E1225-13 Standard Test Method for Thermal Conductivity of Solids Using the Guarded- Comparative-.pdf

Designation: E1225 − 13Standard Test Method for Thermal Conductivity of Solids Using the Guarded- Comparative-Longitudinal Heat Flow Technique1 This standard is issued under the fixed designation E1225; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval. This standard has been approved for use by agencies of the U.S. Department of Defense. 1. Scope 2. Referenced Documents 1.1 This test method describes a steady state technique for 2.1 ASTM Standards:2 the determination of the thermal conductivity, λ, of E230 Specification and Temperature-Electromotive Force homogeneous-opaque solids (see Notes 1 and 2). This test (EMF) Tables for Standardized Thermocouples method is applicable to materials with effective thermal con- 3. Terminology ductivities in the range 0.2 < λ < 200 W/(m·K) over the temperature range between 90 and 1300 K. It can be used 3.1 Descriptions of Terms and Symbols Specific to This outside these ranges with decreased accuracy. Standard: 3.1.1 Terms: NOTE 1—For purposes of this technique, a system is homogeneous if 3.1.1.1 thermal conductivity, λ—the time rate of heat flow, the apparent thermal conductivity of the specimen, λA, does not vary with changes of thickness or cross-sectional area by more than 65 %. For under steady conditions, through unit area, per unit temperature composites or heterogeneous systems consisting of slabs or plates bonded gradient in the direction perpendicular to the area; together, the specimen should be more than 20 units wide and 20 units 3.1.1.2 apparent thermal conductivity—when other modes thick, respectively, where a unit is the thickness of the thickest slab or of heat transfer through a material are present in addition to plate, so that diameter or length changes of one-half unit will affect the conduction, the results of the measurements performed accord- apparent λA by less than 65 %. For systems that are non-opaque or partially transparent in the infrared, the combined error due to inhomo- ing to this test method will represent the apparent or effective geneity and photon transmission should be less than 65 %. Measurements thermal conductivity for the material tested. on highly transparent solids must be accompanied with infrared absorption 3.1.2 Symbols: coefficient information, or the results must be reported as apparent thermal conductivity, λA. λM(T) = thermal conductivity of meter bars (reference materials) as a function of temperature, (W/ NOTE 2—This test method may also be used to evaluate the contact (m·K)), thermal conductance/resistance of materials. λM1 = thermal conductivity of top meter bar (W/ 1.2 The values stated in SI units are to be regarded as (m·K)), standard. No other units of measurement are included in this λM2 = thermal conductivity of bottom meter bar (W/ standard. (m·K)), λS(T) = thermal conductivity of specimen corrected 1.3 This standard does not purport to address all of the for heat exchange where necessary, (W/ safety concerns, if any, associated with its use. It is the (m·K)), responsibility of the user of this standard to establish appro- λ'S(T) = thermal conductivity of specimen calculated priate safety and health practices and determine the applica- by ignoring heat exchange correction, (W/ bility of regulatory limitations prior to use. (m·K)), λI(T) = thermal conductivity of insulation as a func- tion of temperature, (W/(m·K)), 1 This test method is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.05 on Thermo- 2 physical Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or Current edition approved Oct. 1, 2013. Published November 2013. Originally contact ASTM Customer service at [email protected]. For Annual Book of ASTM approved in 1987. Last previous edition approved in 2009 as E1225 – 09. DOI: Standards volume information, refer to the standard’s Document Summary page on 10.1520/E1225-13. the ASTM website. Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States 1 polymers.2. at any position and uniform heat transfer at each meter q' = heat flow per unit area. δT.2 A force is applied to the column to ensure good Table 1 lists some of the recognized reference materials.1. (m).2 Table 1 is not exhaustive and other materials may be enclosed in a guard shell with a radius. rB = guard cylinder inner radius. (m). A more complex but apparatus are outlined in Section 10.2 Insulation Materials: 6.3 The requirements for any reference material include bottom at temperature TB. λI. λM. The value of λS .. assumes no heat exchange between the column and insulation Ti = the temperature at Zi. and fiber 3 The boldface numbers in parentheses refer to a list of references at the end of materials exists for reducing both radial heat flow in the this test method.1.1 A large variety of powder. A temperature gradient is imposed on the values shall be stated in the report. At equilibrium 5. = position as measured from the upper end of the λs 5 · ·S Z4 2 Z3 λM T2 2 T1 T6 2 T5 1 T4 2 T3 2 Z2 2 Z1 Z6 2 Z5 D (1) column. insulation material of thermal conductivity. A specimen of unknown tion of this test method is not intended to restrict in any way the thermal conductivity. = uncertainty in λ. etc. tempera- 4. Requirements for qualifying an similar thermal conductance. 