ISO 8302:1991 断熱—定常状態の熱抵抗と関連する特性の決定—ガード付きホットプレート装置 | ページ 4

1.5.1 熱伝達特性に影響を与える要因

材料試験片の熱伝達特性は、

• 材料またはそのサンプルの組成の変動により異なります。
• 湿気やその他の要因の影響を受ける。
• 時間とともに変化する。
• 平均気温に応じて変化します。そして
• 熱履歴に依存します。

したがって、特定の用途における材料を代表する熱伝達特性の典型的な値の選択は、これらの要因の考慮に基づくものであり、必ずしもすべての使用条件に修正なしで適用されるわけではないことを認識する必要があります。

一例として、この方法では、乾燥した試験片で熱伝達特性が得られるはずですが、実際にはそのような条件が実現できない可能性があります。

さらに基本的なのは、熱伝達特性が平均温度や温度差などの変数に依存することです。これらの依存関係は、典型的な使用条件下で測定またはテストする必要があります。

1.6.1 装置の原理

ガード付きホットプレート装置は、平坦な平行面を有する均一なスラブの形で、定常状態で存在するような一方向の均一な熱流量密度を試験片内に確立することを目的としています。 2 つの平らで平行な等温面で囲まれた無限のスラブ。

1.6.2.1 2 検体装置

2 つの試料装置 [図 1a) を参照] では、ヒーターと金属表面プレートで構成され、加熱ユニットと呼ばれる中央の円形または正方形の平板アセンブリが 2 つのほぼ同一の試料の間に挟まれています。熱流量は試験片を通って、冷却ユニットと呼ばれる別個の円形または四角形の等温平面アセンブリに伝達されます。

1.7.1 接触抵抗による制限

熱伝導性が高く剛性の高い試験片（つまり、加熱ユニットと冷却ユニットの圧力によって形状が大きく変化するには硬すぎて変形しない材料の試験片）を試験する場合、試験片と試験片の両方の表面に小さな不均一性があっても、装置（表面が完全に平坦でない場合）では、試料と加熱ユニットおよび冷却ユニットのプレートとの間で接触抵抗が均一に分布しない可能性があります。

これらは、試験片内で不均一な熱流量分布と熱場の歪みを引き起こします。さらに、正確な表面温度測定を行うことが困難になります。熱抵抗が 0.1 m ²・K/W 未満の試験片の場合、表面温度を測定するための特別な技術が必要になります。金属表面は機械加工または切断して平らかつ平行にし、応力を緩和する必要があります。

1.8.1 熱抵抗、熱コンダクタンスまたは伝達係数

1.8.1.1 試験片の均質性

不均質な試験片の熱抵抗または熱コンダクタンスを測定する場合、試験片内および計量領域の面上の熱流量密度は一方向または均一ではない可能性があり、熱場の歪みが試験片内に存在する可能性があります。重大なエラーを引き起こします。測定領域に隣接する試験片の領域、特にこの領域の端近くが最も重要です。

このような場合にこの方法が適用できるかどうかについて、信頼できるガイドラインを与えることは困難です。主なリスクは、不均一性が試験片内で異なる相対位置を取る場合に、不均衡誤差やエッジ熱損失誤差などが予測不能に変化する可能性があることです。その結果、3.4 で提案されたすべてのチェックは、さまざまなテストに関連する真の違いを覆い隠す系統的エラーの影響を受ける可能性があります。

一部の標本では、構造の変化が短い距離で発生する場合があります。これは多くの断熱材に当てはまります。

他の試験片では、加熱ユニットおよび冷却ユニットのプレートと接触している試験片の表面間に直接的な熱短絡が存在する可能性があります。最大の効果は、熱を容易に伝導する材料の部分が、試験片の両側に広い表面積を持ち、他の経路に比べて熱抵抗の低い経路で接続されている場合に発生します。

1.8.1.2 温度差の相関関係

熱抵抗または熱伝導率は、多くの場合、試験片全体の温度差の関数です。報告書では、2 つの特性の報告値に適用される温度差の範囲を定義するか、報告値が単一の温度差で決定されたことを明確に記載する必要があります。

Section 1 General

1.1 Scope

This International Standard lays down a test method which defines the use of the guarded hot plate method to measure the steady-state heat transfer through flat slab specimens and the calculation of its heat transfer properties.

This is an absolute or primary method of measurement of heat transfer properties, since only measurements of length, temperature and electrical power are required.

