# ASTM F433-02 (Reapproved 2014)e1

Designation: F433 − 02 (Reapproved 2014)´1Standard Practice forEvaluating Thermal Conductivity of Gasket Materials1This standard is issued under the fixed designation F433; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon (´) indicates an editorial change since the last revision or reapproval.ε1NOTE—Editorially corrected Footnote 6 in July 2014.1. Scope1.1 This practice covers a means of measuring the amountof heat transfer quantitatively through a material or system.1.2 This practice is similar to the Heat Flow Meter Systemof Test Method C518, but modified to accommodate small testsamples of higher thermal conductance.1.3 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusD2214 Test Method for Estimating the Thermal Conductiv-ity of Leather with the Cenco-FitchApparatus (Withdrawn2008)3F104 Classification System for Nonmetallic Gasket Materi-als3. Terminology3.1 Definitions:3.1.1 thermal conductivity, k, of a solid material—the timerate of steady heat flow, watts (or Btu/h), through a unit area,m2(or ft2), per unit temperature gradient in the directionperpendicular to an isothermal surface °C/m (or °F/in.). Thek-factor is expressed W/m·K (Btu·in./h·ft2·°F).3.2 Symbols:k = thermal conductivity, W/m·K (Btu·in./h·ft2·°F)C = thermal conductance, W/m2·K (Btu/h·ft2·°F)∆x = sample thickness, mm (in.)A = sample cross-sectional area, m2(ft2)q = heat flow, W (Btu/h)φ = heat flow transducer output, mVN = heat flow transducer calibration constant,W/m2·mV (Btu/h·ft2·mV)Nφ = heat flux, W/m2(Btu/h·ft2)∆T = temperature difference, °C (°F) or mVT1= temperature of lower sample surface,°C (°F) ormVT2= temperature of upper sample surface, °C (°F)or mVTh= temperature of HFT surface facing sample,° C(°F) or mVTc= temperature of upper heater surface facingsample, °C (°F) or mVT = temperature, °C (°F)δ = total temperature drop across interfaces be-tween sample and adjacent surfaces, °C (°F) ormVρ = coefficient of thermal resistance at interfaces,m2·K/W (h·ft2·°F/Btu)α = correction constantsubscripts = unknown samplesubscriptr = known calibration sample4. Summary of Practice4.1 The sample and the heat flow transducer (HFT) aresandwiched between two controlled heater plates. The lowerheater is set at a higher temperature than the upper plate toproduce a flow of heat through the sample. The differential ofthese two temperatures, ∆ T, sensed by thermocouples, isamplified along with the electrical output, φ, of the HFT and isdirectly proportional to the heat flow through the sample,expressed as W/m2(Btu/h·ft2). See Appendix for further1This practice is under the jurisdiction ofASTM Committee F03 on Gaskets andis the direct responsibility of Subcommittee F03.10 on Composite Gaskets.Current edition approved July 1, 2014. Published November 2014. Originallyapproved in 1964. Last previous edition approved in 2009 as F433 – 02 (2009).DOI: 10.1520/F0433-02R14E01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1information. This recommended practice can be used formeasuring heat transfer at a hot side temperature up to 200°C(392°F). See Figs. 1-5.5. Significance and Use5.1 This practice is designed to compare related materialsunder controlled conditions and their ability to maintain aminimum amount of thermal conductance. Test results shouldbe correlated with field results in order to predict heat transferproperties in particular applications.5.2 This practice may be used as a routine test when agreedupon by the user and the producer.6. Apparatus6.1 Heat Flow Transducer (HFT), with controlled heaterplates, thermocouples, and an analog computer module.47. Test Specimen7.1 The sample size shall be a 50.8-mm (2-in.) diameterdisk 60.25 mm (60.010 in.) from 2.29 to 12.7 mm (0.090 to0.500 in.) thick.8. Conditioning8.1 Condition the cut specimens in accordance with theirclassification, as required in Classification F104.9. Procedure9.1 Test temperatures are suggested from 100 to 175°C (212to 347°F) or whatever is agreed upon between the producer anduser. (The guard heater is usually set at or near the averagesample temperature between the lower and upper heaterplates.)9.1.1 Release the compressive load, pull out the tray, andload the sample. Care must be maintained to ensure that thetray compartment is free of any foreign matter. Clean asrequired.9.1.2 Push the tray back into the chamber with a ball andplunger locking the tray into position.9.1.3 Close the test section door and switch the air control to“stack clamped.” The sample holder is now raised automati-cally until the sample is clamped in place between the upperand lower heaters. The