JP2000356612A - Method and apparatus for measuring emissivity of fine single wire - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and an apparatus for measuring the emissivity of a fine single line, which can easily measure the emissivity of an ultrafine single line itself. SOLUTION: Two heating wires 1 and 2 generating uniform volume heat
Are arranged in parallel, and these two heat wires 1, 2
A thin sample wire 3 is connected between them, and the two hot wires 1 and 2 are directly energized and heated, and the amount of heat applied from one hot wire 1 to the sample thin wire 3 is equal to the amount of heat applied from the other hot wire 2 to the sample thin wire 3. Then, all the heat applied to the thin sample wire 3 is radiated from the sample thin wire 3 by radiation, and the volume average temperature rise of the hot wire obtained by the theoretical solution of the steady-state heat conduction with respect to the volume average temperature of the two hot wires 1 and 2 and the measurement. The emissivity of the sample thin line 3 is obtained by comparing the steady values of

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 the emissivity of a fine single wire.

[0002]

2. Description of the Related Art Conventionally, technical documents in such a field include: D. Edie, K .; E. FIG. Robinson,
O. Fleurot, S.M. P. Jones and
C. C. Fain, Carbon, 32, 1045 (1
994). (2) S.I. H. Yoon, Y .; Korai and
I. Mochida, Carbon, 31, 849 (1
993). (3) H. Masuda, M .; Higano, Tran
s. ASME, J.A. Heat Transf. , 11
0, 1 (1988). (4) Zhang, Fujiwara, Fujii, Report of Institute for Functional Materials Science, Kyushu University, 12, 1 (1998). was there.

[0003] In recent years, ultrafine functional wires with ultra-high thermal conductivity, such as carbon fiber materials, have been developed. These wires are expected to have various industrial uses as heat sink materials and the like because of their properties. However, when such a wire is applied as a heat sink material, particularly in a high-temperature region or a space environment, heat radiation by radiation is dominant, and the emissivity of the wire is an important thermophysical property value.

[0004]

There are two methods for measuring the emissivity: (1) an optical method for measuring the radiance or reflectance emitted by the sample itself to obtain the emissivity; and (2) emissivity from the sample surface. There is a calorimetric method that measures the total emissivity of the hemisphere by measuring the amount of heat lost at

[0005] The calorimetric method is divided into a stationary method and an unsteady method.

When the optical method is applied to emissivity measurement of an extremely fine wire (several μm to several tens μm) as in the present invention, the measurement becomes difficult due to the limitation of the spatial resolution of the radiometer. come.

On the other hand, in the case of the calorimetric method, it is necessary to measure the calorific value and the temperature with high accuracy.

[0008] In the past, studies on emissivity measurement of wires have been performed by an unsteady calorimetric method in which heat loss from a thermocouple for temperature measurement is reduced by a sophisticated technique.

However, in the case of the unsteady method, the heat capacity of the measurement sample is required due to the principle of the measurement method, and it cannot be applied to a sample whose heat capacity is unknown.

The method of reducing heat loss in the above research is considered to be applicable to the stationary method for a wire rod having a diameter of about 1 mm and a length of about 50 mm. It is difficult to apply to measurement of several μm to several tens μm).

The present invention has been made in view of the above circumstances, and has as its object to provide a method and an apparatus for measuring the emissivity of a fine single line, which can easily measure the emissivity of an ultrafine single line itself.

[0012]

According to the present invention, there is provided a method for measuring emissivity of a fine single wire, comprising the steps of: (a) arranging two heat wires having uniform volumetric heat generation in parallel; The sample thin wire is connected between the two heat wires, and (b) the two heat wires are directly energized and heated, and the amount of heat applied from one heat wire to the sample wire and the other heat wire to the sample Equalizing the amount of heat applied to the thin wire, (c) radiating all the heat applied to the sample thin wire from the sample thin wire by radiation, and calculating the theoretical solution and measurement of steady-state heat conduction with respect to the volume average temperature of the two hot wires. The emissivity of the thin sample wire is obtained by comparing the steady value of the volume average temperature rise of the obtained hot wire.

[2] The method for measuring the emissivity of a fine single wire according to the above [1], wherein a fine platinum wire is used as the two heating wires.