1: 6. reasonable cost. δλ. the reference material with the higher λM should be uncorrected for heat shunting) can then be determined using used to reduce the total temperature drop along the column.1 The general features of the guarded longitudinal heat ture measurements. contingencies that might offer difficulties to a person without 4. particularly at elevated temperatures a λM nearest to λS should be used for the meter bars. TT. λS. Since heat shunting errors for a specific λI unguarded system is not recommended due to the potential increase as λM/λs varies from unity.1. as materials. and the 6.1 A test specimen is inserted under load between two conductivity is especially useful for engineering materials similar specimens of a material of known thermal properties. it is preferable to use standards available from a described as the flat slab comparative method.2. T. 5. (1) the reference which has very large heat losses. E1225 − 13 T Z = absolute temperature (K). Fig. rB. Essentially.2 General Features of Test Method: technical knowledge concerning theory of heat flow. the temperature gradients along the 6. etc. The errors caused by these two as- rA = specimen radius. is mounted between two meter bars of improved procedures. column by maintaining the top at a temperature. thermal conductivities must be used for the meter bars. Tg(z). and an accurately known thermal the average temperature of the specimen may also be used. (K). refractories. held at the used as references. However. The stack is surrounded by an shows the approximate variation of λM with temperature. suitable arrangement is a column consisting of a disk heater with a specimen and a meter bar on each side between heater 6. as long as the meter bars and specimen have available because numerous measurements of λ have been the same conduction areas. cult and it is not practical in a method of this type to try to sured temperature gradients in the respective specimens and establish details of construction and procedures to cover all the thermal conductivity of the reference materials. The reference material and the source of λM temperature. and graphites including combinations and other com- losses are minimized by use of a longitudinal guard having posite forms of each. Requirements and heat sink. the thermal conductivity is derived from the mea. z.4 If a sample’s thermal conductivity λs is between the sections are calculated from measured temperatures along the thermal conductivity values of two types of reference two meter bars and the specimen. the following equation where the notation is shown in Fig. column-guard annulus and surrounds. 1. Approximately one-half of the power would then 6.2. (1). Summary of Test Method 5. Tg(z) is usually a linear temperature stability over the temperature range of operation. (W/m2). any National Metrology Institute. When the meter bars and speci.1 Meter Bar Reference Materials: flow through each specimen. A including ceramics. sumptions vary widely and are discussed in Section 10. (m). 6. temperature gradient is established in the test stack and heat carbons.1 Reference materials or transfer standards with known men are right-circular cylinders of equal diameter the tech. This is a highly idealized situation. however. compatibility gradient matching approximately the gradient established in with other system components.3 At steady state.2 Proper design of a guarded-longitudinal system is diffi- conditions. 4. new or improved techniques known thermal conductivity. and Because of these two effects. The insulation is 6. particulate. (K). When the cross. (m). the minimum measurement error of the method is the uncer- sectional dimensions are larger than the thickness it is tainty in λM. However. metals and alloys. of the same cross-section and must be thoroughly tested. bar-specimen interface. ease of tem- the test stack. made and general acceptance of the values has been obtained. since it l = specimen length. Standardiza- flow technique are shown in Fig. An conductivity.1. an isothermal guard with Tg(z) equal to perature sensor attachment. restrictions must be placed on this Tg(z) = guard temperature as a function of position. approximately the same temperature gradient. λM/lM. but having an estimated thermal future development by research workers of new or methods or conductance of λS/ lS. Other reference materials are shape can be used. Since nique is described as the cut-bar method. and for heat shunting 2 . if the desired accuracy is to be achieved.1 The comparative method of measurement of thermal 4. and general testing practices. Significance and Use 4. test method. 2 contact between specimens. thermal wire grounds on the guard. This reference can be an ice-cold slurry (3). they should be fabricated from wires which are 0. 1 3 . The insulation must be stable over the anticipated temperature range. 