WO2013001950A1 - Heat conductivity measuring method and heat conductivity measuring apparatus - Google Patents

Heat conductivity measuring method and heat conductivity measuring apparatus Download PDF

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Publication number
WO2013001950A1
WO2013001950A1 PCT/JP2012/063524 JP2012063524W WO2013001950A1 WO 2013001950 A1 WO2013001950 A1 WO 2013001950A1 JP 2012063524 W JP2012063524 W JP 2012063524W WO 2013001950 A1 WO2013001950 A1 WO 2013001950A1
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temperature
thermal conductivity
test body
heat
hot plate
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PCT/JP2012/063524
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French (fr)
Japanese (ja)
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高弘 大村
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ニチアス株式会社
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity

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  • the present invention relates to a thermal conductivity measurement method and a thermal conductivity measurement device, and more particularly to improvement in accuracy in measurement of thermal conductivity.
  • the measurement of the thermal conductivity of a heat insulating material or the like is performed by a guarded hot plate (GHP) method or a heat flow meter method.
  • the thermal conductivity at a temperature of 100 ° C. or higher is mainly measured by the GHP method.
  • the measurement of thermal conductivity by the GHP method a thermal gradient is formed in the test body, and the heat conductivity propagating through the test body is measured to obtain the thermal conductivity of the test body.
  • Non-Patent Document 1 a thermal conductivity measurement method
  • a protective hot plate is provided around the main hot plate, and the main hot plate and the protective hot plate are formed in the same shape.
  • Generated in the main heat plate by sandwiching between the two test bodies, and further sandwiching the two test bodies between a pair of cooling plates and making the temperature difference between the main heat plate and the protective heat plate zero. It was assumed that the heat that flowed was one-dimensionally flowing inside the specimen toward the cooling plate.
  • Non-Patent Document 2 describes a method for theoretically calculating the heat flow inside the specimen.
  • Non-Patent Document 1 describes that it is best to set the temperature of the outer peripheral edge of the test body to the average temperature of the surface temperature on the main hot plate side and the temperature on the cooling plate side of the test body. Has been.
  • the measurement error is evaluated on the assumption that there is no temperature distribution at the outer peripheral end of the specimen.
  • the influence of the heat flow (heat flow in the width direction) through the outer peripheral edge of the specimen on the measurement result of the thermal conductivity is large. For this reason, for example, when the temperature of the atmosphere surrounding the specimen changes, the measured thermal conductivity may also change.
  • a composite including a plurality of portions having different thermal conductivities for example, a heat insulating structure formed by attaching a foam (foam rubber, etc.) to a plate of a material (metal plate, etc.) having a high thermal conductivity, a metal
  • a heat insulating structure formed by attaching a foam (foam rubber, etc.) to a plate of a material (metal plate, etc.) having a high thermal conductivity, a metal when measuring the thermal conductivity of a heat insulating structure formed by sandwiching glass with a heat insulating material and a vacuum heat insulating material covered with a foil film formed by vapor deposition of metal and having a vacuum inside, in the conventional method, A remarkable heat flow occurs in the width direction of the composite through the metal, glass, foil film, etc., and the thermal conductivity in the thickness direction of the composite cannot be accurately measured. .
  • the present invention has been made in view of the above problems, and an object of the present invention is to provide a thermal conductivity measuring method and a thermal conductivity measuring apparatus with improved measurement accuracy.
  • a test body is disposed between a hot plate and a cooling plate, and the thickness direction is directed from the hot plate toward the cooling plate.
  • Qm is the heat flow from the hot plate
  • d is the thickness of the specimen
  • ⁇ t is the temperature gradient in the thickness direction
  • S is the thickness in the thickness direction.
  • the measurement condition included in the variable is at least one selected from the group consisting of a temperature gradient ⁇ w in the width direction, the thickness d, and the heat transfer area S. It is good as well.
  • a thermal conductivity measuring device for solving the above problems is a thermal conductivity measuring device including a hot plate and a cooling plate respectively disposed on one side and the other side of a test body.
  • the sensor further includes a sensor for measuring a temperature distribution in a width direction from the center of the test body to the outer peripheral end or from the outer peripheral end toward the center. According to the present invention, it is possible to provide a thermal conductivity measuring device with improved measurement accuracy.
  • FIG. 1 shows an example of a thermal conductivity measuring device (hereinafter referred to as “present device 1”) used in a thermal conductivity measuring method (hereinafter referred to as “present method”) according to the present embodiment. It is explanatory drawing which shows the cross section of a various structure.
  • FIG. 2 is an explanatory view showing members constituting a part of the example of the apparatus 1 in perspective.
  • FIG. 3 is an explanatory diagram showing, in an enlarged manner, a part of the apparatus 1 surrounded by the alternate long and short dash line III shown in FIG.
  • the present apparatus 1 is a thermal conductivity measuring apparatus including a hot plate 100 and a cooling plate 200 disposed on one side and the other side of a test body 10, respectively. That is, in the apparatus 1, the test body 10 is sandwiched between the hot plate 100 and the cooling plate 200.
  • the hot plate 100 heats the surface on one side of the test body 10 (hereinafter referred to as “high temperature surface 11”).
  • the cooling plate 200 keeps the surface on the other side of the test body 10 (hereinafter referred to as “low temperature surface 12”) at a temperature lower than the temperature of the high temperature surface 11.
  • the hot plate 100 is a high-temperature side heater that heats the high-temperature surface 11 of the test body 10 at a first temperature
  • the cooling plate 200 includes the low-temperature surface 12 of the test body 10 as the first temperature. It is a low temperature heater that heats at a second temperature lower than the temperature.
  • the hot plate 100 includes a main hot plate 110 that heats the central portion of the test body 10 and a protective hot plate 120 that is disposed so as to surround the main hot plate 110.
  • a heat insulating layer 130 (so-called gap) is formed between the main hot plate 110 and the protective hot plate 120 to suppress heat conduction therebetween.
  • the present apparatus 1 further includes an outer peripheral heater 300 arranged so as to surround the outer periphery of the test body 10, the hot plate 100, and the cooling plate 200.
  • the outer peripheral heater 300 heats the outer peripheral side of the test body 10, the hot plate 100 and the cooling plate 200.
  • the apparatus 1 is disposed on the heat insulating material 400 on the opposite side of the hot plate 100 from the test body 10 and on the heat insulating material 400 on the opposite side of the heat plate 100.
  • the compensation heater 410 is controlled so that its temperature becomes equal to the temperature of the main heating plate 110, the heat insulating material 420 disposed on the opposite side of the heat insulating material 400 of the compensation heater 410, and the test body of the cooling plate 200.
  • a heat insulating material 430 disposed on the opposite side to 10 and a heat insulating material 440 disposed so as to surround the outer periphery thereof and surrounded by the outer peripheral heater 300 are further provided.
  • the high temperature surface 11 of the test body 10 is kept at the first temperature, and the low temperature surface 12 of the test body 10 is kept at the second temperature lower than the first temperature. At this time, based on the temperature difference between the high temperature surface 11 and the low temperature surface 12 (difference between the first temperature and the second temperature), the specimen 10 mainly from the high temperature surface 11 toward the low temperature surface 12. Heat flow is generated inside.
  • the temperature of the protective hot plate 120 is controlled to be equal to the temperature of the main hot plate 110, the heat flow in the width direction Fw from the center 13 of the test body 10 toward the outer peripheral end 14 is suppressed.
  • the heat insulating material 400 is disposed on the opposite side of the hot plate 100 from the test body 10, and the temperature of the compensation heater 410 is controlled to be equal to the temperature of the main hot plate 110, thereby the main hot plate 110. Therefore, it is possible to suppress the heat flow from being generated on the opposite side of the test body 10 and to realize an efficient heat flow from the main hot plate 110 to the cooling plate 200.
  • test object 10 to be measured in the present method and the apparatus 1 is not particularly limited as long as it can be sandwiched between the hot plate 100 and the cooling plate 200. That is, examples of the test body 10 include a heat insulating material, plastic, wood, gypsum board, and cement.
  • the heat insulating material examples include a fibrous heat insulating material, a porous heat insulating material, and a vacuum heat insulating material.
  • the fibrous heat insulating material examples include rock wool heat insulating material, glass wool heat insulating material, alumina fiber wool heat insulating material, alumina fiber heat insulating material, and alumina silica fiber heat insulating material.
  • the porous heat insulating material examples include calcium silicate heat insulating material, foam rubber, foamed urethane, and polystyrene foam.
  • the heat insulating material may be a composite heat insulating material such as a heat insulating structure formed by laminating a heat insulating material and metal or glass, for example.
  • the shape of the test body 10 is not particularly limited as long as it can be sandwiched between the hot plate 100 and the cooling plate 200. For example, as shown in FIGS.
  • the present apparatus 1 can be used, for example, for measurement of thermal conductivity by the GHP method or the heat flow meter method, and can be particularly preferably used for measurement by the GHP method.
  • the thermal conductivity is measured by a so-called single sheet method.
  • the measurement of the thermal conductivity by the present method and the present apparatus 1 is not limited to this.
  • two test bodies 10 are arranged on one side and the other side of the hot plate 100 (that is, the two tests). It is also possible to carry out the so-called two-sheet method by sandwiching the hot plate 100 with the body 10).
  • the thickness direction from the hot plate 100 toward the cooling plate 200 in the test body 10 (the direction indicated by the arrow Ft shown in FIG. 3) ( That is, a one-dimensional steady heat flow is generated in a direction from the high temperature surface 11 toward the low temperature surface 12.
  • Qm is the heat flow from the main heat plate 110 (the amount of heat generated by the main heat plate 110), d is the thickness of the test body 10, and ⁇ t is the temperature in the thickness direction Ft. S is the heat transfer area of the specimen 10 in the thickness direction Ft.
  • the temperature of the outer peripheral end 14 of the test body 10 may be uniform and the average temperature of the temperature of the main hot plate 110 and the temperature of the cooling plate 200.
  • the heat flow from the main heat plate 110 and the heat flow from the cooling plate 200 are offset from the center in the thickness direction Ft of the outer peripheral end 14 of the test body 10, and the heat generated in the main heat plate 110 is reduced. It is possible to flow one-dimensionally in the thickness direction Ft.
  • the temperature of the outer peripheral end 14 of the test body 10 is uniform throughout the outer peripheral end 14 and the temperature of the main hot plate 110. If the average temperature of the cooling plate 200 is not reached, a heat flow in the width direction Fw is generated. In this regard, in reality, it is difficult to make the temperature of the outer peripheral end 14 of the test body 10 uniform and accurately control the temperature.
  • the inventor of the present invention uses the heat flow in the width direction Fw inside the test body 10 as described later. I thought it was necessary to consider.
  • the heat flow Qm from the main hot plate 10 is actually the heat flow Qt flowing in the thickness direction Ft inside the test body 10 and the heat flowing in the width direction Fw. It is divided into the flow rate Qw.
  • the temperature ⁇ h may be the temperature of the portion of the high temperature surface 11 of the test body 10 that is in contact with the main hot plate 110 (the center portion of the high temperature surface 11), or the surface 101 of the main hot plate 110 on the test body 10 side. It is good also as temperature of.
  • the temperature ⁇ c may be a temperature of a portion corresponding to the position of the main hot plate 110 of the low temperature surface 12 of the test body 10 (a central portion of the low temperature surface 12), or on the test body 10 side of the cooling plate 200. It is good also as the temperature of the part (center part of the said surface 201) facing the main hot platen 110 of the surface 201.
  • FIG. A thermocouple is preferably used for measuring the temperature.
  • the heat flow rate in the width direction Fw (heat flow rate flowing in or out via the outer peripheral end 14 of the test body 10) Qw is expressed by the following formula (IV ).
  • H is a coefficient.