[3] In the emissivity measuring apparatus for a fine single wire, (a) two heating wires which are arranged in parallel and generate uniform volume heat, and (b) a sample connected between the two heating wires. A thin wire, and (c) means for directly energizing and heating the two hot wires to equalize the amount of heat applied from one of the hot wires to the sample thin wire and the amount of heat applied from the other hot wire to the sample thin wire. It was made.

[4] In the fine single-wire emissivity measuring apparatus according to the above [3], the two heating wires are platinum fine wires.

[5] In the fine single wire emissivity measuring apparatus according to the above [3], the sample fine wire is connected to a central portion of the two heating wires.

[6] In the fine single-wire emissivity measuring apparatus according to the above [3], the sample fine line has an order of 1 to 10 μm.

[0018]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a view showing a configuration of a measuring section of an apparatus for measuring emissivity of an ultrafine wire according to an embodiment of the present invention.

As shown in this figure, the measuring section is composed of heating wires 1 and 2 which generate uniform volumetric heat and a thin wire 3 for a sample to be measured. The thin sample wire 3 is connected to the center of the hot wires 1 and 2, and heat is applied to the thin sample wire 3 by directly heating the hot wires 1 and 2. Here, the temperature of the connection point 3A between the hot wire 1 and the sample wire 3 and the connection point 3A between the heat wire 2 and the sample wire 3
Assume that the temperatures of B are equal. In this case, the amount of heat applied from the heating wire 1 to the sample wire 3 and the amount of heat applied from the heating wire 2 to the sample wire 3 are equal, and if the measurement is performed in a vacuum chamber, the amount of heat applied to the sample wire 3 is all radiated. Heat is radiated from the sample thin wire 3.

The principle of the emissivity measuring method of the present invention is obtained by a theoretical solution and measurement of the steady-state heat conduction with respect to the volume average temperature of the heating wires when the heating wires 1 and 2 are uniformly heated in the measuring apparatus of FIG. The emissivity of the sample thin wire 3 as the measurement sample is obtained by comparing the steady value of the volume average temperature rise of the heated wire. Heat wires 1 and 2 are provided at both ends of the sample wire 3 in order to reduce the influence of the thermal conductivity of the sample wire 3.

As the heating wires 1 and 2, fine platinum wires can be used. When a platinum wire is used, uniform volumetric heat generation can be obtained by direct energization, and platinum has a very high dependence of the electrical resistance value on temperature. Therefore, highly accurate temperature measurement (absolute value ± 0.01K or less) is possible. The volume average temperature T _v of the platinum thin wire (heat rays) 1, 2 by measuring the electrical resistance value Ri of the platinum thin line portion in energization heating,
It is calculated by the following equation.

[0023]

(Equation 1)

Here, Rt ₀ is a platinum thin wire 1, 2 at 0 ° C.
Is a temperature coefficient [1 / K], which is previously determined by a test.

As described above, in the method for measuring the emissivity of an ultrafine wire according to the present invention, a platinum thin wire is used as a heating source, a calorific value, and a temperature sensor for a sample fine wire, and the heating amount and the temperature are measured with high accuracy. It is characterized by trying to measure the emissivity of fine wires. In addition, by performing heating, temperature measurement, and support of the measurement sample with the same heating wire, it is possible to reduce an error factor due to heat loss.

Next, a theoretical analysis of heat conduction is performed on the emissivity measuring apparatus for an ultrafine wire shown in FIG.

In FIG. 1, since the temperature at the connection point 3A between the heating wire 1 and the sample wire 3 and the temperature at the connection point 3B between the heating wire 2 and the sample wire 3 are equal, the temperature distribution of the sample wire 3 is at the center (dashed line). It becomes vertically symmetrical, so that adiabatic conditions can be given. Therefore, only the thin sample wire 3 and the hot wire 1 above the dashed line are considered here.

In FIG. 1, the left side of the connecting point 3A of the sample wire 3 of the hot wire 1 is called a hot wire portion I and the right side thereof is called a hot wire portion II.

Further, the frames F _h1 ,
F _h2 (lead terminal), because of sufficiently large thermal capacity as compared with the hot wire 1 and the sample thin line 3, after heating the hot wire 1 even if the temperature of this portion is maintained at the initial temperature T _0.

