JPS6240659B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring thermal conductivity called the so-called unsteady hot wire method, and an apparatus for automatically measuring thermal conductivity based on this method.

To explain the conventional unsteady hot wire method in detail, for example, a heating wire is placed on the central axis of a cylindrical sample,
A constant power is supplied to this heating wire, and the temperature change at or near the heating wire is measured by a temperature measuring element, and the thermal conductivity of the sample is calculated based on this temperature change. . That is, when power is supplied to the heating wire, heat is generated from the heating wire, and this heat diffuses within the sample and escapes to the outside. Therefore,
If the thermal conductivity of the sample is high, the heat generated by the heating wire will easily diffuse and the temperature of the heating wire will rise slowly, but if the thermal conductivity of the sample is low, the heat generated by the heating wire will not easily diffuse. Therefore, the temperature of the heating wire rises at a steep gradient. (Note that this phenomenon does not apply immediately after the start of power supply, but occurs after a certain period of time has elapsed since the start of power supply, as will be described later). Focusing on such a phenomenon, thermal conductivity can be measured by measuring the temperature change of the heating wire.

Next, the above phenomenon will be logically explained. The heat diffusion equation is generally expressed by the following equation.

∂T/∂τ=α(∂ ² T/∂ ² r ₂ +1/r ∂T/
∂r)...(1) Here, T: Temperature τ: Time α: Thermal diffusivity r: Distance from the heat source (heating line) When solving the above equation (1), substitute the following three conditions.

The first condition is τ=0, 0≦r<∞ and T=T ₀ = constant. The second condition is τ>0, r→∞ and T=T _0. The third condition is q=-2πrλ∂T/ ∂r=constant Here, q is the heat flow from the heating wire and can be expressed as q=RI ₂ /L (W/m).

However, R: Resistance of the heating wire I: Current flowing through the heating wire L: Length of the heating wire Solving equation (1) in consideration of the above three conditions, we get: Here, Ei represents an integral index function, λ: Thermal conductivity of the sample γ: Euler's constant (=0.5772...) In the above equation (2), if r ² /4πτ is sufficiently small, the height after r ² /4ατ The next term can be ignored and is expressed by the following equation.

T=q/4πλ{ln4ατ/r ² -γ}+T ₀ ...(3) Here, if the critical time for which the assumption that r ₂ /4ατ is sufficiently small holds true is τ' ₀ , then equation (3) becomes ττ' This holds true under the condition of ₀ . In the conventional method for measuring thermal conductivity, the thermal conductivity is determined by measuring temperatures T ₁ and T _{2 at two points τ 1 and τ 2 after the} above-mentioned point τ′ ₀ . To explain in detail, when the measured temperature at time τ ₁ is substituted into equation (3) as T ₁ , Ti=q/4πλ{ln(4ατ ₁ /r ² )−γ}+T ₀ ...
(4) Furthermore, if the measured temperature at time τ ₂ is substituted into equation (3) as T ₂ , then T ₂ =q/4πλ{ln(4ατ ₂ /r ² )−γ}+T ₀ ...
(5) Here, by performing the calculation of equations (5) and (4), T ₂ −T ₁ =q/4πλln(τ ₂ /τ ₁ ), therefore, λ=q/4π・ln(τ ₂ /τ ₁ )/ _T2 - _T1 ...(6
) holds true. As is clear from equation (6), the thermal conductivity λ is determined by measuring the heating wire or the temperatures T ₁ and T ₂ near the heating wire at times τ ₁ and τ ₂ .

However, in the conventional method described above,
The following inconvenience occurs. In other words, a certain range of error is unavoidable in the measured value, and as mentioned above, τ ₁
Measure the heating wire temperature at time point and time point τ _{2 ,} and calculate the thermal conductivity by substituting _the measured temperatures T ₁ and T ₂ into equation (6). This affected the conductivity value, making it difficult to accurately measure thermal conductivity. In particular, when calculating the thermal conductivity by automatically measuring the measured temperatures T ₁ and T ₂ with a thermal conductivity measuring device, it is necessary to correct any errors caused by noise during the temperature measurement. It was difficult to measure the thermal conductivity accurately. In addition, especially in the case of a sample with a high thermal conductivity, the output from the thermocouple (temperature measuring element) is small, and therefore the measurement error of the above temperatures T ₁ and T ₂ has a large effect on the thermal conductivity. Accurately measuring thermal conductivity was even more difficult.

The conventional unsteady hot wire method described above was for cases in which the heating wire was completely surrounded by the sample, but an improved method in which the heating wire is placed between the sample and a material whose thermal conductivity is known is used for measurement. unsteady hot wire method (for example, patent application 1976-127653, patent application 1972-107514, etc.)
Similarly, it can be said that the error in the measured temperatures T ₁ and T ₂ has a large influence.