6. temperature range. However. powders and particulates are used since they pack readily. All thermocouples shall be fabricated from either calibrated thermocouple wire (4) or from wire that has been certified by the supplier to be within the limits of error specified in Table 1 of Standard E230. and gas within the system. Whenever possible. it must have low toxicity. the thermocouple resides in a radial slot. The extra sensors are useful in confirming linearity of temperature versus distance along the column. Any sensor possessing adequate accuracy may be used for temperature measurement (2) and be used in large systems where heat flow perturbation by the temperature sensors would be negligible.5 In Fig.3 When thermocouples are employed. special care must be taken to determine the Matching of Temperature Gradients correct distance between sensors and to calculate the possible error resulting from any uncertainty. Several factors must be considered during selection of the most appropriate insulation. have a low λI.2.3. In addition. 3 should include wire tempering on the surfaces. 1(a) Schematic of a Comparative-Guarded-Longitudinal Heat Flow constant temperature reference shall always be provided for all System Showing Possible Locations of Temperature Sensors cold junctions.6 Since uncertainty in temperature sensor location leads FIG. In general.3. and the system environment as con- trolled by the insulation.3 Temperature Sensors: 6. wire loops in isothermal zones. 6.3.3. and be easy to handle.2 Some candidate insulations are listed in Table 2. 3d can be used.2 The type of temperature sensor depends on the system size. Thermocouples are normally employed. E1225 − 13 along the column. a constant temperature zone box. 3a). 6. Butt or bead welded thermocouples junc- tions can be rigidly attached by peening. low density fiber blankets can also be used. 3b. In the latter three cases. FIG. or an electronic ice point reference. 3c the thermocouple is pulled through a radial hole in the material. and in Fig.4 Thermocouple attachment is important to this tech- nique in order to ensure that reliable temperature measure- ments are made at specific points. the thermocouple attachment shown in Fig. All four of the procedures shown in Fig. cementing. 6. 6. the meter bars and specimen should each contain three sensors. the thermocouple should be thermally connected to the solid surface using a suitable glue or high temperature cement. and 3d). 6. 3c. or a combination of all three (5). 3b. 6. Their small size and the ease of attachment are distinct advantages. specimen. 3. or indicating an error due to a temperature sensor decalibration. When a sheathed thermocouple or a thermo- couple with both thermoelements in a two-hole electrical insulator is used. The various techniques are illustrated in Fig. the insulation should not contaminate system components such as the temperature sensors.3.1 mm diameter or less. and it should not conduct electricity.1 There shall be a minimum of two temperature sensors on each meter bar and two on the specimen.3. or welding in fine grooves or small holes (Fig. Intrinsic junctions can be obtained with metals and alloys by welding individual thermo-elements to the surfaces (Fig. meter bars. 1(b) Schematic of Typical Test Stack and Guard System Illustrating to large errors. A FIG. 589 x 10-2 (T-273. R Clark.1 This test method requires uniform heat transfer at the materials having a low thermal conductivity. D. Thermal Conductivity – Tungsten. Gaithersburg. and Tye. D. R. TungstenC 4 to 300 2 See Table 4. S Inconel is a trademark by Special Metals Corporation.. P. P. pp.15)2 Inconel 600S. a very thin layer of a compatible highly conductive fluid. 2003/2004. G. Roebben. L. Research Materials 8420 and 8421.. N Pyrex is a trademark by Corning Incorporated. Measurements in 6.15)2 A SRM 8420 is available from National Institute of Standards and Technology (NIST). Geel. pp.. M. P. and Salmon. G Salmon. A. and Giarratano. 3.15)2 Nimonic 75T. R.332 + 515. “Report of Investigation. C Hurst.. of minimizing interfacial resistances at meter bar-specimen 4 .. the temperature meter bar to specimen interfaces whenever the temperature sensors must be mounted close to the surface and in conse- sensors are within a distance equal to rA from an interface (6)..G. NY.648 x 10-2 (T-273.K. 382–390. Vol 45. 2005. 1976. quence the uniformity of contact resistance is critical. D. This is paste. In such This requirement necessitates a uniform contact resistance cases. Huntington WV.R 300 to 1020 4 λ = 12. R89–R98... Gaithersburg.R 300 to 1020 4 λ = 12. and Giaarratano. CopperE 85 to 1250 <2 λ M = 416. “Thermal Conductivity Certified Reference Materials: Pyrex 7740 and Polymethylmethacrylate. Indiana. P. 1984. and McElroy.O.. Geel. F Pyroceram is a trademark by Corning Incorporated.982 140 to 470 x 10-6 (T-273.R 300 to 770 4 λ = 20.15)3 K 310 Stainless SteelK.252 x 10-6 (T-273.U B Hurst.H. and Brandt.479 + 1.94 × 10 −4 Up to 900 K T + 9. M Recommended values from Table 3017 A-R-2 of the Thermophysical Properties Research Center Data Book. Lancaster PA. D. D Hurst.15) – 3. and Mixtures. DEStech Publications. T Nimonic is a trademark by Special Metals Corporation. MD. pp. DEStech Publications. J..0872 ×107/T3 PyroceramF. National Institutes of Standards and Technology (nee National Bureau of Standards). L Above 700 K a large fraction of heat conduction in fused silica will be by radiation and the actual effective values may depend on the emittances of bounding surfaces and meter bar size. R. Huntington WV. Porter.I. L. “Nonmetallic Elements..” Thermal Conductivity 26 / Thermal Expansion 14. Graves. J. H.64042 × 10-4 T – 218. D. PA.15)2 + 6. R. E Moore..P.2 For the relatively thin specimens normally used for 6. I BCR-2013 is available from the Institute for Reference Materials and Measurements (IRMM)..65367 – 6. 