  • the horizontal axis represents the dimensionless temperature ⁇
  • the vertical axis represents the apparent thermal conductivity ⁇ a obtained by the above formula (I)
  • the apparent thermal conductivity ⁇ a against the dimensionless temperature ⁇ is plotted.
  • a linear relationship indicating a correlation between the dimensionless temperature ⁇ and the apparent thermal conductivity ⁇ a is obtained.
  • the thermal conductivity ⁇ t in the thickness direction Ft of the test body 10 is obtained as an intercept of the straight line thus obtained.
  • the temperature gradient ⁇ w in the width direction Fw is changed by changing the temperature of the outer peripheral heater 300 (see FIG. 1) arranged so as to surround the outer peripheral end 14 of the test body 10. Can be changed. At this time, the temperature gradient ⁇ t in the thickness direction Ft may also be changed.
  • the thermal conductivity ⁇ t at a predetermined temperature T ° C. is measured.
  • the temperature ⁇ h of the high temperature surface 11 is set to a predetermined temperature Th (° C.) in the first measurement.
  • the temperature ⁇ c of the low temperature surface 12 is set to a predetermined temperature Tc (° C.)
  • the temperature of the outer peripheral heater 300 is set to the first temperature Ts1 (° C.).
  • the heat flow rate Qm from the main hot plate 110 necessary for maintaining the high temperature surface 11 at the temperature Th (° C.) is a predetermined value Q1 (W).
  • the temperature of the outer heater 300 is increased and set to the second temperature Ts2 (° C.) higher than the first temperature Ts1 (° C.).
  • the heat flow Qm from the main heating plate 110 necessary to keep the high temperature surface 11 at the same temperature Th (° C.) as the first time becomes Q2 (W) which is smaller than the first time Q1 (W).
  • the temperature gradient ⁇ w in the width direction Fw is changed, and as a result, the heat flow rate Qm from the main heat plate 110 is also changed.
  • the variable is the dimensionless temperature ⁇ ( ⁇ w / ⁇ t) in the above formula (X), for example, the fluctuation of the temperature ⁇ h of the high temperature surface 11 and / or the temperature ⁇ c of the low temperature surface 12 is measured. Does not introduce errors.
  • the width direction at an arbitrary position in the range from the high temperature surface 11 to the low temperature surface 12 of the test body 10 (for example, a virtual plane extending in the width direction Fw inside the high temperature surface 11, the low temperature surface 12, or the test body 10).
  • the above formula (X) is established for the temperature gradient ⁇ w of Fw. Furthermore, even if the coefficient a in the above formula (X) changes depending on the temperature gradient ⁇ w, the slope of the straight line (the coefficient a) changes as shown in FIG. A certain thermal conductivity ⁇ t does not change and is constant.
  • the measurement of the dimensionless temperature ⁇ and the apparent thermal conductivity ⁇ a is repeated based on the temperature gradient ⁇ w in the width direction Fw at an arbitrary position in the thickness direction Ft of the test body 10, and the above formula ( By obtaining the correlation shown in X), the thermal conductivity ⁇ t in the thickness direction Ft of the specimen 10 can be obtained.
  • the plane for measuring the temperature gradient ⁇ w (for example, a virtual plane extending in the width direction Fw inside the high temperature surface 11, the low temperature surface 12, or the test body 10), as shown in FIG. 3, it corresponds to the position of the heat insulating layer 130.
  • the position is determined as the origin, and the temperature distribution in the plane is represented by a function f (x).
  • the position of the origin is not particularly limited.
  • the center in the width direction Fw of the heat insulating layer 130 is the origin.
  • FIG. 6 shows an example of the temperature distribution function f (x).
  • the temperature distribution function f (x) is determined from the origin from a position ( ⁇ x m ) separated from the origin (0) by a predetermined distance x m on the minus side (main heat plate 110 side).
  • This is a function representing a temperature distribution to a position (x e ) that is a predetermined distance x e away from the plus side (protective heat plate 120 side), that is, to the outer peripheral end 14 of the specimen 10.
  • the average temperature ⁇ e in the range (plus side) from the origin to the outer peripheral end 14 of the specimen 10 is expressed by the following formula (XI).
  • the average temperature ⁇ m in the range (minus side) from the origin to an arbitrary position (x m ) on the center 13 side of the specimen 10 is represented by the following formula (XII). However, here, it is assumed that the temperature is constant on the center 13 side of the test body 10 further than the position ( ⁇ x m ).
  • the temperature gradient ⁇ w in the width direction Fw is obtained by the following formula (XIII) from the above formulas (XI) and (XII). That is, this temperature gradient ⁇ w is the difference between the average temperature ⁇ m of the test body 10 on the main heat plate 110 side from the heat insulating layer 130 and the average temperature ⁇ e of the test body 10 on the protective heat plate 120 side from the heat insulating layer 130. As required.
  • thermocouples Pc1 to Pc5 are installed at five locations on the low temperature surface 12 of the test body 10, and the temperature ⁇ c is measured at the five locations. Then, taking the distance x from the origin on the horizontal axis and the temperature ⁇ c measured on the vertical axis, the temperature ⁇ c with respect to the distance x is plotted, and the plot is approximated by a quadratic curve by the least square method to obtain the temperature distribution. A function f (x) is obtained.
  • the temperature distribution function f (x) is not limited to a quadratic curve, and can be approximated by an arbitrary function such as a polynomial such as a linear curve, a cubic curve, or a quartic curve, or an exponential function.
  • the thermal conductivity ⁇ t in the thickness direction Ft of the test body 10 is obtained by changing the thickness d of the test body 10 while considering the heat flow in the width direction Fw.
  • the heat flow rate Qw in the width direction Fw is proportional to the area of the outer peripheral end 14 of the test body 10
  • the heat flow rate Qw is It is represented by the following formula (XVII).
  • variable d 2 that is the square of the thickness d of the test body 10 is taken on the horizontal axis, and the apparent thermal conductivity ⁇ a is taken on the vertical axis, and the apparent heat with respect to the variable d 2 is taken.
  • plotted conductivity [lambda] a linear relationship showing the correlation between the variables d 2 and the apparent thermal conductivity [lambda] a is obtained.
  • the thermal conductivity ⁇ t in the thickness direction Ft is obtained as an intercept of this straight line.
  • a variable including the reciprocal (1 / S) of the heat transfer area S in the thickness direction Ft of the test body 10 is determined, and the apparent thermal conductivity ⁇ a is measured while changing the heat transfer area S, Based on the formula (XIX), a linear relationship between the variable and the apparent thermal conductivity ⁇ a may be obtained.
  • this method determines the variable including the measurement condition for changing the heat flow rate Qw in the width direction Fw, and the correlation between the variable and the apparent thermal conductivity ⁇ a represented by the above formula (I). Determining the thermal conductivity.
  • the thermal conductivity ⁇ t in the thickness direction Ft of the specimen 10 is calculated based on the correlation between the variable including the measurement condition for changing the heat flow rate Qw in the width direction Fw and the apparent thermal conductivity ⁇ a. Ask.
  • the apparent thermal conductivity ⁇ a is measured while changing the measurement conditions included in the variable, and based on the correlation between the variable obtained by the measurement and the apparent thermal conductivity ⁇ a, the specimen A thermal conductivity ⁇ t of 10 is obtained.
  • the measurement condition included in the variable is selected from the group consisting of the temperature gradient ⁇ w in the width direction Fw, the thickness d of the test body 10 and the heat transfer area S in the thickness direction Ft of the test body 10. It may be one or more.
  • the apparatus 1 may be a thermal conductivity measuring apparatus including a sensor P for measuring the temperature distribution in the width direction Fw, as shown in FIG. .
  • the conventional thermal conductivity measuring apparatus is not provided with the sensor P for measuring the temperature distribution in the width direction Fw. That is, the present apparatus 1 including the sensor P for measuring the temperature distribution in the width direction Fw is specialized for measuring the thermal conductivity ⁇ t in the thickness direction Ft in consideration of the heat flow rate Qw in the width direction Fw. This is an unprecedented thermal conductivity measuring device.
  • the temperature gradient ⁇ w in the width direction Fw is obtained by measuring temperatures at a plurality of positions in the width direction Fw of the test body 10 as described above. Therefore, the apparatus 1 includes a plurality of sensors P arranged at a plurality of positions in the width direction Fw of the test body 10 as shown in FIG.
  • the apparatus 1 includes a plurality of temperatures for measuring temperatures at a plurality of positions on the low temperature surface 12 of the test body 10 or the surface 201 of the cooling plate 200 on the test body 10 side.
  • Sensors Pc1 to Pc5 may be provided, and a plurality of sensors Ph1 to Ph5 for measuring temperatures at a plurality of positions on the high temperature surface 11 of the test body 10 or the surface 101 of the hot plate 100 on the test body 10 side may be provided.
  • the test body 10 when the test body 10 is thin and / or when the test body 10 is small, the presence of a sensor (for example, a thermocouple) is detected on the surface (for example, the high temperature surface 11 and the low temperature surface 12 of the test body 10, the hot plate). Since the influence on the measurement of the temperature at the surface 101 of the 100 and the surface 201 of the cooling plate 200 becomes large, the temperature gradient ⁇ w at the surface may not be measured accurately.
  • a sensor for example, a thermocouple
  • the thermal conductivity ⁇ t in the thickness direction Ft can be obtained from the linear relationship between the variable (d 2 ) and the apparent thermal conductivity ⁇ a.
  • the heat in the thickness direction Ft is calculated from the linear relationship between the variable (d 2 / ⁇ t) and the apparent thermal conductivity ⁇ a based on the above formula (XIX).
  • the conductivity ⁇ t can be obtained.
  • the present method is not limited to the example described above. That is, for example, the method determines a variable including at least one of the parameters (L, d 2 , S, ⁇ w, and ⁇ t) included in the second term on the right side of the formula (XIX), and changes the variable.
  • the apparent thermal conductivity ⁇ a of the left side by the above formula (I) obtaining a linear relationship between the variable and the apparent thermal conductivity ⁇ a, and based on the linear relationship
  • It may be a method of obtaining the thermal conductivity ⁇ t.
  • the temperature at which the thermal conductivity ⁇ t is measured is not particularly limited. For example, the thermal conductivity ⁇ t at a temperature of ⁇ 170 ° C. or higher and 100 ° C. or lower may be measured, and at a temperature of 100 ° C. or higher and 1500 ° C. or lower.
  • the thermal conductivity ⁇ t may be measured.
  • alumina-silica fiber at 200.degree. C., 400.degree. C., 500.degree. C., 600.degree. C., 700.degree.
  • the thermal conductivity ⁇ t in the thickness direction Ft of the heat insulating material was measured.
  • the dimensionless temperature ⁇ represented by the above formula (IX) was determined as a variable.
  • the apparent thermal conductivity ⁇ a was measured by the above formula (I) while changing the dimensionless temperature ⁇ (particularly the temperature gradient ⁇ w in the width direction Fw) by changing the temperature of the outer heater 300.
  • the temperature gradient ⁇ w is, as shown in FIG. 3, the sensors (thermocouples) Pc1 to Pc5 arranged at five locations on the low temperature surface 12 of the heat insulating material (test body 10), or the thickness direction Ft center of the heat insulating material. Based on the temperature measured by the sensors (thermocouples) Pi1 to Pi5 arranged at the five locations, the above formula (XIII) was used.
  • the apparent thermal conductivity ⁇ a was plotted against the dimensionless temperature ⁇ , and a linear relationship as shown in FIG. 2 was obtained by linearly approximating the plot by the least square method.
  • the value of the obtained intercept of the straight line was obtained as the thermal conductivity ⁇ t.
  • the thermal conductivity of the heat insulating material was similarly measured using the thermal conductivity measuring apparatus by a period heating method for the comparison.
  • FIG. 7 shows the results of obtaining the thermal conductivity ⁇ t of the heat insulating material at each temperature.