This invention was made based on the above-mentioned circumstances, and its purpose is to measure thermal conductivity based on the integral value of measured temperature over time, thereby eliminating the influence of measurement errors caused by specific points in time. It is an object of the present invention to provide a method for accurately measuring thermal conductivity without any problems, and to provide an apparatus that can implement this measuring method and automatically measure thermal conductivity.

Next, the theory to which the present invention refers will be developed.

Integrating the above-mentioned equation (3) over time τ ₁ to _{τ 2} results in the following.

∫〓 ² 〓 ₁ Tdτ=q/4πλ∫〓 ² 〓 ₁ (ln4ατ/r ² −γ)dτ+∫〓 ² 〓 ₁ T ₀ dτ =q/4πλ [(ln4α/r ² −γ)τ+τlnτ−τ]∫ 〓 ² 〓 ₁ + [T ₀ τ] 〓 ² 〓 ₁ ...(7) Move the second term on the right side of equation (7) to the left side and divide both sides by τ ₂ - τ ₁ (however, τ ₂ > τ ₁ ) The following formula is obtained.

1/τ ₂ −τ ₁ ∫〓 ² 〓 ₁ Tdτ−T ₀ =q/4πλ{(ln4α/r ₂ −γ)+τ ₂ lnτ ₂ −τ ₁ lnτ ₁ /τ ₂ −
τ ₁ −1}...(8) Similarly, equation (3) can be expressed as time τ ₃ ~ τ ₄ (however, τ ₄ > τ
₃ , τ ₁ <τ ₄ ), the following equation is obtained.

1/τ ₄ −τ ₃ ∫〓 ⁴ 〓 ₃ Tdτ−T ₀ =q/4πλ{(ln4α/r ² −γ)+τ ₄ lnτ ₄ −τ ₃ lnτ ₃ /τ ₄ −
τ ₃ −1}...(9) Then, the following equation is obtained by calculating equations (9)-(8).

1/τ ₄ −τ ₃ ∫〓 ⁴ 〓 ₃ Tdτ−1/τ ₂ −τ ₁ ∫〓 ² 〓 ₁ Tdτ =q/4πλ{τ ₄ lnτ ₄ −τ ₃ lnτ ₃ /τ ₄ −τ ₃ −τ ₂ lnτ ₂ −τ ₁ lnτ ₁ /τ ₂ −τ ₁
}...(10) Calculating the thermal conductivity from this equation (10), we get This equation (11) is a general equation for determining the thermal conductivity λ when all the samples are present around the heating wire.

Therefore, in the method according to equation (11), τ
₁ , τ ₂ , τ ₃ , τ ₄ and set the time τ ₁ to _{τ 2}
By determining the integral value ∫〓 ² 〓 ₁ Tdτ and ∫〓 ⁴ 〓 ₃ Tdτ of the measured temperature T of the heating wire for time τ ₃ - τ ₄ and substituting these into equation (11), the thermal conductivity λ can be found. In this way, since the thermal conductivity λ is determined based on the integral value of the measured temperature ∫〓 ² 〓 ₁ Tdτ, ∫〓 ⁴ 〓 ₃ Tdτ, the error in the measured temperature at a specific point in time will affect the value of the thermal conductivity λ. It is possible to prevent direct influence and obtain accurate thermal conductivity λ.

Note that by adding the condition τ ₂ −τ ₁ =τ ₄ −τ ₃ , equation (11) becomes simpler as follows.

Furthermore, by adding the condition τ ₂ =τ ₃ =τ ₂₃ , equation (12) becomes even simpler as shown in the following equation.

In addition, regarding the thermal conductivity measurement method mentioned above,
This is applicable to cases where the entire sample is made of a material whose thermal conductivity is unknown, but the present invention splits the sample in half and forms one half of a material whose thermal conductivity is unknown, and the other half of which is made of a material whose thermal conductivity is known. This is for measuring thermal conductivity by interposing a heating wire and a temperature measuring element between these materials. In this case, in the conventional measurement method, the thermal conductivity λ of the unknown sample was calculated by the following equation.

λ=K・I ² ln(τ ₄ /τ ₁ )/T ₄ −T ₁ −H…
(14) However, H is a value corresponding to the thermal conductivity of a known sample, and K is a constant. Furthermore, I is the constant current flowing through the heating wire.

Referring to the above equation (12) (τ ₂ −τ ₁ =τ ₄ −τ
₃ ), the following equation can be obtained as the integral form of equation (14).

Furthermore, by adding the condition τ ₂ =τ ₃ =τ ₂₃ to equation (15), the equation becomes simple as shown below.

Here, the constants K' and H' can be determined using a separately prepared standard sample with a fixed thermal conductivity, and τ ₁ to τ ₄ are also constants that can be determined in advance. Therefore, ∫〓 ⁴ 〓 ₃ Tdτ−∫〓 ² 〓 ₁ The value of Tdτ,
Furthermore, the thermal conductivity λ can be determined based on the value of ∫〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓 ₁ Tdτ.