Reports conforming to this standard test method shall never refer to specimens with thermal resistance lower than 0,1 m²·K/W provided that thickness limits given in 1.7.4 are not exceeded.

The limit for thermal resistance may be as low as 0,02 m²·K/W but the accuracy stated in 1.5.3 may not be achieved over the full range.

If the specimens satisfy only the requirements outlined in 1.8.1 , the resultant properties shall be described as the thermal conductance and thermal resistance or transfer factor of the specimen.

If the specimens satisfy the requirements of 1.8.2, the resultant property may be described as the mean measurable thermal conductivity of the specimen being evaluated.

If the specimens satisfy the requirements of 1.8.3, the resultant property may be described as the thermal conductivity or transmissivity of the material being evaluated.

1.2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this International Standard. At the time of publication, the editions indicated were valid. All standards are subject to revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of currently valid International Standards.

1.3 Definitions

For the purposes of this International Standard, the following definitions apply.

The following quantities are defined in ISO 7345 or in ISO 9251:

The following definitions related to material properties are given in ISO 9251:

porous medium

homogeneous medium

homogeneous porous medium

heterogeneous medium

isotropic medium

anisotropic medium

stable medium

Other terms not defined in ISO 7345 or ISO 9251:

1.4 Symbols and units

1.5 Significance

1.5.2 Sampling

Heat transfer properties need an adequate amount of test information to be considered representative of a material. A heat transfer property of a material can be determined by a single measurement only if the sample is typical of the material and the specimen(s) is (are) typical of the sample. The procedure for selecting the sample should normally be specified in the material specification. The selection of the specimen from the sample may be partly specified in the material specification. As sampling is beyond the scope of this test method, when the problem is not covered by a material specification, appropriate documents shall be considered.

1.5.3 Accuracy and reproducibility

The evaluation of the accuracy of the method is complex and is a function of the apparatus design, of the related instrumentation and of the type of specimen under test. However, apparatus constructed and operated in accordance with this method is capable of measuring heat transfer properties accurate to within ± 2 % when the mean temperature of the test is near the room temperature.

With adequate precautions in the design of the apparatus, and after extensive checking and crossreferencing of measurements with other similar apparatus, an accuracy of about ± 5 % should be obtainable anywhere in the full operating range of an apparatus. Such accuracy is normally easier to attain using separate apparatus for the extremes in the range. The reproducibility of subsequent measurements made by the apparatus on a specimen maintained within the apparatus without changes in test conditions is normally much better than 1 %. When measurements are made on the same reference specimen removed and then mounted again after long time intervals, the reproducibility of measurements is normally better than ± 1 %. This larger figure is due to minor changes in test conditions, such as the pressure of the plates on the specimen (that affect contact resistances), the relative humidity of the air around the specimen (that affects its moisture contents), etc.

These levels of reproducibility are required to identify errors in the method and is desirable in quality control applications.

1.6 Principle

1.6.2 Apparatus types

From this basic principle were derived two types of guarded hot plate apparatus:

• a) with two specimens (and a central heating unit);
• b) with a single specimen.

1.6.2.2 Single-specimen apparatus

In the single specimen apparatus [see figure 1b)], the second specimen is replaced by a combination of a piece of insulation and a guard plate. A zero temperature-difference is then established across this combination. Providing all other applicable requirements of this Internation Standard are fulfilled, accurate measurements and reporting according to this method may be accomplished with this type of apparatus, but particular reference to the modification of the normal hot plate apparatus with two specimens should be made in the report.

1.6.3 Heating and cooling units

The heating unit consists of a separate metering section ここで, the unidirectional uniform and constant density of heat flow-rate can be established, surrounded by a guard section separated by a narrow gap. The cooling units may consist of a continuous flat plate assembly but it is preferable to have them in a similar form to the heating unit.

1.6.4 Edge insulation and auxiliary guarded sections

Additional edge insulation and/or auxiliary guard sections are required, especially when operating above or below room temperature.

1.6.5 Definition of the guarded hot plate apparatus

The term “guarded hot plate” applies to the entire assembled apparatus, that, hence, is called “guarded hot plate apparatus”. The general features of the apparatus with specimens installed are shown in figure 1.

1.6.6 Measuring the density of heat flow-rate

With the establishment of steady-state in the metering section, the density of heat flow-rate, q, is determined from measurement of the heat-flow-rate, Φ, and the metering area, A, that Φ crosses.

1.6.7 Measuring the temperature difference

The temperature difference across the specimen, ΔT, is measured by temperature sensors fixed at the surfaces of the metal plates and/or those of the specimens where appropriate.

