Designation: C1045 − 19Standard Practice forCalculating Thermal Transmission Properties Under Steady-State Conditions1This standard is issued under the fixed designation C1045; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides the user with a uniform procedurefor calculating the thermal transmission properties of a materialor system from data generated by steady state, one dimensionaltest methods used to determine heat flux and surface tempera-tures. This practice is intended to eliminate the need for similarcalculation sections in Test Methods C177, C335, C518,C1033, C1114 and C1363 and Practices C1043 and C1044 bypermitting use of these standard calculation forms by refer-ence.1.2 The thermal transmission properties described include:thermal conductance, thermal resistance, apparent thermalconductivity, apparent thermal resistivity, surface conductance,surface resistance, and overall thermal resistance or transmit-tance.1.3 This practice provides the method for developing theapparent thermal conductivity as a function of temperaturerelationship for a specimen from data generated by standardtest methods at small or large temperature differences. Thisrelationship can be used to characterize material for compari-son to material specifications and for use in calculationprograms such as Practice C680.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 This practice includes a discussion of the definitions andunderlying assumptions for the calculation of thermal trans-mission properties. Tests to detect deviations from theseassumptions are described. This practice also considers thecomplicating effects of uncertainties due to the measurementprocesses and material variability. See Section 7.1.6 This practice is not intended to cover all possible aspectsof thermal properties data base development. For newmaterials, the user should investigate the variations in thermalproperties seen in similar materials. The information containedin Section 7, theAppendix and the technical papers listed in theReferences section of this practice may be helpful in determin-ing whether the material under study has thermal propertiesthat can be described by equations using this practice. Someexamples where this method has limited application include:(1) the onset of convection in insulation as described inReference (1);(2) while a phase change is taking place in oneof the insulation components causing an unsteady-state condi-tion; and (3) the influence of heat flow direction and tempera-ture difference changes for reflective insulations.1.7 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2C168 Terminology Relating to Thermal InsulationC177 Test Method for Steady-State Heat Flux Measure-ments and Thermal Transmission Properties by Means ofthe Guarded-Hot-Plate ApparatusC335 Test Method for Steady-State Heat Transfer Propertiesof Pipe InsulationC518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusC680 Practice for Estimate of the Heat Gain or Loss and theSurface Temperatures of Insulated Flat, Cylindrical, andSpherical Systems by Use of Computer ProgramsC1033 Test Method for Steady-State Heat Transfer Proper-ties of Pipe Insulation Installed Vertically (Withdrawn2003)3C1043 Practice for Guarded-Hot-Plate Design Using Circu-lar Line-Heat Sources1This practice is under the jurisdiction of ASTM Committee C16 on ThermalInsulation and is the direct responsibility of Subcommittee C16.30 on ThermalMeasurement.Current edition approved April 1, 2019. Published May 2019. Originallyapproved in 1985. Last previous edition approved in 2013 as C1045 – 07 (2013).DOI: 10.1520/C1045-19.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] 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 StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1C1044 Practice for Using a Guarded-Hot-Plate Apparatus orThin-Heater Apparatus in the Single-Sided ModeC1058 Practice for Selecting Temperatures for Evaluatingand Reporting Thermal Properties of Thermal InsulationC1114 Test Method for Steady-State Thermal TransmissionProperties by Means of the Thin-Heater ApparatusC1199 Test Method for Measuring the Steady-State ThermalTransmittance of Fenestration Systems Using Hot BoxMethodsC1363 Test Method for Thermal Performance of BuildingMaterials and Envelope Assemblies by Means of a HotBox ApparatusE122 Practice for Calculating Sample Size to Estimate, WithSpecified Precision, the Average for a Characteristic of aLot or Process3. Terminology3.1 Definitions— The definitions and terminology of thispractice are intended to be