First, the probe section 1 used in the method of the present invention will be explained with reference to FIG. That is, the sample part 2 whose thermal conductivity is to be measured is, for example, a semi-cylindrical sample 2a, and the other part 2b is a material (semi-cylindrical) with known thermal conductivity, and by polymerizing these, it can be made into a circular cylinder. It is columnar. Also, heating wire 3
is sandwiched between the sample constructs 2a and 2b, and is arranged on the central axis of the sample section 2 when these are polymerized. This heating wire 3 is made of a round wire, a band wire, or the like. A temperature measuring element, such as a hot junction 4a of a thermocouple 4, is attached to the center of the heating wire 3 by means such as spot welding. Further, in the figure, reference numeral 5 denotes a U-shaped support frame, and both ends of the heating wire 3 are fixed to terminals 6, 6 at the ends of the support frame 5, so that the heating wire 3 is maintained in a straight line. . In addition, other terminals 7, 7 at the end of the support frame 5
Both ends of the thermoelectric body 4 are connected to. Note that the thermal contact point 4a may be placed near the heating wire 3.

Next, a case in which the method of the present invention is implemented based on recording by a pen recorder will be explained with reference to FIG.
That is, the output V of the thermocouple 4 after starting supply of constant electric power to the heating wire 3 is recorded by a pen recorder (not shown). As a result, the curve shown in FIG. 2 is drawn on the recording paper. Then, portion A and portion B of this recording paper are cut out, and their weights are measured separately using a precision scale. The weight of these A part and B part is _mA , _mB unit is for example mg
Then, the following formula holds true.

∫〓 ²³ 〓 ₁ Tdτ=1/η∫〓 ²³ 〓 ₁ Vdτ={Vc(τ ₂₃ −τ ₁ )+m _A 1/a・ρ}1/η …(17) Similarly ∫〓 ⁴ 〓 ₂₃ Tdτ= 1/η∫〓 ⁴ 〓 ₂₃ Vdτ={Vc(τ ₄ −τ ₂₃ )+m _B 1/a・ρ}1/η …(18) Here, Vc: Cut voltage ρ for easy measurement and calculation : Weight per unit area of recording paper (unit: mg/
mm ² ) a: Area of recording paper corresponding to 1 mV, 1 second square (mm ² /mV·S): Average thermoelectric power (°C/mV) Note that V ₀ in FIG. 2 is the pre-cut voltage.
Here, the average thermopower is determined as the thermopower corresponding to T ₁ +T ₄ /2 when the measured temperatures at times τ ₁ and τ ₄ are T ₁ and T ₄ . And these ∫〓 ²³ 〓 ₁ Tdτ,
∫〓 ⁴ 〓 ₂₃ The thermal conductivity λ is determined by substituting Tdτ into equation (16).

Next, the case where the method of the present invention is implemented using a digital printer will be explained with reference to FIG.
In other words, the output V of the thermoelectric body 4 (output at zero point
(You may pre-cut with _V0 ) using a digital printer as shown in Figure 3. To be more specific, the integral values of the temperature T of the heating wire 3 from τ ₁ to τ ₂₃ and from τ ₂₃ to _{τ 4} are obtained by substituting voltage values every second, for example, as follows.

In this example, τ ₁ = 30 seconds, τ ₂₃ = 45 seconds, τ ₄
= 60 seconds.

∫〓 ²³ 〓 ₁ Tdτ=1/η∫〓 ⁴⁵ 〓 ₃₀ Vdτ=(1/2V ₃₀ +V ₃₁ …V ₄₄ +1/2V ₄₅ )1/η …(19) ∫〓 ⁴ 〓 ₂₃ Tdτ=1/η∫ 〓 ⁶⁰ 〓 ₄₅ Vdτ = (1/2V ₄₅ +V ₄₆ ...=V ₅₉ +1/2V ₆₀ ) 1/η ...(20) Here, V ₃₀ ...V ₆₀ is the output voltage at each time point of 30 seconds ... 60 seconds .

The thermal conductivity λ is determined by substituting these ∫〓 ²³ 〓 ₁ Tdτ and ∫〓 ⁴ 〓 ₂₃ Tdτ into equation (16).

Next, an example of an apparatus for implementing the method of the present invention and automatically measuring thermal conductivity by digital calculation will be described with reference to FIG. Reference numeral 1 in FIG. 4 is a probe portion whose details are shown in FIG. 1, reference numeral 2a in FIG. 1 is a sample, and reference numeral 2b is a material whose thermal conductivity is known. The output of the thermoelectric body 4 of this probe section 1 is
The signal is amplified by the mode switch 11, the preamplifier 12, and the temperature measuring amplifier 13, and is supplied to the first input terminal 14a of the analog multiplexer 14. On the other hand, the temperature of the cold junction of the thermocouple 4 is measured by an automatic cold junction compensator 15 that includes, for example, a resistance temperature detector, and the output of this compensator 15 is amplified by a cold junction amplifier 16 and then measured. , is supplied to the second input terminal 14b of the analog multiplexer 14. These analog multiplexers 14
Each output supplied to the first input terminal 14a and the second input terminal 14b of the
This is information for calculating Tm. Further, the output of the thermocouple 4 is connected to the preamplifier 1 described above.
After being amplified by 2 and subtracted by the pre-cut level by the pre-cut circuit 17, it is supplied to an integrator 42, and the output integrated by this integrator 42 is supplied to the third input terminal 14c of the analog multiplexer 14. It is becoming more and more common. The output supplied to the third input terminal 14c becomes information for calculating the thermal conductivity as described later. Each analog data supplied to the analog multiplexer 14 is sent to the A/D converter 18 and converted into digital data in accordance with a control signal output to the control input terminal of the analog multiplexer 14. Further, the data is stored in a storage device 21 via a digital input circuit 19 and a processing device 20.

