JP2787647B2 - Method and apparatus for measuring thermal conductivity - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for measuring thermal conductivity.

[0002]

2. Description of the Related Art
Laser flash method (JIS
R1611) are often used. In this method, one side of the sample is irradiated with a laser beam of a certain wavelength to instantaneously heat the sample, and the thermal diffusivity is obtained from the temperature rise of the other side of the sample, and the thermal conductivity is calculated from this. Things.

[0003] Specifically, assuming that the specific gravity of a sample is ρ, the thermal diffusivity is α (cm ² / sec), and the specific heat is Cp (J / g ° C), the following equation: Thermal conductivity = ρ × α × Cp × 100 Is used to determine the thermal conductivity.

However, when determining the thermal conductivity by this method, it is necessary to first know the specific heat Cp of the sample.
The measured value of the specific heat Cp generally varies greatly. Therefore, the value of the thermal conductivity obtained by the same method is not reliable because of the variation in the measured specific heat Cp and other error factors. The fact was that they were poor.

[0005] On the other hand, as shown in FIG.
04, a temperature difference Th-Tc between the point H (high temperature point) and the point C (low temperature point) of the sample 102 is obtained, and the following equation P = KS (Th-Tc) / L ( Or P / S = K (Th
-Tc) / L) is also known as a method of determining the thermal conductivity K. Here, P represents the amount of heat generated by the heater 100, S represents the cross-sectional area of the sample, and L represents the distance between the point H and the point C.

However, in the case of this method, Th, Tc
Unavoidable loss of heat due to heat conduction through thermocouples and heater wires, heat conduction and convection through air, and radiation that occurs essentially at high temperatures.
This causes a problem that a relatively large error occurs.

To improve this, a method as shown in FIG. 4B has been proposed. This method is called a guarded hot plate method, and its feature is that the main heater 108 is covered by the guard heater 112, so that loss of heat from the main heater 108 is reduced.

More specifically, in the figure, reference numeral 106 denotes a disk-shaped sample; 108, a main heater having a heating wire 110;
2 is a guard heater having a heating wire 114 and a main heater 10
8 are arranged so as to cover them. These main heaters 108
A predetermined gap 116 is formed between the heater and the guard heater 112. Reference numeral 118 denotes a heat sink.

In this method, the temperature of the guard heater 112 is set to be the same as the temperature of the main heater 108, so that the main heater 108
Therefore, the amount of heat that is lost without being supplied to the sample 106 is reduced as much as possible, whereby the measurement error of the thermal conductivity K can be reduced.

However, even with this method, it is inevitable that a calorific value loss occurs, and therefore, a measurement error caused by this loss cannot be avoided. However, in the same method, Th-
If the temperature difference of Tc is made large, the error can be made small. However, if Th-Tc is made large, there arises a problem that the temperature at the time of measuring the thermal conductivity becomes unclear.

Although the thermal conductivity of a substance has almost no dependence on temperature, such as a slide glass shown in FIG. 5A, there is generally a thermal conductivity depending on the temperature, such as silicon rubber shown in B in FIG. Usually, the conductivity changes. If Th-Tc is too large as described above, it becomes unclear how many times the thermal conductivity is measured even when the thermal conductivity is measured.

[0012]

The invention of the present application has been made to solve such a problem. Thus, the gist of the present invention is to heat a heated portion of a sample whose thermal conductivity K is to be measured by a heating means and to detect the temperature of the heated portion, while detecting the temperature of the heated portion at a specific distance from the heated portion. By detecting the temperature and changing the temperature of the specific portion at a temperature lower than the temperature of the heated portion while maintaining the temperature of the heated portion constant, the temperature Th of the heated portion and the temperature Tc of the specific portion are changed. The temperature difference Th-Tc is variously changed, and at that time, the amount of heat P generated by the heating means is measured for each value of Th-Tc in order to keep the temperature Th of the heating portion constant. From a plurality of coordinate values represented by the measured value and the value of Th-Tc, a relational expression P = (KS / L) (Th-T
c) A straight line represented by + Qe is specified, and the thermal conductivity K is obtained from the slope thereof (claim 1).