372–381. “Thermal Conductivity of Insulations Using Guarded Hot Plates. H.. Belgium.K 298 to 1025 K 6. Vols 35/36.K. Wang (ed. Gaithersburg.. Dinwiddie.. 2005.746 x 10-9 (T-273. National Institutes of Standards and technology (nee National Bureau of Standards).U J BCR-724 is available from the Laboratory of the Government Chemists (LGC). Standard Reference Material 730.B 2 to 1000 2 See Table 3. G.15) + 3.K. G.. pp. DEStech Publications.781 x 10-2 (T-273.484 + 4. eds. R.4. J. “Thermophysical Properties of Pyroceram™ 9606. S.” Thermal Conductivity 27/ Thermal Expansion 15. please provide this information to ASTM International Headquarters. Thermitus.2/T 4 for T > 300 K λ = 3. PA. 3849–3865. Thermal Conductivity and Electrical Resistivity as a Function of Temperature from 2 to 1000K.. 2005.” Canadian Journal of Physics.1 which you may attend.. NY.15) 430 Stainless SteelK. ed. and Lankford.). 6. R.4 Reduction of Contact Resistance: 6.” High Temperatures – High Pressures. 1975. UK. R. J. L. H Stroe. 1967. and Salmon. R. Standard Reference Material 735. A. Your comments will receive careful consideration at a meeting of the responsible technical committee.3 Means shall be provided for imposing a reproducible a vacuum environment are not recommended. E.” Purdue University.659 x 10-3 (T-273.657 x 10-2 (T-273.6 × 10 −13T4 PyrexN.U K Tye. Institute for Reference Materials and Measurements (IRMM)..R. MD.Q 90 to 600 <2 for T> 200 K λ = 1. “Development of New Thermal Conductivity Reference Materials: A Summary of Recent Contributions by National Physical Laboratory. Vol.” Measurement Science and Technology.338 + 1. 300 to 2000 2 to 5 >2000 5 to 8 Austenitic StainlessD 200 to 1200 <5 % See Table 5.” Thermal Conductivity 27 / Thermal Expansion 15.1036 + 1. with a conducting medium at the interfaces.4. Electrolytic Iron.4. 2007. “Thermophysical Properties Reference Data for Some Key Engineering Alloy. B. A. Lafayette. Teddington. or screen shall be introduced at the normally attained by use of an applied axial load in conjunction interfaces..31 − 0.937T1 + 116163 T2 Fused SilicaL.958 + 1.” National Institutes of Standards and Technology (nee National Bureau of Standards). MD.05904T + 7. R. Geel..USA. Sparks. Middlesex. Belgium. Certificate. Lancaster.J.741 x 10-6 (T-273.15) + 3.R 300 to 1020 4 λ = 11. Lancaster. unless the and constant load along the column with the primary purpose vacuum is required for protection purposes. O Tye. If you are aware of alternative suppliers. 2001. “Certification of Thermal Conductivity and Thermal Diffusivity up to 1025 K of Glass-Ceramic Reference Material BCR-720.5 λ = 2. Wang. pp.M 1300 <8 λM = (84. U This is the sole source of supply of this material known to the committee at this time. P. Compounds. D. G. E1225 − 13 TABLE 1 Reference Materials For Use as Meter Bars Percentage Temperature Thermal Conductivity Material Uncertainty Range (K) (W/m·K) (± %) Electrolytic IronA. Belgium. across the adjoining areas of meter bars and specimens. and Jacobs – Fedore. MD. “Thermal Conductivity and Electrical Resistivity of High-Purity Copper from 78 to 400 °K. J. W. J. including Recent Developments and Sources of Reference Materials.. Corning.. Thermal Conductivity – Austenitic Stainless Steel. 437–451.” EUR Report 21764. Gaithersburg. J. Vol 12.159 + 1.283 x -5 10 (T-273.15) -1. Corning. 1–14. P BCR-39 is available from the Institute for Reference Materials and Measurements (IRMM). soft metal foil.U Q Salmon. pp.7 ⁄ T) + 1. Certificate.. 4 400 67. by temperature of the guard surface is either isothermal and equal spring action. or by putting a dead weight on the column.09 0. at least three temperature the applied force must be limited to the dead weight of the sensors shall be attached to the guard at known positions to upper meter bar.62 180 190 5 30. Thermal Conductivity and Electrical Resistivity as 6. 1984. Since the force applied to the column usually affects least one heater for controlling the temperature profile along the contact resistance. J.5 (1).5. 1000 32.48 160 194 4 24.1 1600 107 45 168.8 2600 98 90 115. National Institute of Standards and Technology 250 81.154 8 306 Bubbled Alumina 0.76 200 187 6 36. 300 76. In some cases..5 1400 110 40 169. 14 503 Perlite 0. J.0 450 151 12 72. 5 .16 .9 1200 114 35 164. Thermal Conductivity. 100 211 K (W/m·K) 120 202 2 12. The to the approximate mean temperature of the specimen or above load mechanisms have the advantage of remaining preferably has an approximately linear profile with the top and constant with change in column temperature.98 A 6.9 3000 97 150 92.1 2200 101 70 134.10 0. MaterialA K (W/m·K) 300K 800K 1300K 4 154 Poured Powders 6 231 Diatomaceous Earth 0.2 600 53.2 700 132 18 105.5 (nee National Bureau of Standards). Report of Investigation.0 and 3.49 800 41. National Institute of Standards and within a guard tube or pipe normally of right circular symme- Technology (nee Bureau of Standards).7 800 127 20 115. J. 200 86. 