Incidentally, a reset signal and a start signal are input to the input circuit 19 through a reset button 22 and a start button 23. Furthermore, a constant K' and a constant H' are digitally input to the input circuit 19 by a constant setter 43, and are stored in a storage device 21 via a processing device 20. Further, the processing device 20 includes a digital out circuit 2
4. Pre-cut circuit 1 via D/A converter 25
7 to output a pre-cut voltage signal. Furthermore, the processing device 20 is configured to output an integration start signal to the integrator 42 via the digital out circuit 24. In addition, the processing device 20
is adapted to control a thermal conductivity digital display device 26 , a temperature to be measured digital display device 27 , and a ready OK lamp 28 via a digital out circuit 24 . The details will be described later. Further, the output of the thermocouple 4 described above is outputted to a recorder 30 and a moving coil indicator 31 via a preamplifier 12 and another block circuit 29. These recorder 30 and moving coil indicator 31 are designed to constantly display the heating wire temperature in analog form. Further, the circuit can be calibrated by switching the mode switch 11 mentioned above to connect the circuit to the internal reference voltage generator 32. Further, a signal is outputted from the mode switch 11 to the digital input circuit 19 to inform the digital input circuit 19 whether it is in the measurement or calibration mode. Next, a circuit for power supply control will be explained. That is, an input of alternating voltage (AC 100V) is supplied to a power supply circuit 35 via a power switch 33 and a fuse 34. This power supply circuit 35 rectifies and transforms the input optical current voltage (AC 100V), and supplies a DC voltage of 5 to 15V to the power supply circuit 41 for the control circuit described above. Further, this power supply circuit 35 includes a DC constant current circuit 36 and a current controller 37.
Constant power is supplied to the heating wire 3 via the heating wire 3. Note that 38 is an ammeter that constantly displays the current flowing through the heating wire 3 in analog form. Also, 39
is a current value switch which supplies current value information to a current controller 37 and also to a storage device 21 via a digital input circuit 19 and a processing device 20. Further, the start signal from the start button 23 mentioned above is outputted to the current value controller 37 via the processing device 20 and the digital out circuit 24, thereby starting to supply power to the heating wire 3. There is.

Next, the operation of the measuring device having the above-mentioned configuration will be explained. As an example, a case where the temperature to be measured is higher than room temperature will be described. First, the sample part 2 is placed in a heating furnace (not shown) and heated. After a suitable period of time has passed after the start of heating and a stable state has been reached, the power switch 33 is turned on and the reset button 22 is pressed to clear the memory device 21. Thereby, measurement of the heating wire temperature is started. That is, the output of the thermocouple 4 is outputted to the analog multiplexer 14 via the temperature measurement amplifier 13, and further outputted to the analog multiplexer 14.
After being converted into a digital signal by the D converter 18, the digital input circuit 19 and the processing device 20
The data is sent to the storage device 21 via. This temperature information is sent out at predetermined time intervals by a control signal sent to the analog multiplexer 14. In addition, the ready lamp 28 is the start button 23.
It always lights up after a certain period of time after you press the button. After confirming this lighting, the operator presses start button 2.
Press 3. Then, a start signal is supplied to the processing device 20 via the digital input circuit 19. Further, this start signal is transmitted from the processing device 20 to the current controller 37 via the digital out circuit 24.
In response to this, the current controller 37 starts supplying constant power to the heating wire 3. Note that this time point at which power supply starts is referred to as the zero time point.