1.6.8 Measuring the thermal resistance or transfer factor

The thermal resistance, R, is calculated from a knowledge of q, A and ΔT if the appropriate conditions given in 1.8.1 are realized. If the thickness, d, of the specimen is measured, the transfer factor,J, may be computed.

1.6.9 Computing thermal conductivity

The mean thermal conductivity, λ of the specimen may also be computed if the appropriate conditions given in 1.8.2 are realized and the thickness, d, of the specimen is measured.

1.6.10 Apparatus limits

The application of the method is limited by the capability of the apparatus to maintain the unidirectional uniform and constant density of heat flow-rate in the specimen coupled with the ability to measure power, temperature and dimensions to the limit of accuracy required.

1.6.11 Specimen limits

The application of the method is also limited by the form of the specimen(s) and the degree to which they are identical in thickness and uniformity of structure (in the case of two-specimen apparatus) and whether their surfaces are flat or parallel.

1.7 Limitations due to apparatus

1.7.2 Upper limits for the thermal resistance

The upper limit of thermal resistance that can be measured is limited by the stability of the power supplied to the heating unit, the ability of the instrumentation to measure power level and the extent of the heat losses or gains due to temperature imbalance errors (analysed later) between the central metering and guard sections of the specimens and of the heating unit.

1.7.3 Limits to temperature difference

Provided that uniformity and stability of the temperature of the surfaces of the heating and cooling unit plates, the noise, resolution and accuracy of the instrumentation and the restrictions on temperature measurements can be maintained within the limits outlined in sections 2 and 3, temperature differences as low as 5 K, when measured differentially, can be used in the measurements, provided the requirements described in 2.1.4.1.2 to 2.1.4.1.4 are met. Lower temperature differences shall be reported as non-compliance with this International Standard.

If temperature measurements of each plate are made by means of thermocouples with independent reference junctions, the accuracy of the calibration of each thermocouple may be the limiting factor in the accuracy of measured temperature differences. In this case, it is recommended that temperature differences of at least 10 K to 20 K are used in order to minimize temperature-difference measurement errors.

Higher temperature differences are limited only by the capability of the apparatus to deliver enough power while maintaining required temperature uniformity.

1.7.4 Maximum specimen thickness

The boundary conditions at the edges of the specimens due to the effects of edge insulation, of auxiliary guard heaters and of surrounding ambient temperature will limit the maximum thickness of specimen for any one configuration, as described in section 2 (see also 3.2.1). For inhomogeneous, composite or layered specimens, the mean thermal conductivity of each layer should be less than twice that of any other layer.

This shall be regarded as a rough rule of thumb asking only for an estimate made by the operator that does not necessarily imply the measurement of conductivity of each layer, it is expected that in this situation the accuracy will remain close to the one predictable for tests on homogeneous specimens. No guidelines can be supplied to assess measurement accuracy when this requirement is not met.

1.7.5 Minimum specimen thickness

The minimum specimen thickness is limited by contact resistances given in 1.7.1. Where thermal conductivity or thermal resistivity or thermal transmissivity or transfer factor is required, the minimum specimen thickness is also limited by the accuracy of the instrumentation for measuring the thickness.

1.7.6 Metering area definition

Theoretical investigations show that the metering area, i.e. the area of the specimen traversed by the heat flow-rate fed by the central metering section, is related to the specimen thickness and to the gap width. As the thickness tends to zero, the metering area tends to the area of the central metering section, while for thick specimens the metering area is bounded by the line defining the centre of the gap (2.1.1.3). To avoid complex corrections, this definition can be retained, provided the thickness of the specimen is at least ten times the width of the gap. For some special applications see also 3.1c).

1.7.7 Maximum operating temperature

The maximum operating temperature of the heating and cooling units may be limited by oxidation, thermal stress or other factors which degrade the flatness and uniformity of the surface plate and by changes of electrical resistivity of electrical insulations which may affect accuracy of all electrical measurements.

1.7.8 Vacuum conditions

Particular care must be taken if a guarded hot plate apparatus is used for measurements under vacuum conditions. If a high vacuum is desired, the materials of the apparatus must be carefully selected to avoid excessive outgassing. Under vacuum conditions, especially at lower temperatures, serious errors can arise if due care is not taken when installing heater and temperature sensor leads so as to minimize extraneous heat flow-rates and temperature measurement errors.