Another aspect of the present invention relates to an apparatus for measuring thermal conductivity, the gist of which is: (a) a main heater for heating a heated portion of a sample whose thermal conductivity K is to be measured; A temperature detecting section for detecting the temperature Th of the heated portion and the temperature Tc of the specific portion separated by a certain distance from the heated portion; and (c) heating the specific portion and changing the heating temperature to obtain a temperature difference Th−. A temperature difference adjustment heater for changing Tc, (d) a power supply unit for supplying power to the main heater and the temperature difference adjustment heater, and (e) a temperature detection value from the temperature detection unit. A control unit that controls power supply to a main heater and a temperature difference adjustment heater so as to variously change the temperature Tc of the specific part in a temperature range lower than the heating part while maintaining the heating part of the sample at a constant temperature Th; (F) The above A calorie measuring unit for measuring the calorie P generated by the main heater to heat the part; (g) the Th-Tc value changed and the Th-Tc value by the main heater. A storage unit for storing the measured value of the generated heat amount P, and (h) a relational expression P = from the plurality of measured values of P and the value of (Th−Tc) stored in the storage unit by the least square method. A calculation unit that specifies a straight line represented by (KS / L) (Th−Tc) + Qe and calculates the thermal conductivity K from the slope thereof (claim 2).

[0014]

According to the conventional method described above, the amount of heat generated by the heating means, which is lost as a heat loss,
That is, the amount of heat lost as an error is reduced as much as possible to improve the accuracy of measuring the thermal conductivity, but the loss of the amount of heat is actually unavoidable.
Therefore, it is difficult to obtain an accurate measured value of the thermal conductivity unless the thermal conductivity is determined after taking into account the calorific value loss in the calculation.

Based on such knowledge, the present inventor fixes the temperature of the heating portion (high temperature point) Th by the heating means, and sets the temperature Tc of the specific portion (low temperature point) at a certain distance away from this. The amount of heat P generated by the heating means was measured in order to keep Th constant when Tc was changed, and the measured value of P and the value of Th-Tc were plotted. As shown, it has been found that a beautiful linear relationship can be obtained.

Here, the intercept Qe on the vertical axis of the straight line is the amount of heat lost (heat loss), and the slope m of the line is m = K
S / L. Where K is the thermal conductivity of the sample, S is the cross-sectional area of the sample, and L is the distance between the hot and cold points.

When a part of the heat generated by the heating means Qe is lost due to heat loss, the relational expression of the thermal conductivity is actually P = (KS / L) (Th-Tc) + Qe.

In the present invention, Qe is fixed by fixing Th, and the value of the thermal conductivity K can be calculated based on a relational expression taking into account Qe.

In the present invention, generally, P values of three or more points and corresponding Th-Tc values are obtained, and are then linearized by the least square method. That is, a linear equation that minimizes the error is obtained, the intercept of the P axis by this line is obtained as Qe, and the thermal conductivity K is obtained from the slope m = KS / L of the line (S and L are known values). Value).

However, it is not always necessary to actually draw a straight line, but it is also possible to specify a relational expression expressing a straight line by the least squares method, and obtain the values of the thermal conductivity K and Qe from the coefficients or constants. In the case where the measured values are actually plotted and a straight line is drawn so as to substantially connect them, Qe
It is also possible to obtain only the value of K without necessarily calculating the value of.

According to the present invention, it has been confirmed that the correlation coefficient of the straight line obtained from the calorific value of the main heater and the temperature difference of the measurement sample is extremely high, and therefore, the value of the thermal conductivity K is obtained with extremely high accuracy. be able to. Further, there is an advantage that the thermal conductivity K obtained from the slope of the straight line can be determined as a value at the temperature Th.

A second aspect of the present invention relates to an apparatus for measuring the thermal conductivity K. According to the apparatus of the present invention, the method according to the first aspect of the present invention can be suitably implemented, and the relational expression P = KS / L
The thermal conductivity K of the sample can be automatically measured based on (Th-Tc) + Qe.