Then, the processing device 20 receives the output information V ₁ of the thermocouple 4 when τ ₁ hour has passed from this zero point.
outputs the information _V1 to the D/A converter 25,
Upon receiving this, the D/A converter 25 supplies analog information _V1 to the pre-cut circuit 17. Therefore, at time τ ₁ , the output sent from the thermocouple 4 to the pre-cut circuit 17 is transmitted to the D/A converter 2.
Therefore, the output from this pre-cut circuit 17 to the integrator 42 becomes OV at this time _τ1 . Then, the processing device 20 determines that the output to the integrator 42 is OV.
After the detection, an integration start signal is output from the processing device 20 to the integrator 42 via the digital out circuit 24, and in response to this, the integrator 42 starts an integration operation. Incidentally, since the output of the pre-cut level signal, the confirmation of the OV output to the integrator 42, etc. are performed in a very short time, it can be assumed that the integrator 42 starts the integrating operation at time _τ1 . Furthermore, at time τ ₂₃ , the processing device 2
0 outputs a control signal to the analog multiplexer 14, which outputs the integral value ∫ of the output of the pre-cut thermocouple 4 from time τ ₁ to time τ ₂₃ .
The analog information of 〓 ²³ 〓 ₁ Vdτ (this corresponds to the information ∫〓 ² 〓 ₁ Tdτ, which is the integral value when the temperature of the heating wire 3 is T as described later) is obtained by A/D.
The data is converted into digital information by a converter 18 and stored in a storage device 21 via a digital input circuit 19 and a processing device 20. Further, at time τ ₄ , a control signal is output from the processing device 20 to the analog multiplexer 14, and thereby, in the same manner as described above, integral value information ∫ from τ ₁ to τ ₄
⁴ ₁ Vdτ is stored in the storage device 21. and,
Information stored in this storage device 21 ∫〓 ² 〓 ₁ Vdτ,
∫〓 ⁴ 〓 ₁ Based on Vdτ, the processing device 20 performs the following calculation. That is, first, the above information is subtracted to obtain the next value.

X=∫〓 ⁴ 〓 ₁ Vdτ−2∫〓 ²³ 〓 ₁ Vdτ …(21) From the following equation, this value X is the same as ∫〓 ⁴ 〓 ₂₃ Vdτ−∫〓 ²³ 〓 ₁ Vdτ.

_{That is} ^{, −∫ _} _{_} ^_ _{_} ^_ _{_} ^_ _{_} 〓 ²³ 〓 ₁ Vdτ...(22) Here, the value ∫〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓 ₁ Tdτ in the above-mentioned formula (16) can be obtained by the formula (22).

∫〓 ⁴ 〓 ₂₃ Vdτ−∫〓 ²³ 〓 ₁ It has the following relationship with the value of Vdτ.

∫〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓 ₁ Tdτ = (∫〓 ⁴ 〓 ₂₃ Vdτ−∫〓 ²³ 〓 ₁ Vdτ) 1/η
…(23) where is the average thermopower.

Therefore, the processing device 20 calculates equation (16) by performing the following division, and can determine the thermal conductivity λ.

λ=K′・I ²・・(τ ₄ lnτ ₄ −2τ ₂₃ lnτ ₂₃ +τ ₁ lnτ ₁ )÷X−H′ Here, K′・I ²・・(τ ₄ lnτ ₄ −2τ ₂₃ lnτ ₂₃ +τ ₁ ln
τ ₁ ) and H′ are constants stored in the storage device 21 in advance. Information on the current value I is supplied from the current value switch 39, and constants K' and H' are supplied from the constant setter 43 to the storage device 21 via the digital input circuit 19 and the processing device 20. , thermopower,
Information on times τ ₁ , τ ₂₃ , τ ₄ is also provided to the processing device 20 in advance.
The signal is supplied to the memory circuit 21 via. Information on the thermal conductivity λ calculated in this way is sent to the thermal conductivity digital display device 26 via the digital out circuit 24 and displayed there. Further, the temperature to be measured Tm is determined from the temperature information T ₀ and T ₄ stored in the storage device 21 by the calculation of the following equation in the processing device 20.

Tm=T ₀ +T ₄ /2 (24) These temperature information T ₀ and T ₄ are input to the first and second input terminals 14 of the analog multiplexer 14.
It is determined by the calculation of the processing device 20 based on the data output to a and 14b. Further, the temperature to be measured Tm is digitally displayed on the temperature to be measured display device 27 under the control of the processing device 20.

Next, an example of an apparatus for implementing the method of the present invention and automatically measuring thermal conductivity by analog calculation will be described based on FIG. That is, 1 in FIG. 5 indicates the probe section in FIG. 1, and numeral 2 in FIG.
A is a sample, and 2b is a material whose thermal conductivity is known. The heating wire 3 is connected to a DC constant current power source 51 via a current controller 50. On the other hand, the output of the thermocouple 4 is amplified by the preamplifier 52 and becomes information for calculating the temperature to be measured, as well as information for calculating the thermal conductivity. First, the case where the information is used as information on the temperature to be measured will be described. The output from the preamplifier 52 is sent to a storage circuit 55 via a cold junction compensation circuit 53 and an adjustment amplifier 54. This memory circuit 55 has a relay _R1 as a switching means.
It is constructed by connecting in parallel a circuit of memory _M1 consisting of a capacitor and a relay _R2 as a switching means and a circuit of memory _M2 . The analog information stored in each memory M ₁ and M ₂ is added by an adder 56 to obtain the temperature to be measured.
Tm is calculated, and the calculation result is sent to the measured temperature display device 57. The detailed operation will be described later.