  • the horizontal axis indicates the temperature (° C.) at which the thermal conductivity ⁇ t is measured
  • the vertical axis indicates the thermal conductivity ⁇ t (W / (m ⁇ K)) measured at each temperature.
  • a white square mark indicates the thermal conductivity ⁇ t obtained using the temperature distribution on the low temperature surface 12 of the test body 10
  • a white triangle mark indicates the center in the thickness direction Ft of the test body 10.
  • the thermal conductivity ⁇ t obtained by using the temperature distribution in Fig. 5 is shown, and the black circles indicate the thermal conductivity obtained by the periodic heating method.
  • the area surrounded by two broken lines indicates a range in which the error from the measurement result by the periodic heating method is plus 10% (+ 10%) to minus 10% ( ⁇ 10%).
  • the thermal conductivity ⁇ t obtained by the present method using the apparatus 1 almost coincided with the thermal conductivity obtained by the periodic heating method. That is, according to this apparatus 1 and this method, it was confirmed that the thermal conductivity ⁇ t in the thickness direction Ft can be measured with high accuracy by considering the heat flow in the width direction Fw.

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Abstract

Provided is a heat conductivity measuring method having improved measurement accuracy. In this heat conductivity measurement method, a body to be tested (10) is disposed between a heating plate (100) and a cooling plate (200), and a heat conductivity (λt) of the body to be tested (10), said heat conductivity being in the thickness direction (Ft) from the heating plate (100) toward the cooling plate (200), is measured. The method includes: a step of determining variable numbers that include measurement conditions of changing a heat flow rate in the width direction (Fw) from the center (13) toward the outer circumferential end (14) of the body to be tested (10); and a step of obtaining a correlative relationship between the variable numbers and an apparent heat conductivity (λa), which is measured on the basis of a rate of a heat flow from the heating plate (100), thickness of the body to be tested (10), temperature gradient in the thickness direction (Ft), and heat transfer area of the body to be tested (10), said heat transfer area being in the thickness direction (Ft).

Description

熱伝導率測定方法及び熱伝導率測定装置Thermal conductivity measuring method and thermal conductivity measuring device
　本発明は、熱伝導率測定方法及び熱伝導率測定装置に関し、特に、熱伝導率の測定における精度の向上に関する。 The present invention relates to a thermal conductivity measurement method and a thermal conductivity measurement device, and more particularly to improvement in accuracy in measurement of thermal conductivity.
　断熱材等の熱伝導率の測定は、保護熱板（Ｇｕａｒｄｅｄ　Ｈｏｔ　Ｐｌａｔｅ：ＧＨＰ）法や熱流計法により行われている。特に、１００℃以上の温度における熱伝導率は、ＧＨＰ法により測定することが主流である。ＧＨＰ法による熱伝導率の測定では、試験体に温度勾配を形成し、当該試験体の内部を伝播する熱流を測定することにより、当該試験体の熱伝導率を求める。 The measurement of the thermal conductivity of a heat insulating material or the like is performed by a guarded hot plate (GHP) method or a heat flow meter method. In particular, the thermal conductivity at a temperature of 100 ° C. or higher is mainly measured by the GHP method. In the measurement of thermal conductivity by the GHP method, a thermal gradient is formed in the test body, and the heat conductivity propagating through the test body is measured to obtain the thermal conductivity of the test body.
　従来、ＧＨＰ法では、試験体に温度勾配を形成し、当該試験体の内部を熱が一次元方向にのみ流れると仮定して熱伝導率を測定していた。このような熱伝導率の測定方法においては、例えば、非特許文献１に記載されているように、主熱板の周囲に保護熱板を設け、当該主熱板及び保護熱板を同一形状の２つの試験体で挟み、さらに当該２つの試験体を一対の冷却板で挟んだ上で、当該主熱板と当該保護熱板との温度差をゼロにすることで、当該主熱板で発生した熱が、当該試験体の内部を当該冷却板に向けて一次元的に流れると仮定していた。また、非特許文献２においては、試験体の内部の熱流を理論的に計算する方法が記載されている。 Conventionally, in the GHP method, a thermal gradient was formed in a test body, and heat conductivity was measured on the assumption that heat flows only in the one-dimensional direction inside the test body. In such a thermal conductivity measurement method, for example, as described in Non-Patent Document 1, a protective hot plate is provided around the main hot plate, and the main hot plate and the protective hot plate are formed in the same shape. Generated in the main heat plate by sandwiching between the two test bodies, and further sandwiching the two test bodies between a pair of cooling plates and making the temperature difference between the main heat plate and the protective heat plate zero. It was assumed that the heat that flowed was one-dimensionally flowing inside the specimen toward the cooling plate. Non-Patent Document 2 describes a method for theoretically calculating the heat flow inside the specimen.
　しかしながら、上記従来の熱伝導率測定方法では、試験体の内部において熱は主熱板から冷却板に向かう厚さ方向に一次元的に流れると仮定し、当該試験体の中央から外周端又は当該外周端から当該中央に向かう幅方向（厚さ方向に略直交する方向）の熱流を無視していた。このため、例えば、試験体の厚さが大きい場合や、試験体の熱伝導率が大きい場合には、当該試験体の外周端を介した熱流量（幅方向の熱流量）が大きくなり、その結果、測定誤差が大きくなっていた。 However, in the above conventional thermal conductivity measurement method, it is assumed that heat flows one-dimensionally in the thickness direction from the main hot plate to the cooling plate in the inside of the test body, and from the center of the test body to the outer peripheral edge or the The heat flow in the width direction (direction substantially orthogonal to the thickness direction) from the outer peripheral end toward the center is ignored. For this reason, for example, when the thickness of the specimen is large or when the thermal conductivity of the specimen is large, the heat flow (heat flow in the width direction) through the outer peripheral end of the specimen increases. As a result, the measurement error was large.
　また、試験体のサイズが小さい場合（熱の流れる面積が小さい場合）には、厚さ方向に伝播する熱流に対する、当該試験体の外周端を介した熱流（幅方向の熱流）の影響が大きくなるため、測定誤差が大きくなっていた。 In addition, when the size of the test specimen is small (when the heat flow area is small), the influence of the heat flow (heat flow in the width direction) through the outer peripheral edge of the test specimen on the heat flow propagating in the thickness direction is large. Therefore, the measurement error is large.
　また、上記非特許文献１には、試験体の外周端の温度を、当該試験体の主熱板側の表面の温度と冷却板側の表面の温度との平均温度にすることが最良と記載されている。そして、非特許文献１及び非特許文献２においては、試験体の外周端に温度分布が無いと仮定して測定誤差を評価している。 Non-Patent Document 1 describes that it is best to set the temperature of the outer peripheral edge of the test body to the average temperature of the surface temperature on the main hot plate side and the temperature on the cooling plate side of the test body. Has been. In Non-Patent Document 1 and Non-Patent Document 2, the measurement error is evaluated on the assumption that there is no temperature distribution at the outer peripheral end of the specimen.
　しかしながら、現実には、試験体の外周端の温度を均一にすることは不可能である。特に、１００℃以上の高温で熱伝導率を測定する場合には、試験体の温度と、当該試験体を取り巻く雰囲気の温度（例えば、室温）との差が非常に大きくなるため、当該試験体の幅方向に温度分布が生じてしまう。 However, in reality, it is impossible to make the temperature of the outer peripheral edge of the specimen uniform. In particular, when the thermal conductivity is measured at a high temperature of 100 ° C. or higher, the difference between the temperature of the test body and the temperature of the atmosphere surrounding the test body (for example, room temperature) becomes very large. Temperature distribution occurs in the width direction.
　したがって、実際には、試験体の外周端を介した熱流（幅方向の熱流）が熱伝導率の測定結果に与える影響は大きい。このため、例えば、試験体を取り巻く雰囲気の温度が変わることで、測定される熱伝導率も変わってしまうことがあった。 Therefore, actually, the influence of the heat flow (heat flow in the width direction) through the outer peripheral edge of the specimen on the measurement result of the thermal conductivity is large. For this reason, for example, when the temperature of the atmosphere surrounding the specimen changes, the measured thermal conductivity may also change.
　さらに、熱伝導率が互いに異なる複数の部分を含む複合体、例えば、熱伝導率が大きい材料（金属板等）の板に発泡体（発泡ゴム等）を張り付けて形成された断熱構造体、金属又はガラスを断熱材で挟んで形成された断熱構造体、及び金属を蒸着して形成した箔膜で覆われ内部が真空である真空断熱材等の熱伝導率を測定する場合、従来の方法では、金属、ガラス、箔膜等の部分を介して、当該複合体の幅方向に顕著な熱流が生じてしまい、当該複合体の厚さ方向の熱伝導率を正確に測定することができなかった。 Further, a composite including a plurality of portions having different thermal conductivities, for example, a heat insulating structure formed by attaching a foam (foam rubber, etc.) to a plate of a material (metal plate, etc.) having a high thermal conductivity, a metal Or, when measuring the thermal conductivity of a heat insulating structure formed by sandwiching glass with a heat insulating material and a vacuum heat insulating material covered with a foil film formed by vapor deposition of metal and having a vacuum inside, in the conventional method, A remarkable heat flow occurs in the width direction of the composite through the metal, glass, foil film, etc., and the thermal conductivity in the thickness direction of the composite cannot be accurately measured. .
　本発明は、上記課題に鑑みて為されたものであって、測定精度が向上した熱伝導率測定方法及び熱伝導率測定装置を提供することをその目的の一つとする。 The present invention has been made in view of the above problems, and an object of the present invention is to provide a thermal conductivity measuring method and a thermal conductivity measuring apparatus with improved measurement accuracy.
　上記課題を解決するための本発明の一実施形態に係る熱伝導率測定方法は、試験体を熱板と冷却板との間に配置して、前記熱板から前記冷却板に向かう厚さ方向における前記試験体の熱伝導率λｔを測定する方法であって、前記試験体の中央から外周端又は前記外周端から前記中央に向かう幅方向における熱流量を変化させる測定条件を含む変数を決定すること、及び前記変数と、下記式（Ｉ）で示される見かけ熱伝導率λａとの相関関係を求めること、を含むことを特徴とする。本発明によれば、測定精度が向上した熱伝導率測定方法を提供することができる。
Figure JPOXMLDOC01-appb-M000002
 （式（Ｉ）において、Ｑｍは前記熱板からの熱流量であり、ｄは前記試験体の厚さであり、Δθｔは前記厚さ方向における温度勾配であり、Ｓは前記厚さ方向における前記試験体の伝熱面積である。） In the thermal conductivity measurement method according to an embodiment of the present invention for solving the above-described problem, a test body is disposed between a hot plate and a cooling plate, and the thickness direction is directed from the hot plate toward the cooling plate. Is a method for measuring the thermal conductivity λt of the test body in which a variable including a measurement condition for changing a heat flow in the width direction from the center of the test body to the outer peripheral end or from the outer peripheral end toward the center is determined. And obtaining a correlation between the variable and the apparent thermal conductivity λa represented by the following formula (I). According to the present invention, it is possible to provide a thermal conductivity measurement method with improved measurement accuracy.
Figure JPOXMLDOC01-appb-M000002
 (In Formula (I), Qm is the heat flow from the hot plate, d is the thickness of the specimen, Δθt is the temperature gradient in the thickness direction, and S is the thickness in the thickness direction. (The heat transfer area of the specimen.)
　また、前記熱伝導率測定方法において、前記変数に含まれる前記測定条件は、前記幅方向における温度勾配Δθｗ、前記厚さｄ及び前記伝熱面積Ｓからなる群より選択される１つ以上であることとしてもよい。 In the thermal conductivity measurement method, the measurement condition included in the variable is at least one selected from the group consisting of a temperature gradient Δθw in the width direction, the thickness d, and the heat transfer area S. It is good as well.