50 330 60 275 70 245 80 229 TABLE 3 Thermal Conductivity of Electrolytic IronA 90 218 Temperature.044 0.050 0. This 6..7 900 123 25 137.1 The specimen-meter bar column shall be enclosed a Function of Temperature from 2 to 1000K.053 0.96 temperature sensors away from any heat flow perturbation at 900 37.5 500 60.07 0.. G. E1225 − 13 TABLE 2 Suitable Thermal Insulation Materials TABLE 4 Thermal Conductivity of TungstenA Typical Thermal Conductivity (W/(m·K)) Temperature. Thermal Conductivity.0 350 164 9 55.5 Guard Cylinder: Hurst.. In this case. Research Materials 8420 and 8421.7 A Hurst.19 0.6 2000 102 60 149.88 250 180 7 42.25 30 585 A All materials listed can be used up to the 1300 K limit of the comparative 40 438 longitudinal except where noted.33 0. and Lankford.0 400 157 10 61. Electrolytic Iron. hydraulically. This guard cylinder shall contain at interfaces.13 0. In each case.7 Thermal Conductivity — Tungsten.6 errors caused by poor contact.97 300 172 8 49. 1976. special care must be taken to limit measure the temperature profile.. 16 553 Blankets and Felts 18 591 Aluminosilicate 60–120 kg/m3 0. P.41 10 377 Bubbled Zirconia 0.8 500 146 14 84.039 0.17 .5.21 0. and Giarratano.. to ensure that λS does not change with force variation. G. by judicious positioning of 700 47. try. Standard Reference Material 730.2 600 138 16 95.. Certificate.37 0.. This guard cylinder can be either a metal or a ceramic but its inside radius should be such that the ratio rB/rA will be between 2.32 140 197 3 18. A.9 2400 99 80 123.12 the interfaces.2 The guard shall be constructed and operated so that the force can be applied either pneumatically.37 12 444 Vermiculite 0. bottom ends of the guard matched to corresponding positions the compressive strength of the specimen might be so low that along the column.4 2800 97 100 108.33 20 618 Zirconia 60–90 kg/m3 0. B.4 1000 120 30 153. it is desirable that this force be variable the guard.3 1800 105 50 163. .55 90 8.0 and 3.28 70 7.6.565 7 0. The specimen length should be selected based on maintain the required temperature control and measure all considerations of radius and thermal conductivity. sensor attachment to be far enough away from the interfaces to ensure that 6. J.40 25 3.47 50 5.1 1200 26.9 NOTE 1—The material selected for the meter bars should have a thermal 200 12.80 95 9.1 The combination of temperature sensor and the instru.5 %.34 40 4.1 500 17. L.92 45 5. NOTE 3—In some cases this requirement is not necessary.6. long specimens with length / rA system capability. Each flat surface of the specimen and reference must be flat with a surface finish equal to or better than 32− and the normal to each end shall be parallel with the 6.88 65 7. 1975.1 conductivity as near as possible to the thermal conductivity of the 250 13.2 450 17. 6.9 160 11.796 9 0. For example.45 60 6. 300 14.27 85 8.3 eral Possible Reference Materials for Meter Bars 400 16.65 120 9.25 110 9. 2 Approximate Values for the Thermal Conductivity of Sev- 350 15. G.99 130 10.5.2 unknown.4 180 11.32 14 1. 61 % and the specimen radius. Although control can be manual. Certificate. P. must be such that rB/rA is between 2.64 75 7.3 7. General practice is to use cylindrical or 1000 24.04 100 9.9 7.6 190 11..3 140 10. Thermal Conductivity — Austenitic Stainless Steel. K (W/m·K) 5 0.98 55 6.6 800 21.3 FIG.97 80 8. because uncertainty due to the heat shunting becomes too large.86 18 2. acquires all pertinent conductivity of stainless steal. For the cylindrical configuration.05 12 1. calculations of the result.04 K and of λM and λS so that thermal shunting errors would be small for long sections. L.13 20 2.1 Test Specimens—This test method is not restricted to a 900 23.921 10 1.58 16 1. When λM is lower than the thermal carries out all the control functions. When λM is higher than pertinent output voltages with accuracy commensurate with the the thermal conductivity of stainless steel.1 square cross-sections.6 150 10. E1225 − 13 TABLE 5 Thermal Conductivity of Austenitic Stainless SteelA Temperature. and calculates the thermal conductivity (7)..0 particular geometry.9 600 19.07 30 3. and Giarratano.1 reference samples must be the same to within 1 % (see Note 3) A and any difference in area shall be taken into account in the Hurst. National Institute of radii of the specimen and meter bars must agree to within Standards and Technology (nee National Bureau of Standards). Standard Reference Material 735. These sections might be long enough to permit temperature an absolute error less than 60. Thermal Con. ment used for measuring the sensor output shall be adequate to some apparatus might consist of meter bars and specimen with high values ensure a temperature measurement precision of 60. Sampling and Conditioning Test Specimens 700 20. the sample’s length must be reduced voltages. the ductivity as a Function of Temperature (5 to 1200 K). Sparks.2 Instrumentation for this technique shall be adequate to heat flow was uniform. rA. These long specimens permit the use of large distances between temperature sensors and this reduces the percentage error derived of this general description can be automated so that a computer from the uncertainty in sensor position.676 8 0. 