consistent with Terminology C168.However, because exact definitions are critical to the use of thispractice, the following equations are defined here for use in thecalculations section of this practice.3.2 Symbols—The symbols, terms and units used in thispractice are the following:A = specimen area normal to heat flux direction, m2,C = thermal conductance, W/(m2· K),hc= surface heat transfer coefficient, cold side,W/(m2· K),hh= surface heat transfer coefficient, hot side,W/(m2· K),L = thickness of a slab in heat transfer direction, m,Lp= metering area length in the axial direction, m,q = one-dimensional heat flux (time rate of heat flowthrough metering area divided by the apparatusmetering area A), W/m2,Q = time rate of one-dimensional heat flow through themetering area of the test apparatus, W,r = thermal resistivity, K · m⁄K,ra= apparent thermal resistivity, K · m⁄K,rin= inside radius of a hollow cylinder, m,rout= outside radius of a hollow cylinder, m,R = thermal resistance, m2· K⁄W,Rc= surface thermal resistance, cold side, m2· K⁄W,Rh= surface thermal resistance, hot side, m2· K⁄W,Ru= overall thermal resistance, m2· K⁄W,T = temperature, K,T1= area-weighted air temperature 75 mm or more fromthe hot side surface, K,T2= area-weighted air temperature 75 mm or more fromthe cold side surface, K,Tc= area-weighted temperature of the specimen coldsurface, K,Th= area-weighted temperature of specimen hot surface,K,Tin= temperature at the inner radius, K,Tm= specimen mean temperature, average of two oppo-site surface temperatures, (Th+ Tc)/2, K,Tout= temperature at the outer radius, K,∆T = temperature difference, K,∆Ta-a= temperature difference, air to air, (T1− T2), K,∆Ts-s= temperature difference, surface to surface,(Th− Tc), K,U = thermal transmittance, W/(m2· K), andx = linear dimension in the heat flow direction, m,λ = thermal conductivity, W/(m · K),λa= apparent thermal conductivity, W/(m · K),λ(T) = functional relationship between thermal conductiv-ity and temperature, W/(m · K),λexp= experimental thermal conductivity, W/(m · K),λm= mean thermal conductivity, averaged with respect totemperature from Tcto Th, W/(m · K), (see sections6.4.1 and Appendix X3).NOTE 1—Subscripts h and c are used to differentiate between hot sideand cold side surfaces.3.3 Thermal Transmission Property Equations:3.3.1 Thermal Resistance, R, is defined in TerminologyC168. It is not necessarily a unique function of temperature ormaterial, but is rather a property determined by the specificthickness of the specimen and by the specific set of hot-sideand cold-side temperatures used to measure the thermal resis-tance.R 5A ~Th2 Tc!Q(1)3.3.2 Thermal Conductance, C:C 5QA~Th2 Tc!51R(2)NOTE 2—Thermal resistance, R, and the corresponding thermalconductance, C, are reciprocals; that is, their product is unity. These termsapply to specific bodies or constructions as used, either homogeneous orheterogeneous, between two specified isothermal surfaces.3.3.3 Eq 1, Eq 2, Eq 3, Eq 5and Eq 7-13 are for rectangularcoordinate systems only. Similar equations for resistance, etc.can be developed for a cylindrical coordinate system providingthe difference in areas is considered. (See Eq 4 and Eq 6.) Inpractice, for cylindrical systems such as piping runs, thethermal resistance shall be based upon the pipe external surfacearea since that area does not change with different insulationthickness3.3.4 Apparent–Thermal conductivity, λa, is defined in Ter-minology C168.Rectangular coordinates:λa5QLA ~Th2 Tc!(3)Cylindrical coordinates:λa5Qln~rout/rin!2 π Lp ~Tin2 Tout!(4)3.3.5 Apparent Thermal Resistivity, ra, is defined in Termi-nology C168.Rectangular Coordinates:ra5A ~Th2 Tc!QL51λa(5)Cylindrical Coordinates:ra52 π Lp ~Tin2 Tout!Qln~rout/rin!51λa(6)C1045 − 192NOTE 3—The apparent thermal resistivity, ra, and the correspondingthermal conductivity, λa, are reciprocals, that is, their product is unity.These terms apply to specific materials tested between two specifiedisothermal surfaces. For this practice, materials are considered homoge-neous when the value of the thermal conductivity or thermal resistivity isnot significantly affected by variations in the thickness or area of thesample within the normally used range of those variables.3.4 Transmission Property Equations for ConvectiveBoundary Conditions:3.4.1 Surface Thermal Resistance, Ri, the quantity deter-mined by the temperature difference at steady-state between anisothermal surface and its surrounding air that induces a unitheat flow rate per unit area to or from the surface. Typically,this