　上記課題を解決するための本発明の一実施形態に係る熱伝導率測定装置は、試験体の一方側及び他方側にそれぞれ配置される熱板及び冷却板を備えた熱伝導率測定装置であって、前記試験体の中央から外周端又は前記外周端から前記中央に向かう幅方向における温度分布を測定するためのセンサーをさらに備えたことを特徴とする。本発明によれば、測定精度が向上した熱伝導率測定装置を提供することができる。 A thermal conductivity measuring device according to an embodiment of the present invention for solving the above problems is a thermal conductivity measuring device including a hot plate and a cooling plate respectively disposed on one side and the other side of a test body. The sensor further includes a sensor for measuring a temperature distribution in a width direction from the center of the test body to the outer peripheral end or from the outer peripheral end toward the center. According to the present invention, it is possible to provide a thermal conductivity measuring device with improved measurement accuracy.
　本発明によれば、測定精度が向上した熱伝導率測定方法及び熱伝導率測定装置を提供することができる。 According to the present invention, it is possible to provide a thermal conductivity measuring method and a thermal conductivity measuring device with improved measurement accuracy.
本発明の一実施形態に係る熱伝導率測定方法において使用される熱伝導率測定装置の一例について、その主な構成の断面を示す説明図である。It is explanatory drawing which shows the cross section of the main structure about an example of the heat conductivity measuring apparatus used in the heat conductivity measuring method which concerns on one Embodiment of this invention. 本発明の一実施形態に係る熱伝導率測定方法において使用される熱伝導率測定装置の一例について、その一部を構成する部材を斜視で示す説明図である。It is explanatory drawing which shows the member which comprises the part about an example of the thermal conductivity measuring apparatus used in the thermal conductivity measuring method which concerns on one Embodiment of this invention with a perspective view. 図１に示す一点鎖線ＩＩＩで囲まれた熱伝導率測定装置の一部を拡大して示す説明図である。It is explanatory drawing which expands and shows a part of thermal conductivity measuring apparatus enclosed with the dashed-dotted line III shown in FIG. 本実施形態に係る熱伝導率測定方法において、式（Ｘ）の直線関係の一例を概念的に示す説明図である。In the thermal conductivity measuring method concerning this embodiment, it is explanatory drawing which shows notionally an example of the linear relationship of Formula (X). 本実施形態に係る熱伝導率測定方法において、式（Ｘ）の直線関係の他の例を概念的に示す説明図である。In the thermal conductivity measuring method concerning this embodiment, it is explanatory drawing which shows notionally other examples of the linear relationship of Formula (X). 本実施形態に係る熱伝導率測定方法において、温度分布関数ｆ（ｘ）の一例を概念的に示す説明図である。In the thermal conductivity measuring method concerning this embodiment, it is explanatory drawing which shows notionally an example of temperature distribution function f (x). 本実施形態に係る実施例において熱伝導率λｔを求めた結果の一例を示す説明図である。It is explanatory drawing which shows an example of the result of having calculated | required thermal conductivity (lambda) t in the Example which concerns on this embodiment.
　以下に、本発明の一実施形態について説明する。なお、本発明は、本実施形態に限られるものではない。 Hereinafter, an embodiment of the present invention will be described. Note that the present invention is not limited to this embodiment.
　図１は、本実施形態に係る熱伝導率測定方法（以下、「本方法」という。）において使用される熱伝導率測定装置（以下、「本装置１」という。）の一例について、その主な構成の断面を示す説明図である。図２は、本装置１の一例について、その一部を構成する部材を斜視で示す説明図である。図３は、図１に示す一点鎖線ＩＩＩで囲まれた本装置１の一部を拡大して示す説明図である。 FIG. 1 shows an example of a thermal conductivity measuring device (hereinafter referred to as “present device 1”) used in a thermal conductivity measuring method (hereinafter referred to as “present method”) according to the present embodiment. It is explanatory drawing which shows the cross section of a various structure. FIG. 2 is an explanatory view showing members constituting a part of the example of the apparatus 1 in perspective. FIG. 3 is an explanatory diagram showing, in an enlarged manner, a part of the apparatus 1 surrounded by the alternate long and short dash line III shown in FIG.
　図１～図３に示すように、本装置１は、試験体１０の一方側及び他方側にそれぞれ配置される熱板１００及び冷却板２００を備えた熱伝導率測定装置である。すなわち、本装置１において、試験体１０は、熱板１００と冷却板２００とに挟持される。 As shown in FIG. 1 to FIG. 3, the present apparatus 1 is a thermal conductivity measuring apparatus including a hot plate 100 and a cooling plate 200 disposed on one side and the other side of a test body 10, respectively. That is, in the apparatus 1, the test body 10 is sandwiched between the hot plate 100 and the cooling plate 200.
　熱板１００は、試験体１０の一方側の表面（以下、「高温表面１１」という。）を加熱する。冷却板２００は、試験体１０の他方側の表面（以下、「低温表面１２」という。）を高温表面１１の温度より低い温度に保つ。 The hot plate 100 heats the surface on one side of the test body 10 (hereinafter referred to as “high temperature surface 11”). The cooling plate 200 keeps the surface on the other side of the test body 10 (hereinafter referred to as “low temperature surface 12”) at a temperature lower than the temperature of the high temperature surface 11.
　具体的に、例えば、熱板１００は、試験体１０の高温表面１１を第一の温度で加熱する高温側ヒータであり、冷却板２００は、当該試験体１０の低温表面１２を当該第一の温度より低い第二の温度で加熱する低温側ヒータである。 Specifically, for example, the hot plate 100 is a high-temperature side heater that heats the high-temperature surface 11 of the test body 10 at a first temperature, and the cooling plate 200 includes the low-temperature surface 12 of the test body 10 as the first temperature. It is a low temperature heater that heats at a second temperature lower than the temperature.
　熱板１００は、試験体１０の中央部分を加熱する主熱板１１０と、当該主熱板１１０を囲むように配置された保護熱板１２０とを有している。主熱板１１０と保護熱板１２０との間には、これらの間の熱伝導を抑制するための断熱層１３０（いわゆるギャップ）が形成されている。 The hot plate 100 includes a main hot plate 110 that heats the central portion of the test body 10 and a protective hot plate 120 that is disposed so as to surround the main hot plate 110. A heat insulating layer 130 (so-called gap) is formed between the main hot plate 110 and the protective hot plate 120 to suppress heat conduction therebetween.
　本装置１は、試験体１０、熱板１００及び冷却板２００の外周を囲むように配置された外周ヒータ３００をさらに備えている。外周ヒータ３００は、試験体１０、熱板１００及び冷却板２００の外周側を加熱する。 The present apparatus 1 further includes an outer peripheral heater 300 arranged so as to surround the outer periphery of the test body 10, the hot plate 100, and the cooling plate 200. The outer peripheral heater 300 heats the outer peripheral side of the test body 10, the hot plate 100 and the cooling plate 200.
　また、図１～図３に示す例において、本装置１は、熱板１００の試験体１０と反対側に配置された断熱材４００、当該断熱材４００の当該熱板１００と反対側に配置されて、その温度が主熱板１１０の温度と等しくなるように制御される補償ヒータ４１０、当該補償ヒータ４１０の当該断熱材４００と反対側に配置された断熱材４２０、冷却板２００の当該試験体１０と反対側に配置された断熱材４３０、これらの外周を囲むように配置され、その外周を外周ヒータ３００で囲まれる断熱材４４０をさらに備えている。 In the example shown in FIGS. 1 to 3, the apparatus 1 is disposed on the heat insulating material 400 on the opposite side of the hot plate 100 from the test body 10 and on the heat insulating material 400 on the opposite side of the heat plate 100. Thus, the compensation heater 410 is controlled so that its temperature becomes equal to the temperature of the main heating plate 110, the heat insulating material 420 disposed on the opposite side of the heat insulating material 400 of the compensation heater 410, and the test body of the cooling plate 200. Further, a heat insulating material 430 disposed on the opposite side to 10 and a heat insulating material 440 disposed so as to surround the outer periphery thereof and surrounded by the outer peripheral heater 300 are further provided.
　熱伝導率の測定時には、試験体１０の高温表面１１を第一の温度に保ち、当該試験体１０の低温表面１２を当該第一の温度より低い第二の温度に保つ。このとき、高温表面１１と低温表面１２との温度差（第一の温度と第二の温度との差）に基づいて、主に当該高温表面１１から当該低温表面１２に向けて、試験体１０内に熱流が生じる。 When measuring the thermal conductivity, the high temperature surface 11 of the test body 10 is kept at the first temperature, and the low temperature surface 12 of the test body 10 is kept at the second temperature lower than the first temperature. At this time, based on the temperature difference between the high temperature surface 11 and the low temperature surface 12 (difference between the first temperature and the second temperature), the specimen 10 mainly from the high temperature surface 11 toward the low temperature surface 12. Heat flow is generated inside.
　また、保護熱板１２０の温度を、主熱板１１０の温度と等しくなるように制御することによって、試験体１０の中央１３から外周端１４に向かう幅方向Ｆｗの熱流を抑制する。 Also, by controlling the temperature of the protective hot plate 120 to be equal to the temperature of the main hot plate 110, the heat flow in the width direction Fw from the center 13 of the test body 10 toward the outer peripheral end 14 is suppressed.
　さらに、熱板１００の試験体１０と反対側に断熱材４００を配置し、さらに、補償ヒータ４１０の温度を、主熱板１１０の温度と等しくなるように制御することによって、当該主熱板１１０から当該試験体１０と反対側に熱流が生じることを抑制し、当該主熱板１１０から冷却板２００への効率的な熱流を実現する。 Furthermore, the heat insulating material 400 is disposed on the opposite side of the hot plate 100 from the test body 10, and the temperature of the compensation heater 410 is controlled to be equal to the temperature of the main hot plate 110, thereby the main hot plate 110. Therefore, it is possible to suppress the heat flow from being generated on the opposite side of the test body 10 and to realize an efficient heat flow from the main hot plate 110 to the cooling plate 200.
　本方法及び本装置１において測定の対象となる試験体１０は、熱板１００と冷却板２００との間に挟持できるものであれば特に限られない。すなわち、試験体１０としては、例えば、断熱材、プラスチック、木材、石膏ボード及びセメントが挙げられる。 The test object 10 to be measured in the present method and the apparatus 1 is not particularly limited as long as it can be sandwiched between the hot plate 100 and the cooling plate 200. That is, examples of the test body 10 include a heat insulating material, plastic, wood, gypsum board, and cement.
　断熱材としては、例えば、繊維質断熱材、多孔質断熱材及び真空断熱材が挙げられる。繊維質断熱材としては、例えば、ロックウール断熱材、グラスウール断熱材、アルミナファイバーウール断熱材、アルミナ系繊維質断熱材及びアルミナシリカ系繊維質断熱材が挙げられる。多孔質断熱材としては、例えば、ケイ酸カルシウム断熱材、発泡ゴム、発泡ウレタン及び発泡スチロールが挙げられる。断熱材は、例えば、断熱材と金属又はガラスとを積層して形成された断熱構造体等の複合断熱材であってもよい。 Examples of the heat insulating material include a fibrous heat insulating material, a porous heat insulating material, and a vacuum heat insulating material. Examples of the fibrous heat insulating material include rock wool heat insulating material, glass wool heat insulating material, alumina fiber wool heat insulating material, alumina fiber heat insulating material, and alumina silica fiber heat insulating material. Examples of the porous heat insulating material include calcium silicate heat insulating material, foam rubber, foamed urethane, and polystyrene foam. The heat insulating material may be a composite heat insulating material such as a heat insulating structure formed by laminating a heat insulating material and metal or glass, for example.
