JPS6371644A - Method for measuring thermal diffusivity - Google Patents

Abstract

PURPOSE:To find the thermal diffusibility of a thick sample which has low heat conductivity with a small error relatively easily without damaging the radiated surface of the sample by heating the sample stepwise and employing the same method as a flashing method for analysis. CONSTITUTION:The surface of a plane sample which has constant thickness (l) is radiated with an electromagnetic wave or particle rays with constant energy uniformly and continuously from a certain point of time. The curve of the temperature rise of the rear surface of the sample is recorded and differentiated with time to find a time (t) from the point of time when a differentiated value with a specific rate to the maximum differentiated value is obtained. The heat conduction expression of the step heating method id also differentiated with time to find a Fourier series value (alphat/l<2>, where alpha is thermal diffusivity) with which a differentiated value with a specific rate to the maximum differentiated value of temperature is obtained. The thermal diffusivity alpha is found from this Fourier series value and said time (t) and thickness (l) of the sample. Consequently, the thermal diffusivity with the small error is found relatively easily.

Description

[Detailed description of the invention] (Industrial application field) The present invention relates to a method for measuring thermal diffusivity.

Conventionally, there are two methods for measuring thermal diffusivity by irradiating electromagnetic waves or particle beams onto a flat sample of constant thickness. One is instantaneous heating (flash method) and the other is constant heating (step method).

In the flash method, as shown in Figure 3, when pulsed electromagnetic waves or particle beams such as laser light are uniformly irradiated over the entire surface of a flat sample of a certain thickness, the laser light is absorbed by the sample and heat is generated in the sample. In the absence of losses, the temperature rise 01 curve on the back side of the sample rises according to the well-known heat conduction equation:

θ,=θm [1+2. , (-1) exp (-n"
x” (It / A!”)) - (t) However, α is the thermal diffusivity of the sample! is the thickness of the sample, t, and the time θm after laser beam irradiation is e when t→■.

According to this relational expression, the Fourier numbers α'', /l'' become variables.

From Fig. 4, for example, when the sample temperature rise width reaches half of the maximum temperature rise width, the 7-tier series value αtzs/l''= a
138 B, and the time t6. until the temperature increase width θ of the sample reaches half of the maximum temperature increase width θm. ．． is measured, and the thermal diffusivity α is determined from the following formula.

α=α13887'/to, s...
-(2) Also, the ratio Cp can be used to express the amount of heat absorbed by the sample, Q1, and the weight of the sample.

Therefore, the thermal conductivity λ is λ=
It can be determined from α, Cp, and ρ.

On the other hand, in the step method, i, :t as shown in Figure 5
When light such as halogen light is uniformly irradiated stepwise over the entire surface of the sample from =a, the temperature at the back of the sample under the same conditions as when formula (t) was calculated is as follows, which is well known. It rises according to the heat conduction equation.

...(3) However, q is the energy irradiated and absorbed per unit time and unit area. According to this heat conduction formula, 7-Lier series αt/l! When the relationships θ and λ/ql are determined using variables, the result is shown in FIG. 6.

For example, θ for αts/z” is expressed as θt, ), 2αt
Let θ for 1/2 be θt (2ts),
When the relationship between α11/(θtcztt)/θt(tx) is illustrated, a graph as shown in FIG. 7 is obtained.

When t is specified, θ*(2t1)/θg(t1) can be obtained experimentally, so from Fig. 7, αt at that value can be determined experimentally.
! /l”=k is obtained, and from this equation, the thermal diffusivity α is α=k
l″/tt...calculated from (4).

Next, in equation (3), if t→■, then Σ becomes zero.

Therefore, equation (3) is illustrated and the slope of the curve is determined.

Sample density ρ, sample thickness! If the energy q irradiated and absorbed per unit time and unit area is known, the specific heat Op can be determined by substituting these and the gradient into equation (5).

The thermal conductivity λ is obtained in the same manner as the flash method.

(Problems to be Solved by the Invention) According to the above-mentioned 7-ratio method, thermal diffusivity can be easily determined. In this case, the temperature of the irradiated surface becomes extremely high.Therefore, it is difficult to accurately determine the thermal characteristics of plastic samples and other general samples near the melting point or transition point.

On the other hand, the step method causes less damage to the irradiated surface of the sample and is suitable for measuring samples with poor thermal conductivity, but the time t is inappropriately selected and requires considerable skill to calculate the rate. It takes.