6 .6 System Instrumentation: specimen axis to within 610 min. Thermal Conductivity. The conduction area of the specimen and 1100 25. a technique >>1 can be used.1 170 11.466 6 0. J.72 35 4. 3 When the specimen shape is complex or the specimen After instrumenting and installing the proper meter bars. quired or prescribed. to minimize temperature measurement errors due to heat flow into or out of the hot junction. the is unusually small. one representative specimen shall be For example.4 When changes have been made in the system inserted into the test stack such that it is at aligned between the geometry.6 When the apparatus has been previously operated to a system must be protected from oxidation during the test or if high enough temperature to change the properties of a compo. 9. same order of magnitude as that expected for the test specimen.1. conductivity to the estimated thermal conductivity of the 9. Procedure 8. If the measured thermal conductivity of the specimen 8. FIG.2 Sampling and Conditioning—Unless specifically re. 3 Thermocouple Attachments 7.2 Heaters at either end of the column should be energized unknown sample should be machined according to 6. The predetermined force required least two reference materials in the following manner: for reducing the effects of non-uniform interfacial resistance 8. or both.2 These verification tests shall be run by comparing at gas and pressure established.3 or greater 9. select the reference speci- than 3 and it is not possible to match thermal conductance mens (meter bars) such that the thermal conductance is of the values. specimen should be instrumented similarly. If the 8.5 When meter bar or insulation material other than those contact with the adjacent meter bar. E1225 − 13 3a 3b Intrinsic weld with separate temperature elements welded to specimen or meter Radial slots on the flat surfaces to hold a bare wire or ceramic insulated bars so that signal is through the material. and the operating 8.1.2. using meter bars fabricated from another refer. successfully accomplished. ence material which has the closest λ to that of the specimen. Pyroceram4 specimen using meter bars fabricated from stain- less steel.1.2 The thermal conductivity λ of the specimen fabricated from a reference material shall then be measured as described in Section 9.1. nent such as thermocouples’ sensitivity. thermocouple sensor the may be bonded into slot. and ing medium may be used to reduce interfacial resistance. 4 Pyroceram is a trademark by Corning Incorporated. verification tests might be performed on a prepared from the sample. It should then be 8.1 There are many situations that call for equipment corrections for heat exchange. Soft foil or other contact- listed in 5.1 After initial equipment construction. NOTE 1—In all cases the thermoelements should be thermally tempered or thermally grounded on the guard. These include the following: 8. meter bars with at least 99 % of each specimen surface in 8. Calibration and Verification disagrees with the value from Table 1 after applying the 8.1.1 and 5. Corning. through the hole. 3c 3d Small radial hole drilled through the specimen or meter bar and non-insulated Small Radial hole drilled part way through the specimen or meter bar and a (permitted if the material is an electrical insulator) or insulated thermocouple pulled thermocouple pushed into the hole. operation requires a particular gas or gas pressure to control λI. 7 .2 When the ratio of λM to λS is less than 0. NY.2 are considered for use.2.1 A reference material which has the closest thermal should be applied to the load column. and (see Note 4) and adjusted until the temperature differences 8. additional effort is required to verifications before operations on unknown materials can be find the error source(s).1. the system should be pumped and purged.1. 8.1 Where possible and practical. 10.1 Approximate Specimen Thermal Conductivity: 10.2.2 Using calculations from finite-difference or finite- 10. λI.2. Calculation Didion (1) and Flynn (8). At high ratios 9. departure from ideal heat flow would be small. 10. The heaters can be powered measurements where λ M/λI and λS/λI are greater than 30.2 Measurements on materials where the ratios of λM/λI shall maintain long term temperature drift less than 60. measure the output of all temperature sensors. in the meter bars shall be calculated using the ence materials or transfer standards of different thermal con- following: ductance as specimens. FIG. heaters. NOTE 4—These heaters can either be attached to the ends of the meter the product of Fλ and Fg would be less than 0.1 Use of analytical techniques as described by 10. and the specimen is at the average temperature to that in the specimen is less valid when the specimen or meter desired for the measurement. is constant with respect to time expressed as follows (1): to within 60. q'. The Fλ term is