The temperature distribution in the radial direction of the hot wire 1 and the thin sample wire 3 is made uniform, and the coordinates are taken in the axial direction with the origin at the position where the hot wire is attached to the frames F _h1 and F _h2 and the center of the thin sample wire 3. The dimensionless heat conduction equations for I, II and the sample wire 3 are given by the following equations.

For the hot wire part I

[0032]

(Equation 2)

For the hot wire part II

[0034]

(Equation 3)

For the sample thin wire 3

[0036]

(Equation 4)

Here, the parameter R _c is the ratio of the thermal conductivity of the hot wire 1 to the thin sample wire 3, and R _d is the radius ratio of the hot wire 1 to the thin sample wire 3 and is defined by the following equation.

[0038]

(Equation 5)

The dimensionless temperature θ, Biot number Bi and coordinate X are defined by the following equations, respectively.

[0040]

(Equation 6)

The heat transfer coefficient contained in Bi is an equivalent heat transfer coefficient due to radiation, and the surface area of the thin sample wire 3 and the heat wire 1 is sufficiently smaller than the area of the surrounding (vacuum chamber wall). It can be approximated by the following equation.

For the hot wire 1

[0043]

(Equation 7)

For the sample thin line 3

[0045]

(Equation 8)

Here, σ [= 5.67 × 10 ⁻⁸ (W / m
² K ⁴ )] is the Stefan-Boltzmann constant.

The boundary conditions are as follows.

[0048]

(Equation 9)

Next, an analytical solution will be described.

Here, a steady solution of the heat conduction equations shown in the above equations (2) to (4) will be described.

[0051]

(Equation 10)

When the boundary conditions of the above equation (9) are applied to the above equations (2), (3), and (4), the local temperature in a steady state is obtained as follows.

[0053]

[Equation 11]

[0054]

(Equation 12)

[0055]

(Equation 13)

Here,

[0057]

[Equation 14]

[0058]

(Equation 15)

The volume average temperature θ _vh of the heating wire 1 is obtained by the following equation.

[0060]

(Equation 16)

Next, a procedure for actually measuring the emissivity of an ultrafine line by the measuring method of the present invention will be described.

First, the heating wires 1 and 2 are energized and heated so that the temperature at the connection point 3A between the heating wire 1 and the sample wire 3 in FIG. 1 and the temperature at the connection point 3B between the heating wire 2 and the sample wire 3 become equal. After that, the volume average temperature Τ _vh and the volume calorific value q _v of the heating wire 1 are measured.

[0063] On the other hand, looking at the fundamental formula of the formula (2) to (4), since Bi _h about hot wire 1 is determined by measurements T _vh and the formula (7) (heat rays platinum thin wire, epsilon _h is is previously obtained in the calibration to known or advance), the Bi _f,
Since the value is a function of the volume average temperature Τ _vf of the sample wire 3 from the above equation (8), the value of the emissivity ε _f of the sample wire 3 cannot be explicitly obtained.

Therefore, the emissivity ε of the sample wire 3_fIs
Θ according to equation (16)_vhAnd measurement resultsΤ _vhOrderless obtained from
Repetition by Newton method until the original volume average temperatures match
Perform a return calculation. Where ε_fCalculate
Use a method such as fitting to the measured data
Measurement data (Τ_vh, Q_vRadiation from
Rate ε_fIs determined with an accuracy within the convergence accuracy of the Newton method.
You.

Next, the measurement accuracy will be described.

So far, the theory for obtaining the emissivity ε _f of the ultrafine wire 3 and the method of calculating the ε _f have been described. Here, the fundamental measurement accuracy when measuring the emissivity ε _f by the present measurement method from the above-mentioned formula (16) obtained by theory will be examined.

First, the analysis accuracy of the equations (11) to (14) and the equation (16) will be described.