　試験体１０の形状は、熱板１００と冷却板２００との間に挟持できる範囲であれば特に限られず、例えば、図１～図３に示すように、平板状であることが好ましい。 The shape of the test body 10 is not particularly limited as long as it can be sandwiched between the hot plate 100 and the cooling plate 200. For example, as shown in FIGS.
　本装置１は、例えば、ＧＨＰ法又は熱流計法による熱伝導率の測定に使用することができ、特にＧＨＰ法による測定に好ましく使用することができる。なお、図１～図３に示す例では、熱板１００の一方側にのみ試験体１０が配置されているため、熱伝導率の測定は、いわゆる１枚法により行うこととなる。ただし、本方法及び本装置１による熱伝導率の測定は、これに限られず、例えば、２つの試験体１０を熱板１００の一方側及び他方側にそれぞれ配置して（すなわち、当該２つの試験体１０で熱板１００を挟持して）、いわゆる２枚法により行うこともできる。 The present apparatus 1 can be used, for example, for measurement of thermal conductivity by the GHP method or the heat flow meter method, and can be particularly preferably used for measurement by the GHP method. In the example shown in FIGS. 1 to 3, since the test body 10 is disposed only on one side of the hot plate 100, the thermal conductivity is measured by a so-called single sheet method. However, the measurement of the thermal conductivity by the present method and the present apparatus 1 is not limited to this. For example, two test bodies 10 are arranged on one side and the other side of the hot plate 100 (that is, the two tests). It is also possible to carry out the so-called two-sheet method by sandwiching the hot plate 100 with the body 10).
　ＧＨＰ法では、試験体１０を熱板１００で加熱することにより、当該試験体１０の内部において、当該熱板１００から冷却板２００に向かう厚さ方向（図３に示す矢印Ｆｔの指す方向）（すなわち、高温表面１１から低温表面１２に向かう方向）に一次元定常熱流を生じさせる。 In the GHP method, by heating the test body 10 with the hot plate 100, the thickness direction from the hot plate 100 toward the cooling plate 200 in the test body 10 (the direction indicated by the arrow Ft shown in FIG. 3) ( That is, a one-dimensional steady heat flow is generated in a direction from the high temperature surface 11 toward the low temperature surface 12.
　ここで、従来は、上述のとおり、試験体１０の内部において熱は主熱板１１０から冷却板２００に向かう厚さ方向Ｆｔに一次元的に流れると仮定し、下記式（Ｉ）に示す見かけ熱伝導率λａを、試験体１０の熱伝導率として求めていた。
Figure JPOXMLDOC01-appb-M000003
 Here, conventionally, as described above, it is assumed that heat flows one-dimensionally in the thickness direction Ft from the main hot plate 110 toward the cooling plate 200 in the inside of the test body 10, and the appearance shown in the following formula (I) The thermal conductivity λa was obtained as the thermal conductivity of the test body 10.
Figure JPOXMLDOC01-appb-M000003
　なお、上記式（Ｉ）において、Ｑｍは主熱板１１０からの熱流量（主熱板１１０の発熱量）であり、ｄは試験体１０の厚さであり、Δθｔは厚さ方向Ｆｔにおける温度勾配であり、Ｓは厚さ方向Ｆｔにおける試験体１０の伝熱面積である。 In the above formula (I), Qm is the heat flow from the main heat plate 110 (the amount of heat generated by the main heat plate 110), d is the thickness of the test body 10, and Δθt is the temperature in the thickness direction Ft. S is the heat transfer area of the specimen 10 in the thickness direction Ft.
　しかしながら、実際には、図３に示すように、主熱板１１０を発熱させることにより試験体１０の高温表面１１を加熱すると、当該主熱板１１０からの熱流の一部は、試験体１０の内部を厚さ方向Ｆｔに流れ、当該熱流の他の一部は、当該試験体１０の内部を幅方向Ｆｗにも流れる。 However, in actuality, as shown in FIG. 3, when the hot surface 11 of the test body 10 is heated by causing the main hot plate 110 to generate heat, a part of the heat flow from the main hot plate 110 is The inside flows in the thickness direction Ft, and the other part of the heat flow also flows in the width direction Fw inside the test body 10.
　すなわち、例えば、試験体１０が断熱材である場合、当該試験体１０の外周端１４の温度が均一であって且つ主熱板１１０の温度と冷却板２００の温度との平均温度になっていれば、当該試験体１０の外周端１４の厚さ方向Ｆｔ中心を境に主熱板１１０からの熱流量と冷却板２００からの熱流量とが相殺され、当該主熱板１１０で発生した熱を厚さ方向Ｆｔに一次元的に流すことが可能である。 That is, for example, when the test body 10 is a heat insulating material, the temperature of the outer peripheral end 14 of the test body 10 may be uniform and the average temperature of the temperature of the main hot plate 110 and the temperature of the cooling plate 200. For example, the heat flow from the main heat plate 110 and the heat flow from the cooling plate 200 are offset from the center in the thickness direction Ft of the outer peripheral end 14 of the test body 10, and the heat generated in the main heat plate 110 is reduced. It is possible to flow one-dimensionally in the thickness direction Ft.
　しかしながら、逆にいえば、たとえ試験体１０が断熱材であったとしても、当該試験体１０の外周端１４の温度が、当該外周端１４の全域で均一であって且つ主熱板１１０の温度と冷却板２００の温度との平均温度になっていなければ、幅方向Ｆｗの熱流が発生してしまうことになる。この点、現実には、試験体１０の外周端１４の温度を均一にし、且つ当該温度を正確に制御することは難しい。 However, conversely, even if the test body 10 is a heat insulating material, the temperature of the outer peripheral end 14 of the test body 10 is uniform throughout the outer peripheral end 14 and the temperature of the main hot plate 110. If the average temperature of the cooling plate 200 is not reached, a heat flow in the width direction Fw is generated. In this regard, in reality, it is difficult to make the temperature of the outer peripheral end 14 of the test body 10 uniform and accurately control the temperature.
　したがって、本発明の発明者は、試験体１０の熱伝導率を正確に測定する（測定精度を向上させる）ためには、後述するように、当該試験体１０の内部における幅方向Ｆｗの熱流を考慮する必要があると考えた。 Therefore, in order to accurately measure the thermal conductivity of the test body 10 (to improve the measurement accuracy), the inventor of the present invention uses the heat flow in the width direction Fw inside the test body 10 as described later. I thought it was necessary to consider.
　すなわち、実際には、下記式（ＩＩ）で示されるように、主熱板１０からの熱流量Ｑｍは、試験体１０内部を厚さ方向Ｆｔに流れる熱流量Ｑｔと、幅方向Ｆｗに流れる熱流量Ｑｗとに分けられる。
Figure JPOXMLDOC01-appb-M000004
 That is, as shown in the following formula (II), the heat flow Qm from the main hot plate 10 is actually the heat flow Qt flowing in the thickness direction Ft inside the test body 10 and the heat flowing in the width direction Fw. It is divided into the flow rate Qw.
Figure JPOXMLDOC01-appb-M000004
　このとき、試験体１０の厚さ方向Ｆｔの熱伝導率をλｔとすると、下記式（ＩＩＩ）が成立する。
Figure JPOXMLDOC01-appb-M000005
 At this time, when the thermal conductivity in the thickness direction Ft of the test body 10 is λt, the following formula (III) is established.
Figure JPOXMLDOC01-appb-M000005
　なお、厚さ方向Ｆｔの温度勾配Δθｔは、例えば、試験体１０の高温表面１１の温度θｈと、当該試験体１０の低温表面１２の温度θｃとの差（Δθｔ＝θｈ－θｃ）として求められる。 The temperature gradient Δθt in the thickness direction Ft is obtained, for example, as the difference between the temperature θh of the high temperature surface 11 of the test body 10 and the temperature θc of the low temperature surface 12 of the test body 10 (Δθt = θh−θc). .
　温度θｈは、試験体１０の高温表面１１の主熱板１１０と接している部分（当該高温表面１１の中央部分）の温度としてもよく、また、主熱板１１０の試験体１０側の表面１０１の温度としてもよい。また、温度θｃは、試験体１０の低温表面１２の主熱板１１０の位置に対応する部分（当該低温表面１２の中央部分）の温度としてもよく、また、冷却板２００の試験体１０側の表面２０１の主熱板１１０と対向する部分（当該表面２０１の中央部分）の温度としてもよい。温度の測定には、熱電対が好ましく使用される。 The temperature θh may be the temperature of the portion of the high temperature surface 11 of the test body 10 that is in contact with the main hot plate 110 (the center portion of the high temperature surface 11), or the surface 101 of the main hot plate 110 on the test body 10 side. It is good also as temperature of. Further, the temperature θc may be a temperature of a portion corresponding to the position of the main hot plate 110 of the low temperature surface 12 of the test body 10 (a central portion of the low temperature surface 12), or on the test body 10 side of the cooling plate 200. It is good also as the temperature of the part (center part of the said surface 201) facing the main hot platen 110 of the surface 201. FIG. A thermocouple is preferably used for measuring the temperature.
　さらに、試験体１０の幅方向Ｆｗにおける温度勾配をΔθｗとすると、当該幅方向Ｆｗにおける熱流量（当該試験体１０の外周端１４を介して流入又は流出する熱流量）Ｑｗは、下記式（ＩＶ）のように示される。なお、下記式（ＩＶ）において、Ｈは係数である。
Figure JPOXMLDOC01-appb-M000006
 Furthermore, when the temperature gradient in the width direction Fw of the test body 10 is Δθw, the heat flow rate in the width direction Fw (heat flow rate flowing in or out via the outer peripheral end 14 of the test body 10) Qw is expressed by the following formula (IV ). In the following formula (IV), H is a coefficient.
Figure JPOXMLDOC01-appb-M000006
　一方、見かけの熱伝導率λａは、下記式（Ｖ）を変形して得られる上記式（Ｉ）により求められる。
Figure JPOXMLDOC01-appb-M000007
 On the other hand, the apparent thermal conductivity λa is obtained by the above formula (I) obtained by modifying the following formula (V).
Figure JPOXMLDOC01-appb-M000007
　したがって、式（ＩＩＩ）、式（ＩＶ）及び式（Ｖ）を式（ＩＩ）に代入すると、下記式（ＶＩ）が得られ、これを変形すると下記式（ＶＩＩ）が得られる。
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000009
 Therefore, when the formula (III), the formula (IV) and the formula (V) are substituted into the formula (II), the following formula (VI) is obtained, and when the formula is modified, the following formula (VII) is obtained.
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000009
　さらに、下記式（ＶＩＩＩ）のように定数ａを規定し、下記式（ＩＸ）のように無次元温度Θを規定すると、上記式（ＶＩＩ）は、下記式（Ｘ）のようになる。
Figure JPOXMLDOC01-appb-M000010
Figure JPOXMLDOC01-appb-M000011
Figure JPOXMLDOC01-appb-M000012
 Further, when the constant a is defined as in the following formula (VIII) and the dimensionless temperature Θ is defined as in the following formula (IX), the above formula (VII) becomes the following formula (X).
Figure JPOXMLDOC01-appb-M000010
Figure JPOXMLDOC01-appb-M000011
Figure JPOXMLDOC01-appb-M000012
　したがって、図４に示すように、横軸に無次元温度Θ、縦軸に上記式（Ｉ）により求められる見かけ熱伝導率λａをとり、当該無次元温度Θに対する当該見かけ熱伝導率λａをプロットすれば、当該無次元温度Θと当該見かけ熱伝導率λａとの相関関係を示す直線関係が得られる。そして、図４に示すように、試験体１０の厚さ方向Ｆｔの熱伝導率λtは、こうして得られた直線の切片として求められる。 Accordingly, as shown in FIG. 4, the horizontal axis represents the dimensionless temperature Θ, the vertical axis represents the apparent thermal conductivity λa obtained by the above formula (I), and the apparent thermal conductivity λa against the dimensionless temperature Θ is plotted. Then, a linear relationship indicating a correlation between the dimensionless temperature Θ and the apparent thermal conductivity λa is obtained. Then, as shown in FIG. 4, the thermal conductivity λ t in the thickness direction Ft of the test body 10 is obtained as an intercept of the straight line thus obtained.
