thermocouple 7 …… Electrode 8 …… Stainless steel foil 9 …… Electric heating electrode 10 …… Voltage probe 11 …… Insulation material 12 Vacuum container 13 Optical window 14 Thermal imager

Claims (3)

[Claims] 1. Radiant heat exchange between the surface of the object to be measured and the surroundings by heating the back surface of the object to be measured in a vacuum and causing radiant heat exchange between the surface of the object to be measured and the surroundings. To generate a uniform heat flow density in the thickness direction of the measured object so that the heat flow density of the heat lost becomes equal to the heat flow density in the thickness direction of the measured object, and the surface of the measured object at this time Let T _s be the temperature, T _e be the ambient temperature, ΔT be the temperature difference between the front and back surfaces of the object to be measured, and ε _{ht be the} total hemispherical emissivity of the surface of the object to be measured.
When the Boltzmann constant is σ and the thickness of the measured object is d, the thermal conductivity λ of the measured object is calculated by the following formula λ = ε _ht σd (T _s ⁴ −T _e ⁴ ) / ΔT. And a method for measuring thermal conductivity. 2. A surface of an object to be measured is covered with a metal foil, a black paint is applied to the surface of the metal foil, and the metal foil is energized in a vacuum so that the surface of the object to be measured has a constant area per unit area. By generating a heat quantity H'and performing radiative heat exchange between the surface of the object to be measured and the surroundings, the temperatures of the front surface and the back surface of the object to be measured are equalized,
When the surface temperature of the object to be measured at this time is T _s ′, the ambient temperature is T _e ′, and the Stefan-Boltzmann constant is σ, the hemispherical total emissivity ε of the black paint on the surface of the object to be measured is ε.
_{ht is obtained} by the following equation: ε _ht = H ′ / σ (T _s ′ ⁴ −T _e ′ ⁴ ), and a constant amount of heat H per unit area is applied to the surface of the object to be measured by energizing the metal foil in vacuum. Generate a uniform heat flow density in the thickness direction of the measured object by causing radiant heat exchange between the surface of the measured object and the surroundings, and the surface temperature of the measured object at this time. T _s , the ambient temperature is T _e , the temperature difference between the front and back surfaces of the object to be measured is ΔT, the thickness of the object to be measured is d, and the hemispherical total emissivity of the black paint on the surface of the object to be measured is When ε _ht is the value of the above equation, the thermal conductivity λ of the measured object is obtained by the following equation λ = d {H−ε _ht σ (T _s ⁴ −T _e ⁴ )} / ΔT. Method for measuring thermal conductivity. 3. A surface of an object to be measured is covered with a metal foil, and the metal foil is energized in the atmosphere or an inert gas to generate a constant amount of heat H ″ per unit area on the surface of the object to be measured. By causing radiative heat exchange between the surface of the object to be measured and the environment and heat exchange by convection between the surface of the object to be measured and the environment, the temperatures of the surface and the back surface of the object to be measured are made equal. When the surface temperature of the object to be measured at this time is T _s ″ and the ambient temperature is T _e ″, the convection heat transfer coefficient h in the atmosphere or the inert gas is expressed by the following equation: h = H ″ / ( T _s ″ −T _e ″), and a constant amount of heat H per unit area is generated on the surface of the object to be measured by energizing the metal foil in the atmosphere or an inert gas. Radiative heat exchange with the surroundings And a uniform heat flow density in the thickness direction of the measured object is given by causing heat exchange by convection between the surface of the measured object and the surroundings, and the surface temperature of the measured object at this time is T _s and the ambient temperature is T _e
And the temperature difference between the front surface and the back surface of the measured object is ΔT, and the total hemispherical emissivity of the surface of the measured object is ε _ht.
When the Boltzmann constant is σ, the thickness of the object to be measured is d, and the convection heat transfer coefficient h is the value of the above equation, the thermal conductivity λ of the object to be measured is the following equation: λ = d {H−ε _A method for measuring thermal conductivity, characterized by: _ht σ (T _s ⁴ −T _e ⁴ ) −h (T _s −T _e )} / ΔT.