compressive load can be adjusted bycontrolling the air pressure at the rear of the unit.Apressure of0.345 MPa (50 psi) is the recommended maximum and shouldbe specified by both the producer and user to ensure repeatableresults.9.1.4 Allow from 1 to 2 h for the reading to stabilize. Readthe sample thermal conductance and temperature directly fromdigital meters on the front panel. The instrument has stabilizedwhen the temperature indicated changes by no more than65 %⁄h and the conductance indicated changes no more than62 %⁄h.10. Report10.1 The report shall include the following:10.1.1 Sample conditioning procedure,4The sole source of supply of the apparatus known to the committee at this timeis Holometrix, Inc., 25 Wiggins Avenue, Bedford, MA 01730–2323. If you areaware of alternative suppliers, please provide this information to ASTM Headquar-ters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend.FIG. 1 Heat Flow Meter Assembly With Water-Cooled Heat SinkFIG. 2 HFT Electrical Output and Heat Flow Section With Tem-perature SensorsF433 − 02 (2014)´1210.1.2 Ambient temperature,10.1.3 Sample hot side temperature, Th,10.1.4 Sample cold side temperature, Tc,10.1.5 Sample temperature drop, Th−Tc,10.1.6 Average sample temperature, (Th+ Tc)/2,10.1.7 Sample thickness, ∆x,10.1.8 Thermal conductivity, k, and10.1.9 Compressive load.11. Precision and Bias11.1 The precision of the practice is expected to be within65%.12. Keywords12.1 comparative thermal conductance; heat flow; thermalconductanceFIG. 3 Location of Thermocouples to Produce a Temperature Gradient Through the Test SampleFIG. 4 The Hot and Cold Sample Surface Temperature Differential Amplified with the HFT Output, Divided Electronically, and DisplayedDigitallyFIG. 5 Clarification of Fig. 4 Showing the Calibration to Obtain the Correction Constant Correct Value Before Testing an UnknownSampleF433 − 02 (2014)´13APPENDIXES(Nonmandatory Information)X1. GENERAL INFORMATIONX1.1 If a test specimen in the form of a disk is held betweentwo flat surfaces, each controlled at a different temperature, aflow of heat passes through the sample from the hot to the coldsurface. The thermal conductivity is determined by the follow-ing equation:k 5qA∆x∆T@W/m·K# or @Btu·in./h·ft2·°F# (X1.1)where:q = heat flow through the sample, watt (Btu/h),A = cross-sectional area of the sample, m2(ft2),∆x = sample thickness, mm (in.), and∆T = temperature difference across the sample, °C (°F).X1.2 The heat flow per unit area is measured with a heatflow transducer, a sensitive device producing an electricaloutput that is directly proportional to the heat flux, q/A.If theoutput of the heat flow transducer (HFT) is called φ than thek-factor can be calculated from:k 5 Nφ∆x∆T(X1.2)X1.3 In this equation φ, ∆T, and ∆x can be measured bysimple means, while the calibration constant, N, can bedetermined by testing a sample of known thermal conductivity.X2. CALCULATIONSX2.1 After thermal equilibrium has been established, thevarious sensors may be read and recorded. Data reduction isdependent upon the positions of the thermocouples for mea-suring the sample ∆T, as follows:X2.1.1 If thermocouples are installed in the sample surfacethen:∆T 5 T12 T2~mV! (X2.1)NOTE X2.1—The sample thickness must be adjusted to account for thethermocouples being slightly below the surface, see Fig. 2.X2.1.2 A calibration run must first be made using a calibra-tion standard of known thermal conductivity, kr.5This proce-dure is identical to the procedure for the unknown sample asfollows:X2.1.2.1 k-factor, unknown sample:ks5 Nφs∆xs∆Ts(X2.2)X2.1.2.2 k-factor, known sample:kr5 Nφr∆xr∆Tr(X2.3)X2.1.2.3 Combining the unknown and known samples:ks5 krφsφr∆xs∆xr∆Tr∆Ts(X2.4)X2.1.3 If thermocouples are located permanently in thesurface adjacent to the sample, then, in accordance with Fig. 3,the ∆T obtained by subtracting Thand Tcis not equal to the ∆Tacross the sample itself due to contact resistance. (Acorrectionfactor can be obtained from the calibration test data.)X2.1.4 The calibration sample must have a set of thermo-couples installed in grooves in the upper and lower surfaces.During calibration the following results are obtained:kr5 Nφr∆xr∆Tr(X2.5)where:∆Tr5 T12 T2(X2.6)X2.1.5 From the various thermocouple readings we cancalculate the total interfacial temperature drop as follows:δ 5 ~Th2 Tc!r2 ∆Tr(X2.7)The interfacial temperature drop, δ, is proportional to theheat flux, Nφras follows:δ 5 ρNφr(X2.8)where ρ is a proportionality constant and depends mostly onthe surface conditions and on the applied pressure on the teststack. It is assumed that ρ remains essentiality constant fromtest to test so long as the applied pressure remains the same.The contact coefficient ρ is thus obtained from Eq X2.6.