　なお、無次元温度Θを変化させるには、例えば、試験体１０の外周端１４を囲むように配置された外周ヒータ３００（図１参照）の温度を変化させて、幅方向Ｆｗにおける温度勾配Δθｗを変化させればよい。また、このとき、厚さ方向Ｆｔの温度勾配Δθｔも変化させることとしてもよい。 In order to change the dimensionless temperature Θ, for example, the temperature gradient Δθw in the width direction Fw is changed by changing the temperature of the outer peripheral heater 300 (see FIG. 1) arranged so as to surround the outer peripheral end 14 of the test body 10. Can be changed. At this time, the temperature gradient Δθt in the thickness direction Ft may also be changed.
　具体的に、所定の温度Ｔ℃における熱伝導率λｔを測定する場合について説明する。まず、無次元温度Θと見かけ熱伝導率λａとの相関関係を求めるための複数回の測定のうち、１回目の測定では、高温表面１１の温度θｈを所定の温度Ｔｈ（℃）に設定し、低温表面１２の温度θｃを所定の温度Ｔｃ（℃）に設定し、外周ヒータ３００の温度を第一の温度Ｔｓ１（℃）に設定したとする。このとき、高温表面１１を温度Ｔｈ（℃）に保つために必要な主熱板１１０からの熱流量Ｑｍは、所定値Ｑ１（Ｗ）であったとする。 Specifically, a case where the thermal conductivity λt at a predetermined temperature T ° C. is measured will be described. First, among the plurality of measurements for obtaining the correlation between the dimensionless temperature Θ and the apparent thermal conductivity λa, the temperature θh of the high temperature surface 11 is set to a predetermined temperature Th (° C.) in the first measurement. Assume that the temperature θc of the low temperature surface 12 is set to a predetermined temperature Tc (° C.), and the temperature of the outer peripheral heater 300 is set to the first temperature Ts1 (° C.). At this time, it is assumed that the heat flow rate Qm from the main hot plate 110 necessary for maintaining the high temperature surface 11 at the temperature Th (° C.) is a predetermined value Q1 (W).
　次に、２回目の測定では、外周ヒータ３００の温度を上げて第一の温度Ｔｓ１（℃）より高い第二の温度Ｔｓ２（℃）に設定したとする。このとき、高温表面１１を１回目と同じ温度Ｔｈ（℃）に保つために必要な主熱板１１０からの熱流量Ｑｍは、１回目のＱ１（Ｗ）より小さいＱ２（Ｗ）になる。 Next, in the second measurement, it is assumed that the temperature of the outer heater 300 is increased and set to the second temperature Ts2 (° C.) higher than the first temperature Ts1 (° C.). At this time, the heat flow Qm from the main heating plate 110 necessary to keep the high temperature surface 11 at the same temperature Th (° C.) as the first time becomes Q2 (W) which is smaller than the first time Q1 (W).
　こうして、外周ヒータ３００の温度を変化させると、幅方向Ｆｗにおける温度勾配Δθｗが変化し、その結果、主熱板１１０からの熱流量Ｑｍも変化することとなる。また、外周ヒータ３００の温度を変化させることで、厚さ方向Ｆｔの温度勾配Δθｔ（＝θｈ－θｃ）も変化することとしてもよい。この場合であっても、上記式（Ｘ）では変数が無次元温度Θ（Δθｗ／Δθｔ）であるため、例えば、高温表面１１の温度θｈ及び／又は低温表面１２の温度θｃの変動は、測定誤差をもたらさない。 Thus, when the temperature of the outer peripheral heater 300 is changed, the temperature gradient Δθw in the width direction Fw is changed, and as a result, the heat flow rate Qm from the main heat plate 110 is also changed. Further, the temperature gradient Δθt (= θh−θc) in the thickness direction Ft may be changed by changing the temperature of the outer peripheral heater 300. Even in this case, since the variable is the dimensionless temperature Θ (Δθw / Δθt) in the above formula (X), for example, the fluctuation of the temperature θh of the high temperature surface 11 and / or the temperature θc of the low temperature surface 12 is measured. Does not introduce errors.
　本方法では、試験体１０の高温表面１１から低温表面１２までの範囲の任意の位置（例えば、高温表面１１、低温表面１２又は試験体１０の内部において幅方向Ｆｗに延びる仮想平面）における幅方向Ｆｗの温度勾配Δθｗについて、上記式（Ｘ）が成立する。さらに、仮に、上記式（Ｘ）における係数ａが温度勾配Δθｗに依存して変化した場合であっても、図５に示すように、直線の傾き（当該係数ａ）は変化するものの、切片である熱伝導率λｔは変化せず一定となる。 In this method, the width direction at an arbitrary position in the range from the high temperature surface 11 to the low temperature surface 12 of the test body 10 (for example, a virtual plane extending in the width direction Fw inside the high temperature surface 11, the low temperature surface 12, or the test body 10). The above formula (X) is established for the temperature gradient Δθw of Fw. Furthermore, even if the coefficient a in the above formula (X) changes depending on the temperature gradient Δθw, the slope of the straight line (the coefficient a) changes as shown in FIG. A certain thermal conductivity λt does not change and is constant.
　したがって、本方法によれば、試験体１０の厚さ方向Ｆｔの任意の位置における幅方向Ｆｗの温度勾配Δθｗに基づいて、無次元温度Θ及び見かけ熱伝導率λａの測定を繰り返し、上記式（Ｘ）に示す相関関係を求めることにより、当該試験体１０の厚さ方向Ｆｔの熱伝導率λｔを得ることができる。 Therefore, according to this method, the measurement of the dimensionless temperature Θ and the apparent thermal conductivity λa is repeated based on the temperature gradient Δθw in the width direction Fw at an arbitrary position in the thickness direction Ft of the test body 10, and the above formula ( By obtaining the correlation shown in X), the thermal conductivity λt in the thickness direction Ft of the specimen 10 can be obtained.
　次に、幅方向Ｆｗにおける温度勾配Δθｗを決定する方法について説明する。温度勾配Δθｗを測定する平面（例えば、高温表面１１、低温表面１２又は試験体１０の内部において幅方向Ｆｗに延びる仮想平面）内において、図３に示すように、断熱層１３０の位置に相当する位置を原点に決定し、当該平面内の温度分布を関数ｆ（ｘ）で表すこととする。なお、原点の位置は特に限られず、例えば、図３に示す例では、断熱層１３０の幅方向Ｆｗにおける中央を原点としている。 Next, a method for determining the temperature gradient Δθw in the width direction Fw will be described. In the plane for measuring the temperature gradient Δθw (for example, a virtual plane extending in the width direction Fw inside the high temperature surface 11, the low temperature surface 12, or the test body 10), as shown in FIG. 3, it corresponds to the position of the heat insulating layer 130. The position is determined as the origin, and the temperature distribution in the plane is represented by a function f (x). The position of the origin is not particularly limited. For example, in the example illustrated in FIG. 3, the center in the width direction Fw of the heat insulating layer 130 is the origin.
　図６には、温度分布関数ｆ（ｘ）の一例を示す。図６に示す例において、温度分布関数ｆ（ｘ）は、原点（０）よりマイナス側（主熱板１１０側）に所定の距離ｘｍだけ離れた位置（－ｘｍ）から、当該原点よりプラス側（保護熱板１２０側）に所定の距離ｘｅだけ離れた位置（ｘｅ）、すなわち試験体１０の外周端１４までの温度分布を表わす関数である。 FIG. 6 shows an example of the temperature distribution function f (x). In the example shown in FIG. 6, the temperature distribution function f (x) is determined from the origin from a position (−x m ) separated from the origin (0) by a predetermined distance x m on the minus side (main heat plate 110 side). This is a function representing a temperature distribution to a position (x e ) that is a predetermined distance x e away from the plus side (protective heat plate 120 side), that is, to the outer peripheral end 14 of the specimen 10.
　図３に示す例において、原点から試験体１０の外周端１４までの範囲（プラス側）における平均温度θｅは、下記式（ＸＩ）で表される。
Figure JPOXMLDOC01-appb-M000013
 In the example shown in FIG. 3, the average temperature θe in the range (plus side) from the origin to the outer peripheral end 14 of the specimen 10 is expressed by the following formula (XI).
Figure JPOXMLDOC01-appb-M000013
　一方、原点から試験体１０の中央１３側の任意の位置（ｘｍ）までの範囲（マイナス側）における平均温度θｍは、下記式（ＸＩＩ）で表される。ただし、ここでは、位置（－ｘｍ）よりもさらに試験体１０の中央１３側では、温度は一定になっていると仮定している。
Figure JPOXMLDOC01-appb-M000014
 On the other hand, the average temperature θm in the range (minus side) from the origin to an arbitrary position (x m ) on the center 13 side of the specimen 10 is represented by the following formula (XII). However, here, it is assumed that the temperature is constant on the center 13 side of the test body 10 further than the position (−x m ).
Figure JPOXMLDOC01-appb-M000014
　したがって、上記式（ＸＩ）及び式（ＸＩＩ）より、幅方向Ｆｗの温度勾配Δθｗは下記式（ＸＩＩＩ）で求められる。すなわち、この温度勾配Δθｗは、断熱層１３０より主熱板１１０側における試験体１０の平均温度θｍと、当該断熱層１３０より保護熱板１２０側における当該試験体１０の平均温度θｅと、の差として求められる。
Figure JPOXMLDOC01-appb-M000015
 Therefore, the temperature gradient Δθw in the width direction Fw is obtained by the following formula (XIII) from the above formulas (XI) and (XII). That is, this temperature gradient Δθw is the difference between the average temperature θm of the test body 10 on the main heat plate 110 side from the heat insulating layer 130 and the average temperature θe of the test body 10 on the protective heat plate 120 side from the heat insulating layer 130. As required.
Figure JPOXMLDOC01-appb-M000015
　ここで、図３に示す例では、試験体１０の低温表面１２上の５箇所に熱電対Ｐｃ１～Ｐｃ５を設置し、当該５箇所で温度θｃを測定する。そして、横軸に原点からの距離ｘ、縦軸に測定された温度θｃをとって、当該距離ｘに対する温度θｃをプロットし、当該プロットを最小二乗法により二次曲線で近似して、温度分布関数ｆ（ｘ）を求める。 Here, in the example shown in FIG. 3, thermocouples Pc1 to Pc5 are installed at five locations on the low temperature surface 12 of the test body 10, and the temperature θc is measured at the five locations. Then, taking the distance x from the origin on the horizontal axis and the temperature θc measured on the vertical axis, the temperature θc with respect to the distance x is plotted, and the plot is approximated by a quadratic curve by the least square method to obtain the temperature distribution. A function f (x) is obtained.
　したがって、関数ｆ（ｘ）を下記式（ＸＩＶ）とおいて、上記式（ＸＩ）及び式（ＸＩＩ）より、下記式（ＸＶ）及び式（ＸＶＩ）を得る。なお、式（ＸＩＶ）、式（ＸＶ）及び式（ＸＶＩ）において、ｈ１、ｈ２及びｈ３は係数である。
Figure JPOXMLDOC01-appb-M000016
Figure JPOXMLDOC01-appb-M000017
Figure JPOXMLDOC01-appb-M000018
 Accordingly, assuming that the function f (x) is the following formula (XIV), the following formula (XV) and formula (XVI) are obtained from the above formula (XI) and formula (XII). In formula (XIV), formula (XV), and formula (XVI), h 1 , h 2, and h 3 are coefficients.