Also, to explain the case where the output from the thermocouple 4 is used for thermal conductivity calculation, this output is sent to a pre-cut circuit 58, and further sent from this pre-cut circuit 58 to the inverting input terminal of a subtracter 59. At the same time, it is sent to the non-inverting input terminal via relay _R3 as switching means. A memory _M3 is connected to this relay _R3 . The output of this subtracter 59 is integrated by an integrator 60 and then sent to a storage circuit 61. This memory circuit 61
is constructed by connecting in parallel a circuit consisting of a relay R ₄ and a memory M ₄ as a switching means, and a circuit consisting of a relay R ₅ and a memory M ₅ as a switching means. and,
The information stored in these memories M ₄ and M ₅ is sent to each input terminal of the subtracter 62. The output of this subtracter 62 is sent to an arithmetic unit 63. Further, values corresponding to the constants K' and H' are inputted to the arithmetic unit 63 from a constant setter 68.

Next, the output of the thermocouple 4 is sent to a compensation circuit 64 via a preamplifier 52 and a pre-cut circuit 58. The compensation circuit 64 calculates compensation coefficient information, which will be described later, based on this analog information and outputs it to the arithmetic unit 63.
In the arithmetic unit 63, a memory circuit 61 and a compensation circuit 64
The thermal conductivity λ is calculated based on the information from the constant setting device 68, and the result is sent to the thermal conductivity display device 65. Note that 66 is a control circuit, and this control circuit 66 is connected to a pulse generation circuit 67.
Upon receiving the pulse signal from the DC constant current power source 51,
Control signals are output to relays _R1 to _R5 .

Next, the operation of the device having the above configuration will be explained. As an example, a case where the temperature to be measured is higher than room temperature will be explained. Sample part 2 placed in the heating furnace is at the temperature to be measured.
When the temperature becomes constant near Tm, the volume 58a of the pre-cut circuit 58 is set so that the pre-cut voltage in the pre-cut circuit 58 becomes the same value as the output voltage from the thermocouple. As a result, the output voltage from the pre-cut circuit 58 at this point becomes zero. Next, a start signal is sent to the control circuit 66, and upon receiving the start signal, the control circuit 66 outputs a power supply start signal to the DC constant current power supply 51,
As a result, supply of constant power to the heating wire 3 is started. Then, the control circuit 66 sends a control signal to the relay _R1 at the power supply start point (zero point) to switch the relay _R1 from ON to OFF.
As a result, the voltage corresponding to the temperature information T ₀ at the zero point output from the thermocouple 4 is stored in the memory M ₁ . Further, the control circuit 66 sends a control signal to relay R ₂ at time τ ₄ to switch relay R ₂ from ON to OFF, thereby storing temperature information T ₄ at time τ ₄ in memory M ₂ . Voltage is stored. The temperature information T ₀ and T ₄ stored in these memories M ₁ and M ₂ are sent to the adder 56,
The adder 56 calculates the temperature to be measured Tm.

Tm=T ₀ +T ₄ /2 The measured temperature Tm calculated by this calculation is sent to the measured temperature display device 57 and displayed there. Note that in this display device 57, the adder 5
The analog information outputted from 6 may be displayed in analog form as it is, or may be converted into digital information by an A/D converter and then displayed digitally.

Next, calculation and display of thermal conductivity λ will be explained.

After the above-mentioned zero point, the output from the thermocouple 4 is sent to a subtracter 59 via a preamplifier 52 and a pre-cut circuit 58. Before time τ ₁ , relay R ₃ is
Since the subtracter 59 is in the ON state and the same level voltage is input to each input terminal of the subtracter 59, the output from the subtracter 59 is zero. Therefore, the integrator 60 does not substantially perform an integrating operation. Then, at time τ ₁ , a control signal is output from the control circuit 66 to relay R ₃ , and by switching this relay R ₃ from ON to OFF, memory M ₃ stores the output voltage of thermocouple 4 at time τ ₁ . The voltage stored in the memory _M3 is input to the inverting input terminal of the subtracter 59. On the other hand, the output of the thermocouple 4 after time τ ₁ is input to the non-inverting input terminal of this subtracter 59 . As a result, the output from the subtractor 59 after time _τ1 is τ
It is obtained by subtracting the output at time τ ₁ from the output of the thermocouple 4 after time ₁ , and is output to the integrator 60 . Therefore, the integrator 60 substantially starts the integration operation at time τ ₁ and sends the integration information to the storage circuit 61 . The relay in this memory circuit 61
_R4 is switched from OFF to ON at τ ₁ and OFF at τ ₂₃ by the control signal from the control circuit 66.
As a result, the memory M ₄ stores the integrated voltage ∫〓 ²³ 〓 ₁ Vdτ from τ ₁ to τ ₂₃ . In addition, relay _R5 is turned off at time τ ₁ by a control signal from control circuit 66.
It switches to ON from τ ₄ and turns OFF at time τ 4, and as a result, memory M ₅ receives the integrated voltage ∫〓 ⁴ 〓 ₁ Vd from τ ₁ to τ _4.
Store τ. The information stored in these memories M ₄ and M ₅ is output to a subtracter 62, and the following calculation is performed in this subtracter 62.