[0023]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing an embodiment of the present invention; In FIG. 2, 10 is a disk-shaped sample, 12 is a main heater having a heating wire 14 seated on one surface of the sample 10, and 16 is seated on one surface of the sample 10 so as to cover the main heater 12. A guard heater having a heating wire 18;
2 is a heat sink arranged to receive the other surface of the sample 10.

The heat sink 22 is heated by a heating wire 23.

Here, the main heater 12, the guard heater 16,
A material having a higher thermal conductivity than the sample 10 is used as the material of the heat sink 22.

In this apparatus, heat is supplied to one surface of the sample 10 by the main heater 12 to generate a heat flow toward the sheet sink 22, and a point H (a point inside the main heater 12) near both surfaces of the sample 10. And point C (point inside heat sink 22)
And the amount of heat P generated by the main heater 12.
The effective area of the sample 10 is the area of a portion surrounded by the center circumference of the gap 20 between the main heater 12 and the guard heater 16.

In this apparatus, power is supplied to the main heater 12 and the guard heater 16 from a power supply unit 24, and the power supplied to the main heater 12 is measured by a power measurement unit (heat amount measurement unit) 28, and a personal computer 30 Is input to

Reference numeral 26 denotes a temperature detecting section, which is used to detect the above point H and C
The temperature of the point and the point P in the guard heater 16 is detected and measured through a thermocouple attached to the same site. The result is input to the personal computer 30.

The personal computer 30 calculates Th-Tc in the operation / control section 34 and stores the result in the storage section 32 together with the value (P value) from the power measurement section 28.

The arithmetic and control unit 34 controls the power supply from the power supply unit 24 to the heating wire 23 for heating the heat sink 22 to change the temperature Tc at the point C in various ways, and
The power supply from the power supply unit 24 to the main heater 12 is controlled so that the temperature Th at the point is kept constant.
Control the power supply to the guard heater 16 so as to match the temperature Th at the point H.

On the other hand, a plurality of P values and (Th-Tc) values stored in the storage unit 32 are linearized by the least square method, and a relational expression P = (KS / L) (Th-Tc) + Qe
Qe and thermal conductivity K are calculated based on

Next, a specific procedure of this embodiment will be described below. First, the set value T of the cross-sectional area S, the thickness L, the set temperature Th of the high temperature point H, and the temperature Tc of the point C to be changed of the sample 10
c1, Tc2,... Tcn (where Tc <Th) is input from the input unit of the personal computer 30.

An operation / control unit 34 based on this input value
Controls the power supply to the main heater 12, the guard heater 16, and the heat generating wire 23 of the heat sink 22 until the temperatures of the respective components measured by the temperature detector 26 reach the set temperatures Th, Tc1, and Tp, respectively ( For example, PID control).

The temperature at each of the points H, C and P is the target set temperature T
h, Tc1 and Tp (the error is, for example, 0.01 ° C.), the power P1 supplied to the main heater 12 at that time.
Is read, and the value of Th-Tc and the value of P1 are stored in the storage unit 32 as data.

Next, the calculation / control section 34 calculates the temperature at the point C as Tc.
In addition, power control is performed to maintain the temperature at point H at Th, and when the temperature at point C reaches Tc2, the (Th-Tc) value and the read value of P2 are decomposed in the same manner as described above. The data is stored in the storage unit 32 as data.

Thereafter, the same processing is successively performed to change the temperature at the point C one after another as Tc3, Tc4,...
Each time (Th-Tc3), (Th-Tc4), ...
.. (Th−Tcn) and the values of P3, P4,.

The arithmetic and control unit 34 then linearizes the plurality of stored measurement data by the least squares method, and calculates the measured temperature Th of the sample 10 from Qe and the slope m of the straight line based on the above relational expression. Is calculated based on the equation K = mL / S.

FIG. 3 shows the relationship between the generated heat P and (Th-Tc) when the temperature difference (Th-Tc) is variously changed for the slide glass and the silicone rubber according to the present method.
h-Tc) on the horizontal axis and P on the vertical axis.

From this result, it can be seen that each measurement point is clearly on a straight line. That is, it is understood that the values of Oe and K can be obtained with high accuracy from this straight line or a relational expression representing the straight line.