Figure JPOXMLDOC01-appb-M000016
Figure JPOXMLDOC01-appb-M000017
Figure JPOXMLDOC01-appb-M000018
　なお、温度分布関数ｆ（ｘ）は、二次曲線に限られず、例えば、一次直線、三次曲線、四次曲線等の多項式、指数関数等、任意の関数で近似することができる。 The temperature distribution function f (x) is not limited to a quadratic curve, and can be approximated by an arbitrary function such as a polynomial such as a linear curve, a cubic curve, or a quartic curve, or an exponential function.
　次に、試験体１０の厚さｄを変化させることで、幅方向Ｆｗにおける熱流を考慮しつつ、当該試験体１０の厚さ方向Ｆｔにおける熱伝導率λｔを求める場合について説明する。この場合、幅方向Ｆｗの熱流量Ｑｗは、試験体１０の外周端１４の面積に比例するため、当該試験体１０の外周長をＬとし、比例係数をＫとすると、当該熱流量Ｑｗは、下記式（ＸＶＩＩ）で表される。
Figure JPOXMLDOC01-appb-M000019
 Next, a case where the thermal conductivity λt in the thickness direction Ft of the test body 10 is obtained by changing the thickness d of the test body 10 while considering the heat flow in the width direction Fw will be described. In this case, since the heat flow rate Qw in the width direction Fw is proportional to the area of the outer peripheral end 14 of the test body 10, if the outer peripheral length of the test body 10 is L and the proportionality coefficient is K, the heat flow rate Qw is It is represented by the following formula (XVII).
Figure JPOXMLDOC01-appb-M000019
　上記式（ＩＩ）に、上記式（ＩＩＩ）、式（Ｖ）及び式（ＸＶＩＩ）を代入すると、下記式（ＸＶＩＩＩ）が得られ、これを変形すると下記式（ＸＩＸ）が得られる。
Figure JPOXMLDOC01-appb-M000020
Figure JPOXMLDOC01-appb-M000021
 Substituting the above formula (III), formula (V) and formula (XVII) into the above formula (II) yields the following formula (XVIII), and transforming this yields the following formula (XIX).
Figure JPOXMLDOC01-appb-M000020
Figure JPOXMLDOC01-appb-M000021
　ここで、試験体１０の厚さｄを変化させても、ΔθｗとΔθｔとの比が一定となるように温度を制御すれば、下記式（ＸＸ）のように定数ｂを規定することで、下記式（ＸＸＩ）が得られる。なお、このような精密な温度制御は、例えば、ペルチェヒータを使用することで実現できる。
Figure JPOXMLDOC01-appb-M000022
Figure JPOXMLDOC01-appb-M000023
 Here, even if the thickness d of the test body 10 is changed, if the temperature is controlled so that the ratio of Δθw and Δθt is constant, the constant b is defined as in the following formula (XX): The following formula (XXI) is obtained. Such precise temperature control can be realized, for example, by using a Peltier heater.
Figure JPOXMLDOC01-appb-M000022
Figure JPOXMLDOC01-appb-M000023
　したがって、この場合、横軸に試験体１０の厚さｄの二乗である変数ｄ２をとり、縦軸に測定された見かけ熱伝導率λａをとって、当該変数ｄ２に対して当該見かけ熱伝導率λａをプロットすれば、当該変数ｄ２と当該見かけ熱伝導率λａとの相関関係を示す直線関係が得られる。そして、厚さ方向Ｆｔの熱伝導率λｔは、この直線の切片として求められる。 Therefore, in this case, the variable d 2 that is the square of the thickness d of the test body 10 is taken on the horizontal axis, and the apparent thermal conductivity λa is taken on the vertical axis, and the apparent heat with respect to the variable d 2 is taken. if plotted conductivity [lambda] a, linear relationship showing the correlation between the variables d 2 and the apparent thermal conductivity [lambda] a is obtained. The thermal conductivity λt in the thickness direction Ft is obtained as an intercept of this straight line.
　なお、例えば、試験体１０の厚さｄを変化させると、厚さ方向Ｆｔにおける温度勾配Δθｔも変化する場合には、ｄ２／Δθｔを変数として決定し、上記式（ＸＩＸ）に基づき、当該変数と見かけ熱伝導率λａとの直線関係を得ることとしてもよい。 For example, when the thickness d of the test body 10 is changed, if the temperature gradient Δθt in the thickness direction Ft also changes, d 2 / Δθt is determined as a variable, and based on the above formula (XIX) A linear relationship between the variable and the apparent thermal conductivity λa may be obtained.
　また、例えば、試験体１０の厚さ方向Ｆｔにおける伝熱面積Ｓの逆数（１／Ｓ）を含む変数を決定し、当該伝熱面積Ｓを変化させながら見かけ熱伝導率λａを測定し、上記式（ＸＩＸ）に基づき、当該変数と当該見かけ熱伝導率λａとの直線関係を得ることとしてもよい。 Further, for example, a variable including the reciprocal (1 / S) of the heat transfer area S in the thickness direction Ft of the test body 10 is determined, and the apparent thermal conductivity λa is measured while changing the heat transfer area S, Based on the formula (XIX), a linear relationship between the variable and the apparent thermal conductivity λa may be obtained.
　このように、本方法は、幅方向Ｆｗにおける熱流量Ｑｗを変化させる測定条件を含む変数を決定すること、及び当該変数と、上記式（Ｉ）で示される見かけ熱伝導率λａとの相関関係を求めること、を含む熱伝導率測定方法である。 Thus, this method determines the variable including the measurement condition for changing the heat flow rate Qw in the width direction Fw, and the correlation between the variable and the apparent thermal conductivity λa represented by the above formula (I). Determining the thermal conductivity.
　すなわち、本方法においては、幅方向Ｆｗにおける熱流量Ｑｗを変化させる測定条件を含む変数と、見かけ熱伝導率λａとの相関関係に基づき、試験体１０の厚さ方向Ｆｔにおける熱伝導率λｔを求める。 That is, in this method, the thermal conductivity λt in the thickness direction Ft of the specimen 10 is calculated based on the correlation between the variable including the measurement condition for changing the heat flow rate Qw in the width direction Fw and the apparent thermal conductivity λa. Ask.
　より具体的には、変数に含まれる測定条件を変化させながら、見かけ熱伝導率λａを測定し、当該測定により得られた当該変数と当該見かけ熱伝導率λａとの相関関係に基づき、試験体１０の熱伝導率λｔを求める。 More specifically, the apparent thermal conductivity λa is measured while changing the measurement conditions included in the variable, and based on the correlation between the variable obtained by the measurement and the apparent thermal conductivity λa, the specimen A thermal conductivity λt of 10 is obtained.
　変数に含まれる測定条件は、例えば、上述のとおり、幅方向Ｆｗにおける温度勾配Δθｗ、試験体１０の厚さｄ及び当該試験体１０の厚さ方向Ｆｔにおける伝熱面積Ｓからなる群より選択される１つ以上であることとしてもよい。 For example, as described above, the measurement condition included in the variable is selected from the group consisting of the temperature gradient Δθw in the width direction Fw, the thickness d of the test body 10 and the heat transfer area S in the thickness direction Ft of the test body 10. It may be one or more.
　幅方向Ｆｗにおける温度勾配Δθｗを測定する場合、本装置１は、図３に示すように、幅方向Ｆｗにおける温度分布を測定するためのセンサーＰを備える熱伝導率測定装置であることとしてもよい。 When measuring the temperature gradient Δθw in the width direction Fw, the apparatus 1 may be a thermal conductivity measuring apparatus including a sensor P for measuring the temperature distribution in the width direction Fw, as shown in FIG. .
　ここで、上述のとおり、従来の熱伝導率測定においては、幅方向Ｆｗにおける熱流量Ｑｗを無視していた。このため、従来の熱伝導率測定装置は、幅方向Ｆｗにおける温度分布を測定するためのセンサーＰを備えていなかった。すなわち、幅方向Ｆｗにおける温度分布を測定するためのセンサーＰを備えた本装置１は、幅方向Ｆｗにおける熱流量Ｑｗを考慮して厚さ方向Ｆｔにおける熱伝導率λｔを測定するために特化した従来にない熱伝導率測定装置である。 Here, as described above, in the conventional thermal conductivity measurement, the heat flow rate Qw in the width direction Fw was ignored. For this reason, the conventional thermal conductivity measuring apparatus is not provided with the sensor P for measuring the temperature distribution in the width direction Fw. That is, the present apparatus 1 including the sensor P for measuring the temperature distribution in the width direction Fw is specialized for measuring the thermal conductivity λt in the thickness direction Ft in consideration of the heat flow rate Qw in the width direction Fw. This is an unprecedented thermal conductivity measuring device.
　幅方向Ｆｗの温度勾配Δθｗは、上述のとおり、試験体１０の当該幅方向Ｆｗにおける複数の位置で温度を測定することにより得られる。そこで、本装置１は、図３に示すように、試験体１０の幅方向Ｆｗにおける複数の位置に配置された複数のセンサーＰを備える。 The temperature gradient Δθw in the width direction Fw is obtained by measuring temperatures at a plurality of positions in the width direction Fw of the test body 10 as described above. Therefore, the apparatus 1 includes a plurality of sensors P arranged at a plurality of positions in the width direction Fw of the test body 10 as shown in FIG.
　より具体的に、本装置１は、図３に示すように、試験体１０の低温表面１２又は冷却板２００の当該試験体１０側の表面２０１における複数の位置で温度を測定するための複数のセンサーＰｃ１～Ｐｃ５を備えることとしてもよく、試験体１０の高温表面１１又は熱板１００の当該試験体１０側の表面１０１における複数の位置で温度を測定するための複数のセンサーＰｈ１～Ｐｈ５を備えることとしてもよく、試験体１０の内部（高温表面１１と低温表面１２との間の範囲）において幅方向Ｆｗに延びる仮想平面上の複数の位置で温度を測定するための複数のセンサーＰｉ１～Ｐｉ５を備えることとしてもよい。 More specifically, as shown in FIG. 3, the apparatus 1 includes a plurality of temperatures for measuring temperatures at a plurality of positions on the low temperature surface 12 of the test body 10 or the surface 201 of the cooling plate 200 on the test body 10 side. Sensors Pc1 to Pc5 may be provided, and a plurality of sensors Ph1 to Ph5 for measuring temperatures at a plurality of positions on the high temperature surface 11 of the test body 10 or the surface 101 of the hot plate 100 on the test body 10 side may be provided. A plurality of sensors Pi1 to Pi5 for measuring temperatures at a plurality of positions on a virtual plane extending in the width direction Fw in the inside of the test body 10 (range between the high temperature surface 11 and the low temperature surface 12). It is good also as providing.
　また、試験体１０が薄い場合、及び／又は試験体１０が小さい場合には、センサー（例えば、熱電対）の存在が、表面（例えば、試験体１０の高温表面１１及び低温表面１２、熱板１００の表面１０１、冷却板２００の表面２０１）における温度の測定に与える影響が大きくなるため、当該表面における温度勾配Δθｗを正確に測定できないことがある。 Further, when the test body 10 is thin and / or when the test body 10 is small, the presence of a sensor (for example, a thermocouple) is detected on the surface (for example, the high temperature surface 11 and the low temperature surface 12 of the test body 10, the hot plate). Since the influence on the measurement of the temperature at the surface 101 of the 100 and the surface 201 of the cooling plate 200 becomes large, the temperature gradient Δθw at the surface may not be measured accurately.
　この場合、例えば、上述のとおり、ΔθｗとΔθｔとの比（Δθｗ／Δθｔ）を一定となるように制御すれば、試験体１０の厚さｄを変化させながら見かけ熱伝導率λａを測定することで、上記式（ＸＸＩ）に基づき、変数（ｄ２）と当該見かけ熱伝導率λａとの直線関係から、厚さ方向Ｆｔの熱伝導率λｔを求めることができる。 In this case, for example, as described above, if the ratio of Δθw and Δθt (Δθw / Δθt) is controlled to be constant, the apparent thermal conductivity λa is measured while changing the thickness d of the specimen 10. Thus, based on the above formula (XXI), the thermal conductivity λt in the thickness direction Ft can be obtained from the linear relationship between the variable (d 2 ) and the apparent thermal conductivity λa.