X=∫〓 ⁴ 〓 ₁ Vdτ−2∫〓 ²³ 〓 ₁ Vdτ Here ∫〓 ⁴ 〓 ₁ Vdτ=∫〓 ²³ 〓 ₁ Vdτ＋∫〓 ⁴ 〓 ₂₃ Vd
Since τ, we have essentially calculated X=∫〓 ⁴ 〓 ₂₃ Vdτ−∫〓 ²³ 〓 ₁ Vdτ.

This information X is then sent to the arithmetic unit 63.
On the other hand, the compensation circuit 64 outputs information ηR/η ₀ R ₀ .

The thermal conductivity λ is calculated by this calculator 63,
This will be explained in detail below. In other words, as mentioned above, the thermal conductivity λ is determined by equation (16),
In equation (16), T=V/η, so substitute this into equation (16) to obtain the following equation.

Here, the thermoelectric power η changes slightly depending on the temperature of the thermocouple 4, and the resistance R of the heating wire 3 changes slightly depending on the temperature of the heating wire 3. These changes in η and R are corrected by the compensation circuit 64 described above. That is,
The correction of η and R in equation (25) is given as the product of ηR.

When ηR=η ₀ R ₀ (ηR/η ₀ R ₀ ), η ₀ ·R ₀ is the value at room temperature, for example, 25°C. Adding this to equation (25) as a correction term yields the following equation.

λ=K″η ₀ R ₀ I ² (τ ₄ lnτ ₄ −2τ ₂₃ lnτ ₂₃ +τ ₁ lnτ ₁ )×(ηR/η ₀ R ₀ )÷X−H′…
(26) Here, K″R=K′ Therefore, in the calculator 63, a preset constant η ₀ R ₀ I ² (τ ₄ lnτ ₄ −2τ ₂₃ lnτ ₂₃ +τ ₁ ln
τ ₁ ) is multiplied by the information ηR/η ₀ R ₀ from the compensation circuit 64, for example 1.05, and then the information K″ from the constant setter,
H′ and information X from the subtractor 62, (2
The thermal conductivity λ can be calculated by calculating the formula 6). Note that the information ηR/η ₀ R ₀ output from the compensation circuit 64 is transmitted from the thermocouple 4 to the preamplifier 52.
, is determined based on information outputted to the compensation circuit 64 via the pre-cut circuit 58.

Further, since the value of the information ηR/η ₀ R ₀ outputted from this compensation circuit 64 becomes extremely close to 1 if the operating temperature range is limited, this circuit can be omitted. At this time, since the value of R is a constant value, equation (16) is essentially used as the calculation formula for the thermal conductivity λ.

The thermal conductivity λ thus calculated by the calculator 63 is output to the thermal conductivity display device 65 and displayed there. Note that in this display device 65,
The analog information of the thermal conductivity λ may be displayed as an analog as it is, or may be converted into digital information using an A/D converter and displayed digitally.

As explained above, according to the method recited in claim 1, the integral value of the temperature at or near the heating wire between the two time points τ ₁ and τ ₂ after the start of power supply to the heating wire, that is, after the zero point. ∫〓 ² 〓 ₁ Tdτ and 2 time points τ
Difference from integral value of measured temperature T between _{3 and} τ ∫〓 ⁴ 〓 ₃ Tdτ (however, τ ₁ < τ ₄ ) ∫〓 ⁴ 〓 ₃ Tdτ−∫〓 ² 〓 ₁ Td
τ
Thermal conductivity is measured based on Since the thermal conductivity λ is determined based on the integral value in this way, it is possible to prevent errors in the measured temperature at a specific point from directly affecting the thermal conductivity value, and to obtain an accurate thermal conductivity λ. be able to.
It is particularly effective for materials with high thermal conductivity.

Further, according to the thermal conductivity measuring device described in claim 3, the thermal conductivity can be digitally calculated and automatically measured and displayed, and the thermal conductivity as described in claim 4 can be measured and displayed automatically. The rate measuring device can calculate the thermal conductivity analog and automatically measure and display it.
Moreover, according to these measuring devices, the integration operation of the integrator is started at time τ ₁ , and the integral value information ∫〓 ₂₃ ^〓 ₁ Vdτ, ∫〓 ⁴ 〓 ₁ Vdτ is taken out from the integrator at τ 23 and τ ₄ , and Based on this integral value information, X=∫〓 ⁴ 〓 ₁ Vdτ−2∫〓 ²³ 〓 ₁ Vdτ
∫
〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓 ₁ This corresponds to the information Tdτ. ) and calculate the thermal conductivity from equation (16) based on this X, so only one integrator is required, simplifying the structure and improving calculation accuracy.