shown in Fig.2 Constant with respect to z to within 65 K and of λM/λI and λS/λI. The power to these heaters shall be value of FgFλ is to be kept below 10 %. should agree with each other to within about 610 % when heat exchange with the insulation is small. E1225 − 13 between positions Z1 and Z2.05 K/h.3 Determined experimentally by using several refer- area. If the with alternating or direct current. and the 2 and 3 for the ratio of guard radius to column radius specified specimen midplane.2. In this case.1 for the average meter bar temperature. The apparatus should be designed to minimize to the guard heaters should be adjusted until the temperature these errors. corrections would not be necessary since the matched to the average temperature of the test specimen. and λS (1). good agree- ment is not a sufficient condition (nor always a necessary condition) for low heat shunting error.05 rections can be determined in the following three different K/h).2.1. and converted to temperature.2.03 K on the meter bar temperature sensor nearest the heater.1 The outputs from the temperature sensors shall be element heat conduction codes. the ratios λM/λI and steady enough to maintain short term temperature fluctuations less than 60.2 Corrections for Extraneous Heat Flow: λm/λi for Several Values of λs/λi 8 . the bottom sensor on the bottom bar. the power the insulation. and Z5 and Z6 are 10.2. as uncorrected for heat exchange with the insulation. The Fg term has a value between meter bar. have low thermal conductivities relative to that of profile along the guard is not important for rB/rA ≥ 3.1 K and either: γ 5 F gF λ (5) 9. ways: 10. top bar T6 2 T5 q' B 5 λ M · (3) Z6 2 Z5 bottom bar In each of these equations. in conjunction with the guard shell heater and the system coolant 10. q'T and q'B.3 After the system has reached steady state (T drift <0. and λS/λI do not fall within these boundaries shall be accom- panied with corrections for extraneous heat flow. and Fλ is a places including the temperature at the top sensor on the top function of λM. Although the exact temperature bars.2. Tg(z). 4 Fractional Heat Exchange Between the Meter Bar- Specimen Column and Surrounding Insulation as a Function of 10. Although these two values. The deviation from uniform heat flow has been profile along the guard.2.10 (10 %) for all bars or to a structure adjacent to the meter bar. Z3 and Z4. The procedure must be used cautiously since all such specimens should have the same size as the T2 2 T1 q' T 5 λ M · (2) specimen with an unknown thermal conductivity and have the Z2 2 Z1 same surface finish.1. 4 as a function of λ/λI for various values of λM/λI for a linear guard. the λM value (see Note 5) to be inserted shall be obtained from the information of 6. can then be calculated using the following: ~ q' T 1q' B ! ~ Z 4 2 Z 3 ! λ' S 5 (4) 2 ~ T 4 2 T 3! NOTE 5—This type of calculation procedure actually requires only two temperature sensors on each column section. or both. the third sensor on each section serves as a test for consistency of the other two. These cor- 9. These two λs/λI must be within the boundaries on Fig.2 A value for the specimen thermal conductivity at temperature (T3 + T4)/2. Some λs/λi calculation procedures require more than the two sensors to obtain more knowledge about the temperature gradient dT/dZ.1 Calculation of the specimen thermal conductivity by between 200 times the imprecision of the ∆T measurements a simple comparison of temperature gradients in the meter bars and 30 K.1 Approximately linear so that Tg(z) coincides with the temperature along the sample column at a minimum of three where Fg is a function of system dimensions. For example. 4. or for this system. and the apparent heat flow per unit 10.2.2. ” CRC Critical Reviews in Analytical Chemistry. 1969. ed. Reinhold Publishing Corporation. Although no definite bias could be 12. Thermometry.2 Indeterminate Errors: 11. 1232. Part 2. than those listed in Table 1.2 mm.3 Statements of temperature sensor type. diameter of each sensor is 0. 11. G. A. gas. Contacts”. 11. then all accuracy is to be obtained.. If results are appropriate corrections applied to the data if the desired to be reported as having been obtained by this method. 1968.1.δ ~ Z 6 2 Z 5 ! 5 0. and each temperature measurement position. For example.04 K.1. “All requirements of determined approximately using results from appropriate ex- this method have been met with the exception of . the uncertainty in the 11. if any.. specimen stack temperature out of balance.1 Assumptions for a system where both meter bars and order of 2 % lower than those obtained by absolute methods. and ing: 11.2 The contributions from the last two errors can be such conditions are not met. 171–221. 16.1. New York. D.003 ? (6) 5 Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report RR:E37-1010.5 Column force. “Problems in High Temperature Service. G. “Thermal Conductivity of the Rocks in an Ice Bar.1. mated by assuming an uncertainty of 60. New York.3. No. robin study also involving absolute methods (9. 12.1 There are at least three other errors that can contrib- a statement of the percentage variation of the qualification ute to total system error and these are (1) non-uniform results about the true value. 