It is an object of the present invention to overcome the disadvantages of the two conventional methods.

(Means for Solving the Problems) In order to achieve the above-mentioned object, the present invention continues to irradiate electromagnetic waves or particle beams with a constant energy uniformly from a certain point on the surface of a flat plate sample of a constant thickness. The temperature rise curve on the back side of the sample is recorded and the curve is differentiated with respect to time to determine the time (t) from said point in time at which a differential value of a predetermined ratio to the maximum differential value is obtained; The heat conduction equation is differentiated with respect to time, and the differential value of the predetermined ratio is obtained with respect to the maximum differential value of temperature.
s However, it is characterized in that α: thermal diffusivity) is determined, and thermal diffusivity (φ) is determined from the 7-Lier series value, the time (t), and the thickness of the sample.

(Function) When the step method is used, the temperature rise on the back side of the sample is differentiated by Equation (3). Comparing this Equation (6) with the equation obtained by dividing Equation (t) by θm, the left-hand side of Equation (6) ( dos / cl t) (q/ρ
If C3pl) is replaced with 070m, it becomes the same as the flash method.

The denominator on the left side of equation (6) is (as is clear from equation 5j, t is dθ, /at at ω, so the left side of tGf equation is the differential value of temperature at a certain time, and t is the differential value of temperature at Q. Indicates the ratio to the differential value (maximum differential value).

Therefore, in the same way as the flash method, from FIG.
= α1388, and after the time until the temperature differential value of the sample reaches half of the maximum differential value, S is measured, and the thermal diffusivity is determined from the following formula: %.

(Example〕 Embodiments of the method of the invention will be described with reference to the accompanying drawings.

As a sample, a stainless steel full (S
Using a halogenated halogen lamp as a heating source, energy of α5 W/cTA was applied to one side of the sample from a certain point.

The differential curve of the temperature rise curve on the back side of the sample at that time is
As shown in the figure. This differential curve was obtained through software processing using Funpyuta.

In this differential curve, the time at a differential value of 1/2 of the maximum differential value was α96 seconds. Therefore, by substituting r196 seconds and sample thickness 0.5 (J into equation (2), thermal diffusivity α
was calculated.

α=(α1388X[L5”)/[L96=(LO36
cJ/gscThe specific heat of the sample is t-+ as before.
The differential value of temperature at co, unit time, energy absorbed by the sample per unit area q1 density ρ, and thickness l of the sample are substituted into equation (5). Obtain from comparison.

Similarly, the thermal conductivity λ is determined from λ=Op・ρ・α.

(Effects of the Invention) As explained above, a thick sample with low thermal conductivity is heated by step heating, and analysis is performed using the same method as the flash method, without damaging the irradiated surface of the sample.
This has the effect that the thermal diffusivity can be determined relatively easily with little error.

[Brief explanation of the drawing]

Fig. 1 is a theoretical curve diagram of the temperature change in the method of the present invention, Fig. 2 is a diagram showing the measured curve of the differential value of temperature rise on the back side of the sample when step heating is performed, and Fig. 3 is a diagram showing the measured curve of the temperature rise differential value in the flash method. Figure 4 shows the relationship between energy and time in the step method. Figure 5 shows the relationship between energy and time.
G*l−+−w Q dJ J+ ++ j
G 1- ↓+ I↓ 7field+*a l-+-a
^ruy tw, ul, Figure 64 is a diagram showing a theoretical curve of temperature rise in the step method, and Figure 7 is a diagram showing a curve used for data analysis in the step method. Patent applicant: Shinku Riko Co., Ltd. Representative: Kin Kitamura −゛＼
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Claims (1)

[Claims] Continue to irradiate electromagnetic waves or particle beams with constant energy uniformly from a certain point on the surface of a flat sample with a constant thickness (l), record a temperature rise curve on the back side of the sample, and differentiate the curve with respect to time, Determine the time (t) from the point in time when a differential value of a predetermined ratio is obtained with respect to the maximum differential value, and also differentiate the heat conduction equation of the step heating method with respect to time, and calculate the predetermined value with respect to the maximum differential value of temperature. Find the Fourier series value (αt/l^2, where α: thermal diffusivity) that yields the differential value of the ratio,
The Fourier series value, the time (t) and the sample thickness (l
) A thermal diffusivity measuring method characterized by determining the thermal diffusivity (α) from ).