Table 1 shows the coefficients of thermal expansion of various materials obtained in this manner in comparison with the conventional method shown in FIG. 4 (B). Here, the value obtained by the conventional method is a value obtained by ignoring Qe. In addition, the thickness L = 2.7 was measured.
This was performed by using a sample having a thickness of ３2.8 mm and an effective area S of 314 mm ² and changing Th-Tc within a range of 3 to 30 ° C.

[0041]

[Table 1]

The embodiment of the present invention has been described in detail above, but this is merely an example. For example, in the present invention, (Th-
Tc) / L or S (Th-Tc) / L is a variable, and the measured value is linearized to determine the slope as KS or directly K. Naturally, Qe may be calculated by calculation. The present invention can be implemented in variously modified forms based on the knowledge of those skilled in the art without departing from the gist, for example, it is possible to obtain only K by calculation.

[Brief description of the drawings]

FIG. 1 is a diagram showing the relationship between Th-Tc and P obtained when Th-Tc and P are changed according to the present invention.

FIG. 2 is a diagram showing an example of the measuring device of the present invention.

FIG. 3 is a diagram showing the relationship between Th-Tc and P obtained as a result of actually measuring the thermal conductivity of a slide glass and a silicone rubber using the measuring device of FIG. 2;

FIG. 4 is an explanatory view of a conventional thermal conductivity measuring method.

FIG. 5 is a diagram showing the dependence of thermal conductivity on temperature.

[Explanation of symbols]

 Reference Signs List 10 Sample 12 Main heater 16 Guard heater 23 Heating wire 24 Power supply unit 26 Temperature detection unit 28 Power measurement unit (calorific value measurement unit) 32 Storage unit 34 Operation / control unit

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-2-291950 (JP, A) (58) Fields investigated (Int. Cl. ⁶ , DB name) G01N 25/00-25/72 JICST file ( JOIS)

Claims (2)

(57) [Claims] 1. A heating section of a sample whose thermal conductivity K is to be measured is heated by heating means and the temperature of the heating section is detected, while the temperature of a specific section at a certain distance from the heating section is detected. By changing the temperature of the specific portion at a temperature lower than the temperature of the heating portion while maintaining the temperature of the heating portion constant, a temperature difference Th- between the temperature Th of the heating portion and the temperature Tc of the specific portion is obtained. In order to keep the temperature Th of the heated portion constant at various times, the amount of heat P generated by the heating means is measured for each Th-Tc, and the measured value of P and Th And a relational expression P = (KS / L) (Th-T
c) A method of measuring the thermal conductivity, wherein a straight line represented by + Qe is specified, and the thermal conductivity K is obtained from the slope. However, in the above relational expression, Qe represents the amount of heat that is an error component lost as a loss in the generated heat amount, and S and L represent the cross-sectional area and the thickness of the sample, respectively. (A) a main heater for heating a heated portion of a sample whose thermal conductivity K is to be measured; and (b) a temperature Th of the heated portion and a temperature Tc of a specific portion at a certain distance from the heated portion. (C) a temperature difference adjusting heater for heating the specific portion and changing the heating temperature to change the temperature difference Th-Tc; and (d) the main heater and the temperature difference. A power supply unit for supplying power to the adjustment heater; and (e) a temperature Tc of the specific portion lower than the temperature of the specific portion while maintaining the temperature of the heated portion of the sample at a constant temperature Th based on the detected temperature value from the temperature detecting portion. A control unit for controlling power supply to the main heater and the heater for adjusting the temperature difference so as to make various changes in the temperature range; and (f) a calorific value measuring unit for measuring a heat amount P generated by the main heater to heat the heating portion. When ( ) And the value of the change made to obtained Th-Tc, the Th-
A storage unit for storing a measured value of the amount of heat P generated by the main heater for each value of Tc; and (h) a plurality of measured values of P stored in the storage unit and (Th
−Tc) and the relational expression P = (KS) by the least squares method.
/ L) (Th-Tc) + Qe, and a calculation unit for calculating a thermal conductivity K from a slope of the straight line. However, in the above relational expression, Qe represents the amount of heat that is an error component lost as a loss in the generated heat amount, and S and L represent the cross-sectional area and the thickness of the sample, respectively.