The above equation (16) is calculated by the above equations (2) to (4).
In the above equation, the Bi number (radiant heat transfer coefficient) is calculated using the above equation (7)
As shown in (8), this is a solution obtained by approximating the volume average temperatures of the heating wires 1 and 2 and the sample thin wire 3. However, strictly speaking, as described above, the basic expressions (2) to (4)
Include the term εσ (Τ ⁴ −Τ∞ ⁴ ) of heat transfer due to local radiation of the hot wires 1 and 2 and the sample thin wire 3. Since it is very difficult to find an analytic solution for a strict basic equation, a numerical solution is obtained from the difference, and this numerical solution is compared with the solutions obtained by the above equations (11) to (14) and equation (16). Thus, the validity of the analytical solution by the approximation shown in the above equations (7) and (8) will be examined. Note that, for simplicity of comparison, the thin wire of the sample was disregarded as an analysis object, and the result of analyzing a heat wire (material: platinum, diameter: 100 μm, length: 10 mm) that uniformly generates heat in vacuum is shown. .

FIG. 2 shows the error of the volume average temperature of the hot wire with respect to the environmental temperature Τ∞, that is, the difference between the analytical solution based on the approximation of the above equations (7) and (8) and the numerical solution based on the difference between the strict basic equations. FIG. Volume calorific value q _v in the calculation, the volume in the analytical solution average temperature rise ΔΤ _v = 10,50,1
00 seeking to become q _v (K), was calculated difference using the q _v.

The analysis error increases as the volume average temperature rise of the heating wire increases, and the error increases as the environmental temperature increases. The analysis error has an extreme value near the environmental temperature of 600 ° C. However, the analysis error is at most 2
It is within [%], and is considered to be sufficient accuracy in evaluating the fundamental measurement accuracy of the measurement method of the present invention.

FIGS. 3 to 5 show the results of calculating the relationship between the emissivity of the thin sample wire and the volume average temperature of the hot wire by the above equation (16). The calculation conditions are as shown below. Environmental temperature Τ∞ = 25 [℃] hot wire: r _h = 5 _{[μm], ε h = 0.1, λ h} = 71.
4 [W / mK] (platinum) Sample wire: r _f = 5 [μm], l _f = 50 [mm], λ
_f = 500 [W / mK] volume calorific value q _v of the heat ray 1,2, volume average temperature increase .DELTA..tau _vh heat rays when epsilon _f = 0.1 is 10 [K] (Fig. 3), 5
The calculation was performed by setting 0 [K] (FIG. 4) and 100 [K] (FIG. 5) and changing ε _f while keeping q _v constant. That is, the effect of ε _f on ΔΤ _vh at the same heating value was examined.

In any of the figures, as ε _f increases, the heat radiation due to the radiation from the sample thin wire increases, and ΔΤ _vh
Is declining. That is, by measuring the heating amount and the volume average temperature of the heating wires 1 and 2, the emissivity of the sample thin wire 3 can be obtained. 3 to 5, the change in Δ５ _vh due to the change in ε _f increases as the temperature rise of the hot wires 1 and 2 (heat wire heating amount) increases. Measurement accuracy, .DELTA..tau _vh due to a change in the epsilon _f
It can be seen that the higher the rate of change (sensitivity), the higher the rate of change, the higher the amount of temperature rise can improve measurement accuracy.

Looking at the effect of the length l _h of the heating wire, the amount of temperature rise of the heating wires 1 and 2 is 10 [K] (FIG. 3).
), When ε _f is 0.4 or less, l _h = 50
mm, but the temperature rise is 100
In the case of [K] (see FIG. 5), the sensitivity is high when l _h = 10 mm in any of the emissivities of the sample thin wires 3.

This is because heat loss from the end of the heating wire, heat radiation due to radiation from the heating wires 1 and 2 and the fine wire 3
This is because the ratio of heat radiation due to radiation from each element changes, and it is necessary to set the lengths of the heating wires 1 and 2 according to the measurement conditions in order to perform highly accurate measurement.

FIGS. 6 and 7 show the measurement error of ε _f due to the uncertainty of the hot wire temperature measurement when the amount of increase in the volume average temperature of the hot wire is set to 10 [K] and 100 [K]. This is a fundamental measurement resolution when measuring the emissivity of the sample thin line 3 by the measurement method of the present invention. When the temperature rise is 10 [K] (see FIG. 6), when the uncertainty of the temperature measurement is within 0.01 [K], the measurement accuracy is maintained within 1 [%] at any emissivity. be able to. When the temperature rise amount is 100 [K] (FIG. 7), the measurement accuracy is 1 when the uncertainty of the temperature measurement is 0.1 [K].
It is within [%].