　また、少なくとも幅方向Ｆｗの温度勾配Δθｗを一定に制御すれば、上記式（ＸＩＸ）に基づき、変数（ｄ２／Δθｔ）と見かけ熱伝導率λａとの直線関係から、厚さ方向Ｆｔの熱伝導率λｔを求めることができる。 Further, if at least the temperature gradient Δθw in the width direction Fw is controlled to be constant, the heat in the thickness direction Ft is calculated from the linear relationship between the variable (d 2 / Δθt) and the apparent thermal conductivity λa based on the above formula (XIX). The conductivity λt can be obtained.
　なお、本方法は、上述した例に限られない。すなわち、例えば、本方法は、上記式（ＸＩＸ）の右辺第二項に含まれるパラメータ（Ｌ、ｄ２、Ｓ、Δθｗ及びΔθｔ）の少なくとも一つを含む変数を決定すること、前記変数を変化させながら、左辺の見かけ熱伝導率λａを上記式（Ｉ）により測定すること、当該変数と当該見かけ熱伝導率λａとの直線関係を得ること、及び当該直線関係に基づいて右辺第一項の熱伝導率λｔを求める方法であることとしてもよい。また、熱伝導率λｔを測定する温度は特に限られず、例えば、－１７０℃以上、１００℃以下の温度における熱伝導率λｔを測定することとしてもよく、１００℃以上、１５００℃以下の温度における熱伝導率λｔを測定することとしてもよい。 Note that the present method is not limited to the example described above. That is, for example, the method determines a variable including at least one of the parameters (L, d 2 , S, Δθw, and Δθt) included in the second term on the right side of the formula (XIX), and changes the variable. While measuring the apparent thermal conductivity λa of the left side by the above formula (I), obtaining a linear relationship between the variable and the apparent thermal conductivity λa, and based on the linear relationship, It may be a method of obtaining the thermal conductivity λt. The temperature at which the thermal conductivity λt is measured is not particularly limited. For example, the thermal conductivity λt at a temperature of −170 ° C. or higher and 100 ° C. or lower may be measured, and at a temperature of 100 ° C. or higher and 1500 ° C. or lower. The thermal conductivity λt may be measured.
　次に、本実施形態に係る具体的な実施例について説明する。 Next, specific examples according to this embodiment will be described.
　図１～図３に示すような本装置１を使用して、１枚方式のＧＨＰ法により、２００℃、４００℃、５００℃、６００℃、７００℃及び８００℃における、アルミナ－シリカ系繊維質断熱材の厚さ方向Ｆｔの熱伝導率λｔを測定した。 Using this apparatus 1 as shown in FIGS. 1 to 3, alumina-silica fiber at 200.degree. C., 400.degree. C., 500.degree. C., 600.degree. C., 700.degree. The thermal conductivity λt in the thickness direction Ft of the heat insulating material was measured.
　すなわち、まず、上記式（ＩＸ）で示される無次元温度Θを変数として決定した。次いで、外周ヒータ３００の温度を変えることで無次元温度Θ（特に、幅方向Ｆｗの温度勾配Δθｗ）を変化させながら、上記式（Ｉ）により見かけ熱伝導率λａを測定した。 That is, first, the dimensionless temperature Θ represented by the above formula (IX) was determined as a variable. Next, the apparent thermal conductivity λa was measured by the above formula (I) while changing the dimensionless temperature Θ (particularly the temperature gradient Δθw in the width direction Fw) by changing the temperature of the outer heater 300.
　なお、温度勾配Δθｗは、図３に示すように、断熱材（試験体１０）の低温表面１２の５箇所に配置したセンサー（熱電対）Ｐｃ１～Ｐｃ５、又は当該断熱材の厚さ方向Ｆｔ中央の５箇所に配置したセンサー（熱電対）Ｐｉ１～Ｐｉ５により測定した温度に基づき、上記式（ＸＩＩＩ）により求めた。また、厚さ方向Ｆｔの温度勾配Δθｔは、高温表面１１の主熱板１１０に接する部分の温度θｈ及び低温表面１２の当該部分に対応する位置の温度θｃをセンサー（熱電対）により測定し、当該温度θｈと当該温度θｃとの差として求めた（Δθｔ＝θｈ－θｃ）。 Note that the temperature gradient Δθw is, as shown in FIG. 3, the sensors (thermocouples) Pc1 to Pc5 arranged at five locations on the low temperature surface 12 of the heat insulating material (test body 10), or the thickness direction Ft center of the heat insulating material. Based on the temperature measured by the sensors (thermocouples) Pi1 to Pi5 arranged at the five locations, the above formula (XIII) was used. Further, the temperature gradient Δθt in the thickness direction Ft is measured by a sensor (thermocouple) by measuring the temperature θh of the portion of the high temperature surface 11 in contact with the main hot plate 110 and the temperature θc of the position corresponding to the portion of the low temperature surface 12, The difference between the temperature θh and the temperature θc was obtained (Δθt = θh−θc).
　そして、各測定温度について、無次元温度Θに対して見かけ熱伝導率λａをプロットし、当該プロットを最小二乗法で直線近似することにより、図２に示すような直線関係が得られた。得られた直線の切片の値を熱伝導率λｔとして得た。また、比較のため、周期加熱法による熱伝導率測定装置を使用して、同様に断熱材の熱伝導率を測定した。 Then, for each measured temperature, the apparent thermal conductivity λa was plotted against the dimensionless temperature Θ, and a linear relationship as shown in FIG. 2 was obtained by linearly approximating the plot by the least square method. The value of the obtained intercept of the straight line was obtained as the thermal conductivity λt. Moreover, the thermal conductivity of the heat insulating material was similarly measured using the thermal conductivity measuring apparatus by a period heating method for the comparison.
　図７に、各温度において断熱材の熱伝導率λｔを求めた結果を示す。図７において、横軸は熱伝導率λｔを測定した温度（℃）を示し、縦軸は各温度で測定された熱伝導率λｔ（Ｗ／（ｍ・Ｋ））を示す。 FIG. 7 shows the results of obtaining the thermal conductivity λt of the heat insulating material at each temperature. In FIG. 7, the horizontal axis indicates the temperature (° C.) at which the thermal conductivity λt is measured, and the vertical axis indicates the thermal conductivity λt (W / (m · K)) measured at each temperature.
　図７において、白抜き四角印は、試験体１０の低温表面１２における温度分布を使用して求められた熱伝導率λｔを示し、白抜き三角印は、試験体１０の厚さ方向Ｆｔにおける中央における温度分布を使用して求められた熱伝導率λｔを示し、黒塗り丸印は、周期加熱法により求められた熱伝導率を示す。また、図７において、２本の破線で囲んだ領域は、周期加熱法による測定結果との誤差がプラス１０％（＋１０％）～マイナス１０％（－１０％）である範囲を示している。 In FIG. 7, a white square mark indicates the thermal conductivity λt obtained using the temperature distribution on the low temperature surface 12 of the test body 10, and a white triangle mark indicates the center in the thickness direction Ft of the test body 10. The thermal conductivity λt obtained by using the temperature distribution in Fig. 5 is shown, and the black circles indicate the thermal conductivity obtained by the periodic heating method. In FIG. 7, the area surrounded by two broken lines indicates a range in which the error from the measurement result by the periodic heating method is plus 10% (+ 10%) to minus 10% (−10%).
　図７に示すように、本装置１を使用した本方法により求められた熱伝導率λｔは、周期加熱法により求められた熱伝導率とほぼ一致していた。すなわち、本装置１及び本方法によれば、幅方向Ｆｗの熱流を考慮することにより、厚さ方向Ｆｔの熱伝導率λｔを高い精度で測定できることが確認された。 As shown in FIG. 7, the thermal conductivity λt obtained by the present method using the apparatus 1 almost coincided with the thermal conductivity obtained by the periodic heating method. That is, according to this apparatus 1 and this method, it was confirmed that the thermal conductivity λt in the thickness direction Ft can be measured with high accuracy by considering the heat flow in the width direction Fw.
　１　熱伝導率測定装置、１０　試験体、１１　高温表面、１２　低温表面、１３　試験体の幅方向における中央、１４　外周端、１００　熱板、１０１　試験体側の表面、１１０　主熱板、１２０　保護熱板、１３０　断熱層、２００　冷却板、２０１　試験体側の表面、３００　外周ヒータ、４００，４２０，４３０，４４０　断熱材、４１０　補償ヒータ。 DESCRIPTION OF SYMBOLS 1 Thermal conductivity measuring apparatus, 10 test body, 11 high temperature surface, 12 low temperature surface, 13 center in the width direction of test body, 14 outer peripheral edge, 100 hot plate, 101 test body side surface, 110 main hot plate, 120 protection heat Plate, 130 heat insulation layer, 200 cooling plate, 201 surface on the specimen side, 300 outer peripheral heater, 400, 420, 430, 440 heat insulating material, 410 compensation heater.

Claims (3)

  1. 　試験体を熱板と冷却板との間に配置して、前記熱板から前記冷却板に向かう厚さ方向における前記試験体の熱伝導率λｔを測定する方法であって、
    　前記試験体の中央から外周端又は前記外周端から前記中央に向かう幅方向における熱流量を変化させる測定条件を含む変数を決定すること、及び
    　前記変数と、下記式（Ｉ）で示される見かけ熱伝導率λａとの相関関係を求めること、
    　を含む
    　ことを特徴とする熱伝導率測定方法。
    Figure JPOXMLDOC01-appb-M000001
     （式（Ｉ）において、Ｑｍは前記熱板からの熱流量であり、ｄは前記試験体の厚さであり、Δθｔは前記厚さ方向における温度勾配であり、Ｓは前記厚さ方向における前記試験体の伝熱面積である。）     A method of measuring a thermal conductivity λt of the test body in a thickness direction from the hot plate toward the cooling plate by disposing the test piece between a hot plate and a cooling plate,
    Determining a variable including a measurement condition for changing a heat flow rate in a width direction from the center of the specimen to the outer peripheral end or from the outer peripheral end toward the center; and the apparent heat represented by the following formula (I): Obtaining a correlation with the conductivity λa;
    The thermal conductivity measuring method characterized by including.
    Figure JPOXMLDOC01-appb-M000001
     (In Formula (I), Qm is the heat flow from the hot plate, d is the thickness of the specimen, Δθt is the temperature gradient in the thickness direction, and S is the thickness in the thickness direction. (The heat transfer area of the specimen.)
  2. 　前記変数に含まれる前記測定条件は、前記幅方向における温度勾配Δθｗ、前記厚さｄ及び前記伝熱面積Ｓからなる群より選択される１つ以上である
    　ことを特徴とする請求項１に記載された熱伝導率測定方法。     The measurement condition included in the variable is at least one selected from the group consisting of a temperature gradient Δθw in the width direction, the thickness d, and the heat transfer area S. Thermal conductivity measurement method.
  3. 　試験体の一方側及び他方側にそれぞれ配置される熱板及び冷却板を備えた熱伝導率測定装置であって、
    　前記試験体の中央から外周端又は前記外周端から前記中央に向かう幅方向における温度分布を測定するためのセンサーをさらに備えた
    　ことを特徴とする熱伝導率測定装置。     A thermal conductivity measuring device provided with a hot plate and a cooling plate respectively disposed on one side and the other side of the test body,
    A thermal conductivity measuring device further comprising a sensor for measuring a temperature distribution in a width direction from the center of the test body to the outer peripheral end or from the outer peripheral end toward the center.
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