parameter includes the combined effects of conduction,convection, and radiation. Surface resistances are calculated asfollows:Rh5A ~T12 Th!Q(7)Rc5A ~Tc2 T2!Q(8)3.4.2 Surface Heat Transfer Coeffıcient, hi, is often calledthe film coefficient. These coefficients are calculated as fol-lows:hh5QA ~T12 Th!51Rh(9)hc5QA ~Tc2 T2!51Rc(10)NOTE 4—The surface heat transfer coefficient, hi, and the correspondingsurface thermal resistance, Ri, are reciprocals, that is, their product isunity.These properties are measured at a specific set of ambient conditionsand are therefore only correct for the specified conditions of the test.3.4.3 Overall Thermal Resistance, Ru—The quantity deter-mined by the temperature difference, at steady-state, betweenthe air temperatures on the two sides of a body or assembly thatinduces a unit time rate of heat flow per unit area through thebody. It is the sum of the resistance of the body or assemblyand of the two surface resistances and may be calculated asfollows:Ru5A ~T12 T2!Q(11)5 Rc1R1Rh3.4.4 Thermal Transmittance, U (sometimes called overallcoefficient of thermal transfer), is calculated as follows:U 5QA ~T12 T2!51Ru(12)The transmittance can be calculated from the thermal con-ductance and the surface coefficients as follows:1/U 5 ~1/hh!1~1/C!1~1/hc! (13)NOTE 5—Thermal transmittance, U, and the corresponding overallthermal resistance, Ru, are reciprocals; that is, their product is unity. Theseproperties are measured at a specific set of ambient conditions and aretherefore only correct for the specified conditions of the test.4. Significance and Use4.1 ASTM thermal test method descriptions are complexbecause of added apparatus details necessary to ensure accurateresults.As a result, many users find it difficult to locate the datareduction details necessary to reduce the data obtained fromthese tests. This practice is designed to be referenced in thethermal test methods, thus allowing those test methods toconcentrate on experimental details rather than data reduction.4.2 This practice is intended to provide the user with auniform procedure for calculating the thermal transmissionproperties of a material or system from standard test methodsused to determine heat flux and surface temperatures. Thispractice is intended to eliminate the need for similar calculationsections in the ASTM Test Methods (C177, C335, C518,C1033, C1114, C1199, and C1363) by permitting use of thesestandard calculation forms by reference.4.3 This practice provides the method for developing thethermal conductivity as a function of temperature for aspecimen from data taken at small or large temperaturedifferences. This relationship can be used to characterizematerial for comparison to material specifications and for usein calculations programs such as Practice C680.4.4 Two general solutions to the problem of establishingthermal transmission properties for application to end-useconditions are outlined in Practice C1058. (Practice C1058should be reviewed prior to use of this practice.) One is tomeasure each product at each end-use condition. This solutionis rather straightforward, but burdensome, and needs no otherelaboration. The second is to measure each product over theentire temperature range of application conditions and to usethese data to establish the thermal transmission propertydependencies at the various end-use conditions. One advantageof the second approach is that once these dependencies havebeen established, they serve as the basis for estimating theperformance for a given product at other conditions.Warning— The use of a thermal conductivity curve developedin Section 6 must be limited to a temperature range that doesnot extend beyond the range of highest and lowest test surfacetemperatures in the test data set used to generate the curve.5. Determination of Thermal Transmission Properties fora Specific Set of Temperature Conditions5.1 Choose the thermal test parameter (λ or r, R or C, U orRu) to be calculated from the test results. List any additionalinformation required by that calculation i.e. heat flux,temperatures, dimensions. Recall that the selected test param-eter might limit the selection of the thermal test method used in5.2.5.2 Select the appropriate test method that provides thethermal test data required to determine the thermal transmis-sion property of interest for the sample material being studied.(See referenced papers and Appendix X1 for help with thisdetermination.5.3 Using that test method, determine the required steady-state heat flux and temperature data a