Calibration of fine platinum wires with a measurement accuracy within 0.01 [K] in the normal temperature range is sufficiently possible, but when performing measurements in a high temperature range, calibration of the fine platinum wires is performed within 0.01 [K]. It is difficult. However, it can be seen from FIGS. 6 and 7 that the uncertainty of the temperature measurement can be compensated by increasing the hot wire temperature rise.

As described above, if the temperature measurement accuracy of the heating wires 1 and 2 is within ± 0.1 [K], the emissivity of the sample fine wire having a radius of 5 μm is within ± 1% by the measuring method of the present invention. It became clear that the measurement could be performed with accuracy. In FIG. 2, the solution obtained by approximating the radiant heat transfer coefficient by the above equations (7) and (8) [see the above equation (16)] has an error of about 2% in a high temperature region. Indicated. This means that the heat
The error when the temperature is increased by 00 [K] is 2 [K], indicating that sufficient accuracy cannot be secured as the emissivity measurement accuracy. Therefore, in the measurement in the high-temperature region, it is necessary to obtain a solution by a numerical analysis for a strict basic equation that does not use the approximation of the radiant heat transfer coefficient, and to obtain the emissivity by comparing this solution with the measured data.

FIG. 8 shows the effect of the thermal conductivity λ _{f of the} thin sample wire on the emissivity measurement. As this λ _f becomes smaller,
The rate (sensitivity) at which ΔT _vh decreases due to ε _f decreases. However, when λ _f = 10 to 1000 [W / mK], λ _f
The effect of ± 10% uncertainty on the measurement of ε _f is within ± 1% for all emissivity samples, and the effect of thermal conductivity uncertainty on the measurement error of ε _f It turned out to be small. This means that by using the two heating wires 1 and 2, the heat insulation condition is established at the center of the sample thin wire 3,
This is because the amount of heat transmitted from the hot wires 1 and 2 to the thin sample wire 3 depends on the heat transfer by radiation of the thin sample wire 3.

[0079] shows the effect of radius r _f of the sample thin line on the measurement emissivity in FIG.

[0080] As is apparent from this figure, as the radius r _f of the sample thin line increases, the sensitivity to increase the amount of heat flowing from the heat rays to the sample thin lines is increased.

FIG. 10 shows the effect of the length l _f of the sample thin line on the emissivity measurement.

[0082] As is apparent from this figure, the sensitivity as the length l _f of the sample thin line until 30mm l _f increases is increased, improvement in sensitivity is not observed in 30mm or more. This is because the temperature efficiency of the thin sample wire is almost 1 at l _f = 30 mm, similar to the temperature efficiency of a normal heat exchanger or the like.
Because it has reached Therefore, it should be noted that the advantage of elongating the sample wire is limited.

In the above embodiment, a platinum wire is preferable as the heating wire, but tungsten or the like can be used.

The present invention is not limited to the above-described embodiments, but various modifications are possible based on the spirit of the present invention, and they are not excluded from the scope of the present invention.

[0085]

As described above, according to the present invention, the following effects can be obtained.

(1) The emissivity of an ultrafine single line itself can be easily measured. That is, the hemispherical total emissivity of the thin sample wire can be obtained from the steady value of the volume average temperature rise amount of the heat wire portion that generates heat uniformly.

(2) The heating, temperature measurement, and support of the measurement sample are performed by the same heating wire, so that an error factor due to heat loss can be reduced.

(3) Specifically, taking a sample fine wire having a diameter of 10 μm as an example, the accuracy of emissivity measurement of a fine single wire of the present invention was examined. As a result, the diameter was 10 μm and the length was 10 m.
m using a short wire probe (heat wire) with a diameter of 10 μm,
It has been found that the emissivity of a sample thin wire having a length of about 30 mm can be measured with an accuracy of about ± 1%.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a configuration of a measuring unit of an ultrafine wire emissivity measuring apparatus according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating a difference between an analytical solution of a volume average temperature of a hot wire with respect to an environmental temperature に お け る and a numerical solution based on a difference in an emissivity measurement of an ultrafine wire according to an embodiment of the present invention.