[Brief explanation of the drawing]

FIG. 1 is a perspective view of a probe section used in the thermal conductivity measuring method and apparatus according to the present invention, and FIG. 2 is a diagram illustrating an embodiment of the measuring method according to the present invention.
FIG. 3 is a diagram explaining another embodiment of the measuring method according to the present invention, FIG. 4 is a block diagram showing an apparatus for automatically measuring thermal conductivity by digital calculation, and FIG.
The figure is a block diagram showing an apparatus for automatically measuring thermal conductivity by analog calculation. 2... Sample part, 2a... Sample, 2b... Material with known thermal conductivity, 3... Heating wire, 4... Thermocouple (temperature measuring element),
18... A/D converter, 20... Processing device, 21... Storage device, 26... Thermal conductivity display device, 42... Integrator, 60... Integrator, 61... Memory circuit, 62... Subtractor, 63... Arithmetic unit , 65... thermal conductivity display device, 6
6...Control circuit, _R3 , _R4 , _R5 ...Relay (switching means), _M4 , _M5 ...Memory.

Claims (1)

[Claims] 1. A heating wire and a side heating element for measuring the temperature of the heating wire or the temperature near the heating wire are disposed between a material having a known thermal conductivity and a sample, and a constant temperature is applied to the heating wire. In a method of supplying electric power and determining the thermal conductivity of a sample based on the temperature change at or near the heating wire,
The integral value of the measured temperature T at or near the heating wire between the two time points τ ₁ and τ ₂ after the start of power supply to the heating wire, that is, after the zero point, ∫〓 ² 〓 ₁ Tdτ, and the two time points τ ₃ and τ
∫〓 ₄ 〓 ₃ Tdτ (however ^, τ
₁ <τ ₄ ) ∫〓 ⁴ 〓 ₃ Tdτ−∫〓 ² 〓 ₃ A thermal conductivity measuring method characterized in that the thermal conductivity λ is calculated from the following formula based on Tdτ. (However,: constant current flowing through the heating wire, K′,
H': a constant determined by a standard sample with a fixed thermal conductivity) 2 τ ₂ and τ ₃ are τ ₂ = τ ₃ = τ ₂₃ , as described in claim 1. Thermal conductivity measurement method. 3. A heating wire placed between a material with known thermal conductivity and the sample and supplied with constant power;
A side temperature element that is also placed inside the sample and measures the temperature of the heating wire or the vicinity of the heating wire, an integrator that integrates the output voltage V from this side temperature element, and converts analog information from this integrator into digital information. an A/D converter for converting into After _one hour has elapsed, an integration start signal is output to the integrator, and the integral value information at time τ ₂₃ , τ ₄ ∫〓 ²³ 〓 ₁ Vdτ, ∫〓 ⁴ 〓 ₁ Vdτ is stored in the storage device, and these integral values Subtract the information and X = ∫
〓 ⁴ 〓 ₁ Vdτ−2∫〓 ²³ 〓 ₁ Find Vdτ and from this value X∫
〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓 ₁ A processing device that calculates Tdτ and calculates the thermal conductivity by calculating the following formula based on this value, and a thermal conductivity λ calculated by this processing device. A digital calculation type thermal conductivity measuring device comprising a thermal conductivity display device that displays. (However,: constant current flowing through the heating wire, K′,
H′: constant determined by standard sample with fixed thermal conductivity). 4. A heating wire placed between a material with known thermal conductivity and the sample and supplied with a constant electric power;
A side temperature element that is also arranged in the sample and measures the temperature of the heating wire or the vicinity of the heating wire, an integrator that integrates the output voltage V from this side temperature element, and between the side temperature element and the integrator. Two sets of circuits are connected in parallel, each having a switching means interposed in the circuit, a memory consisting of a capacitor, and the switching means,
A control signal is sent to a storage circuit that stores the output from the integrator, and a switching means interposed between the side temperature element and the integrator after τ ₁ hour has elapsed from the zero time point of the start of power supply. The integral operation is started, and at the time of τ ₂₃ , a control signal is sent to one of the switching means of the storage circuit to switch this switching means from ON to OFF, thereby storing the integral value information ∫〓 ²³ 〓 ₁ Vdτ in one memory. let me,
By sending a control signal to the other switching means of the storage circuit at time τ ₄ and switching this switching means from ON to OFF, the control circuit that stores the integral value information ∫〓 ⁴ 〓 ₁ Vdτ and each memory of the storage circuit. Based on the output of X=∫〓 ⁴ 〓 ₁ Vdτ−
2∫〓 ²³ 〓 ₁ From the subtracter that subtracts Vdτ and the information X from this subtractor, ∫〓 ⁴ 〓 ₂₃ Tdτ−∫〓 ²³ 〓
₁ Td
τ, and based on this value, calculate the following formula to calculate the thermal conductivity λ, and a thermal conductivity display device that receives the output from this calculator and displays the thermal conductivity. An analog calculation type thermal conductivity measurement device characterized by the following: (However,: constant current flowing through the heating wire, K′,
H': constant determined by standard sample with fixed thermal conductivity).