ρ 5δNφr(X2.9)X2.1.6 When the unknown sample is tested, the followingdata must be recorded: φs, Th,Tc, and ∆xs. The correctedtemperature drop across the sample is as follows:∆Ts5 ~Th2 Tc!s2 ρNφs(X2.10)Substituting Eq X2.9 as follows:∆Ts5 ~Th2 Tc!s2 δφsφr(X2.11)The thermal conductivity of the unknown sample is asfollows:5Borosilicate No. 7740 has been found to be a suitable reference standardmaterial. This can be purchased with the test equipment. The reference standardused should be documented in the test report.F433 − 02 (2014)´14ks5 Nφs∆xs∆Ts(X2.12)Combining Eq X2.3 and Eq X2.10 we have the following:ks5 krφsφr∆xs∆xr∆Tr∆Ts(X2.13)where:∆Tr5 T12 T2, (X2.14)and∆Ts5 ~Th2 Tc!s2 δφsφr(X2.15)in which:δ 5 ~Th2 Tc!r2 ∆Tr(X2.16)X2.1.7 Substitution of Eq X2.4, Eq X2.9, and Eq X2.5 wehave the following:ks5 kr∆xs∆xr11 2STh2 TcT12 T2Dr1φrφs~Th2 Tc!s~T12 T2!r(X2.17)NOTE X2.2—If there is no contact resistance, δ, Eq X2.4 goes to zeroand the Eq X2.12 assumes the same form as Eq X2.2. Also, note that thecalibration data, subscript r, needs to be obtained only once at eachtemperature level. Thermocouple readings may be kept in mV and neednot be converted to °C (°F) except for determining the average sampletemperature.)X2.1.8 If an analog calculator is used to obtain the unknownsample k-factor and thermocouples are installed in the samplesurface: The ∆T signal is then obtained by connecting thethermocouples differentially; the HFT and ∆T signals areamplified and divided electronically with the results shown ona digital volt meter (Fig. 4). The gain of the final stageamplifier can be varied to produce an output voltage equal tothe thermal conductance of the sample in any desired set ofunits. In other words, if the thermal conductance, (C=k⁄∆x),of the sample is 15 Btu/h·ft2·°F, the output voltage of theanalog calculator is 15 V. Thek-factor is obtained by multiply-ing the displayed value by the sample thickness, ∆x, measuredseparately.X2.1.9 However, the instrument first must be calibrated bytesting a reference sample of known thermal conductivity.After thermal equilibrium has been established in the test stack,the C-factor is determined by taking k/∆xand the final gain isadjusted until the displayed value equals C.X2.1.10 If thermocouples are located permanently in thesurface adjacent to the sample, a correction must be made inthe determination of the sample ∆Tto account for interfacialresistance. The differential of the two permanentthermocouples, (Th−Tc), must be reduced by a correctionfactor which is proportional to the heat flow transducer output,φ (see Eq X2.8). The temperature drop across the sample is asfollows:∆T 5 ~Th2 Tc! 2 αφ (X2.18)The analog calculator can be used to compute the C-factor ofthe sample (see Fig. 5):C 5φ~Th2 Tc! 2 αφ(X2.19)and the gain of the final stage amplifier can be varied to yieldthe correct value on the digital display.X2.1.11 A calibration run must be made first to obtain thecorrect value for α and to adjust the final gain for the properC-factor. The reference sample must have thermocouplesinstalled in grooves in the surface. After these thermocoupleshave been connected to the ∆T input of the calculator and thecorrection constant α has been adjusted to zero (see Fig. 5).Thefinal gain must be adjusted to obtain the correct C-factor of thereference sample. Next, the permanent thermocouples areconnected to the ∆T channel of the calculator and the correc-tion constant α adjusted until the displayed C-value is the sameas before. Subsequent tests on unknown samples withoutthermocouples yield the correct C-factor directly on the digitaldisplay. Multiplying these C-factors by the correspondingsample thickness gives the k for each case.X3. PROPOSAL FOR INFORMATION PURPOSES ONLYX3.1 A method and apparatus has been established for useas a screening tool which can relate to the relative orders ofthermal conductivity. It is not intended for use in writingspecifications, as it cannot provide reliable results for thethermal conductivity of a material.X3.2 The device referred to is described as a heat-insulatedcopper vessel with a heavy copper plate base, and a receivercontaining a mating copper plug which is also insulated. Whilethe upper plate or vessel and test sample is at a constanttemperature, heat flow through the sample is produced bymeasuring the slowly changing temperature increase of thereceiver with thermocouples. The rate of flow of heat throughthe specimen is proportional to the area and the ∆T of the facesof the specime