1.7.9 Apparatus size

The overall size of a guarded hot plate apparatus will be governed by the specimen dimensions which range normally within the limits of 0,2 m to 1 m diameter or square. Samples smaller than 0,3 m may not be representative of the bulk material, while specimens larger than 0,5 m may create considerable problems in maintaining the flatness of the specimens and plates, temperature uniformity, equilibrium time and total cost within acceptable limits.

For ease of inter-laboratory comparisons and for general improvement in collaborative measurements, it is recommended that the design of future guarded hot plate apparatus be based upon one of the following suggested standard dimensions:

• 0,3 m diameter or square;
• 0,5 m diameter or square;

and in addition:

• 0,2 m diameter or square if only homogeneous materials are tested;
• 1m diameter or square if specimens are to be measured at a thickness that exceeds the limits permitted for an 0,5 m apparatus.

1.8 Limitations due to specimen

1.8.2 Mean thermal conductivity of a specimen

In order to determine the mean thermal conductivity (or thermal transmissivity) of a specimen (see 1.3.4), the criteria of 1.8.1 shall be fulfilled. The specimen shall be homogeneous or homogeneous porous as defined in ISO 9251. Homogeneous porous specimens shall be such that any inhomogeneity has dimensions smaller than one-tenth of the specimen thickness. In addition, at any one mean temperature, the thermal resistance shall also be independent of the temperature difference established across the specimen.

The thermal resistance of a material is known to depend on the relative magnitude of the heat transfer process involved. Heat conduction, radiation and convection are the primary mechanisms. However, the mechanisms can combine or couple to produce non-linear effects that are difficult to analyse or measure even though the basic mechanisms are well researched and understood.

The magnitude of all heat transfer processes depends upon the temperature difference established across the specimen. For many materials, products and systems, a complex dependence may occur at temperature differences which are typical of use. In these cases, it is preferable to use a temperature difference typical of use and then to determine an approximate relationship for a range of temperature differences. The dependence can be linear for a wide range of temperature differences.

Some specimens, while meeting the homogeneity criteria, are anisotropic in that the component of thermal conductivity measured in a direction parallel to the surfaces is different to that measured in a direction normal to the surfaces. For such specimens, this can result in larger imbalance and edge loss errors. If the ratio between these two measurable values is lower than two, reporting according to this method is still possible if imbalance and edge heat loss errors are determined separately with anisotropic specimens mounted in the apparatus.

1.8.3 Thermal conductivity, thermal transmissivity or thermal resistivity of a material

1.8.3.1 General

In order to determine the thermal conductivity or thermal resistivity of a material, the criteria of 1.8.2 shall be fulfilled. In addition, adequate sampling must be performed to ensure that the material is homogeneous or homogeneous porous, and that the measurements are representative of the whole material, product or system. The thickness of the specimens must be greater than that for which the transfer factor of the material, product or system does not change by more than 2 % with further increase in thickness.

1.8.3.2 Dependence on specimen thickness

Of the processes involved, only conduction produces a thermal resistance that is directly proportional to the thickness of a specimen. The others result in a more complex relationship. The thinner and less dense the material, the more likely that the resistance depends on processes other than conduction. The result is a condition that does not satisfy the requirements of the definitions for Ihermal conductivity and thermal resistivity — both of which are intrinsic properties — since the transfer factor shows a dependence on the specimen thickness. For such materials, it may be desirable to determine the thermal resistance at conditions applicable to their use. There is believed to be a lower limiting thickness for all materials below which such a dependence occurs. Below this thickness, the specimen may have unique thermal heat transfer properties, but not the material. It remains, therefore, to establish this minimum thickness by measurements.

1.8.3.3 Determination of minimum thickness for which heat transfer properties of the material may be defined

If the minimum thickness for which the thermal transmissivity can be defined is not known, it is necessary to estimate this thickness.

In the absence of an established method, the somewhat crude procedure outlined in 3.4.2 may be used for determining the thickness and whether it occurs in the range of thicknesses in which a material is likely to be used.

It is important to differentiate between added thermal resistance in measurements caused by the placement of the temperature sensors below the surfaces of the plates, added resistance caused by poor specimen surfaces, and added resistance caused by the coupling of the conduction and radiation modes of heat transfer in the specimens. All three can affect the measurements in the same way, and often the three may be additive.

1.8.4 Warping

Special care should be exercised with specimens with large coefficients of thermal expansion that warp excessively when subjected to a temperature gradient. The warping may damage the apparatus or may cause additional contact resistance that may lead to serious errors in the measurement. Specially designed apparatus may be necessary to measure such materials.

Annex D

Bibliography