FIG. 3 is a diagram showing the result of calculating the relationship between the emissivity of a thin sample wire and the hot-wire volume average temperature by equation (16) showing the embodiment of the present invention (part 1: ΔT _vh = 10K).

FIG. 4 is a diagram showing the result of calculating the relationship between the emissivity of a thin sample wire and the hot-wire volume average temperature by equation (16) showing the embodiment of the present invention (part 2: ΔT _vh = 50K).

FIG. 5 is a diagram showing the result of calculating the relationship between the emissivity of a thin sample wire and the hot-wire volume average temperature by equation (16) showing the embodiment of the present invention (part 3: ΔT _vh = 100 K).

FIG. 6 is a diagram showing an error in measurement of ε _f due to uncertainty in hot wire temperature measurement when the amount of increase in the volume average temperature of the hot wire is set to 10 [K] according to the embodiment of the present invention.

FIG. 7 is a diagram showing an error in measurement of ε _f due to uncertainty in hot wire temperature measurement when the amount of increase in the volume average temperature of the hot wire is set to 100 [K], showing the embodiment of the present invention.

FIG. 8 is a diagram showing the effect of the thermal conductivity λ _f of a sample thin wire on emissivity measurement.

[9] the radius r _f of the sample thin line shows the effect on the measurement emissivity.

[10] of the sample thin line length l _f is a diagram showing the effect on the measurement emissivity.

[Explanation of symbols]

1,2 hot wire 3 samples thin line 3A, the length q _v calorific value per unit volume of 3B connection point Bi Biot number l hot wire and sample wire (volume calorific value) R _c thermal conductivity ratio R _d radius ratio Ri during temperature measurement heat ray unit resistance value r radial coordinate S measurement of the sensitivity of the heat ray unit in the electrical resistance value Rt 0 ₀ ° C. of _{(= dΤ v / dλ f)} Τ temperature T _v volume average temperature X dimensionless longitudinal coordinate β Temperature coefficient of resistance λ Thermal conductivity σ Stephan Boltzmann constant θ Dimensionless temperature θ _v Dimensionless volume average temperature ε Emissivity [subscript] f Sample wire h Heat wire h1 Heat wire I h2 Heat wire II

Continued on the front page F term (reference) 2G040 AB08 AB10 AB12 BA02 BA21 CA13 CB09 DA02 DA12 EA02 EA11 EB02 EC03 FA10 HA07 HA16 ZA05 2G066 AC20 BC11 CA11

Claims (6)

[Claims] 1. A method for measuring the emissivity of a fine single wire, comprising:
(A) two heat wires that generate uniform volume heat are arranged in parallel, and a thin sample wire is connected between the two heat wires;
(B) heating the two heat wires directly by applying current to equalize the amount of heat applied from one heat wire to the sample wire and the amount of heat applied from the other heat wire to the sample wire; (c) adding the heat wire to the sample wire; By radiating all of the obtained heat from the sample fine wire by radiation, by comparing the theoretical solution of steady heat conduction with respect to the volume average temperature of the two heat wires and the steady value of the volume average temperature rise of the heat wire obtained by measurement, A method for measuring the emissivity of a fine single line, wherein the emissivity of the fine sample line is obtained. 2. The emissivity measuring method for a fine single wire according to claim 1, wherein a platinum fine wire is used as said two heating wires. 3. An emissivity measuring apparatus for a fine single wire,
(A) two heating wires arranged in parallel to generate uniform volume heat, and (b) a thin sample wire connected between the two heating wires;
(C) a means for directly energizing and heating the two heat wires to equalize the amount of heat applied from one heat wire to the sample wire and the amount of heat applied from the other heat wire to the sample wire. Emissivity measuring device for fine single wires. 4. The fine single-wire emissivity measuring apparatus according to claim 3, wherein said two heating wires are platinum fine wires. 5. An emissivity measuring apparatus for a fine single wire according to claim 3, wherein said sample fine wire is connected to a center portion of said two heating wires. 6. An emissivity measuring apparatus for a fine single line according to claim 3, wherein the fine line of the sample has an order of 1 to 10 μm.