1983. R.. 3..069| or 66. meter bar height.8 % can be attained over the temperature 12.. Springfield. R. T. requirements prescribed by this method shall be met.2.1. p. Report T 2 2 T 1 . pp.. Academic 3–31. and distances between temperature sensors. the system including r A. Tye. rB.δ ~ T 4 2 T 3 ! .Z 6 2 Z 5 5 13 mm.1. and size. P. 79–90.10 The specific dated version of this standard used. pp. Apparatus for Thermal Conductivity Measurements. pp.2 mm. size.3 Overall—An international. (2) heat exchange between the column ity results on Pyroceram using stainless steel meter bars were and the guard.2 The maximum value of δ(Z2 − Z1) etc.” AD-665789. specimen height.5 all 13 mm and λM ≈ λ S: U U δλ M λM ? 5 0.1. 1965. 11. “Temperatures of Thermocouple Reference Junctions (7) Morgan.δ ~ T 6 2 T 5 ! 5 0.T 6 2 T 5 5 10 K.. Vol 2. available from the National Technical Information (5) Anderson.1. January. Its Measurement and Control in Science and Industry. 10) has shown that a precision of 66. if the attachment procedure.5 (sensor diameter) at 11.1.1. (6) Fried.6 Meter bar material and source of λM values if other will be |0.. and (3) heat shunting through the insulation within 64 % of the accepted values for Pyroceram over the temperature range from 250 to 900 K. Thermal Conductivity.. “An Analysis and Design of a Linear Guarded Cut-Bar (4) American Society of Mechanical Engineers (ASME): PTC 19. “Thermal Conduction Contribution to Heat Transfer at Vol. inter-laboratory round mal conductivity. “thermal conductiv- interfacial resistance.8 Variations. T. Contact ASTM Customer Z 2 2 Z 1 . Section 1. M. A.. and 11. The number for δ(T2 − T1) etc..” 1976. 95–101. C.4 Complete listing of the geometrical dimensions of difference would be 60.1.2 Complete identification of insulation and source of λI 12.3 With these values the fractional uncertainty in λ'S 11. 1962. I. VA. and Kollie.. Precision and Bias range 300 to 600 K. the specimen are of equal length is that the sensor spacings are This cited paper is on file at ASTM as a research report. E. pp.org. Vol 69C. Plenum Press.9 %. ed.Z 4 2 Z 3 . was approxi- values.δ ~ Z 4 2 Z 3 ! . Press. 253–274.7 Reference to the use of this test method shall include 12. E1225 − 13 11.2 mm. from this test method. pp. L. Service at [email protected] Complete specimen identification including shape δ~T2 2 T 1 ! . Vol 6.1. Larsen. 9 . 1974.1 Example of Error Estimation: established these are indications that the values were on the 12. and gas pressure. 2.” shall be periments carried out at different levels of guard temperature to added and a complete list of the exceptions included. Therefore. “General Principles of Thermoelastic Thermometry.” Thermal Conductivity Standards. was calculated based on the sensor absolute accuracy. Temperature Measurement. 11. D. (3) Caldwell.1. the phrase. Temperature. (2) Finch. D. 12.” around the column. Part 3.1 The report of the test results shall include the follow- δ~Z2 2 Z 1 ! . Where 12...” Journal of Research of the National Bureau of in the Bureau of Mines Standard Rock Site. F.9 Measured values of temperature and specimen ther- 12.T 4 2 T 3 . R.2. These three errors must be minimized or 11. and West. REFERENCES (1) Didion. Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center. 1985. l. (9) Hulstrom. “Round-Robin Testing of Thermal Conductivity Reference Materials.” Thermal Conductivity 19. D. Vol 17. United States. 100 Barr Harbor Drive. National Conductivity Reference Materials to 573 K. New York. R. High Temperatures-High Pressures. Your comments are invited either for revision of this standard or for additional standards and should be addressed to ASTM International Headquarters. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the above address or at 610-832-9585 (phone). E. R. or through the ASTM website (www. either reapproved or withdrawn.. W. ed. Plenum Press. pp.org). S.” Bureau of Standards. This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years and if not revised. “Interlaboratory Comparison Testing of Thermal Thermal Properties of Ceramics. Danvers. 610-832-9555 (fax).astm. West Conshohocken. ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentioned in this standard. http://www. MA 01923.. 222 Rosewood Drive. E1225 − 13 (8) Flynn.. which you may attend. Special Publication 303. If you feel that your comments have not received a fair hearing you should make your views known to the ASTM Committee on Standards. L.. C. “Thermal Conductivity of Ceramics. This standard is copyrighted by ASTM International. and Smith. A Progress Report. PO Box C700. Tel: (978) 646-2600. C. Users of this standard are expressly advised that determination of the validity of any such patent rights...com/ 10 . Yarbrough. P. Tye. are entirely their own responsibility.org (e-mail).” Mechanical and (10) Hulstrom.. PA 19428-2959. 1969. 199–211. Your comments will receive careful consideration at a meeting of the responsible technical committee. or service@astm. and the risk of infringement of such rights. 707–708. at the address shown below. 1985. pp.copyright. 63–123. D. pp.