ASTM C1045-19

Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions

SIGNIFICANCE AND USE
4.1 ASTM thermal test method descriptions are complex because of added apparatus details necessary to ensure accurate results. As a result, many users find it difficult to locate the data reduction details necessary to reduce the data obtained from these tests. This practice is designed to be referenced in the thermal test methods, thus allowing those test methods to concentrate on experimental details rather than data reduction.  
4.2 This practice is intended to provide the user with a uniform procedure for calculating the thermal transmission properties of a material or system from standard test methods used to determine heat flux and surface temperatures. This practice is intended to eliminate the need for similar calculation sections in the ASTM Test Methods (C177, C335, C518, C1033, C1114, C1199, and C1363) by permitting use of these standard calculation forms by reference.  
4.3 This practice provides the method for developing the thermal conductivity as a function of temperature for a specimen from data taken at small or large temperature differences. This relationship can be used to characterize material for comparison to material specifications and for use in calculations programs such as Practice C680.  
4.4 Two general solutions to the problem of establishing thermal transmission properties for application to end-use conditions are outlined in Practice C1058. (Practice C1058 should be reviewed prior to use of this practice.) One is to measure each product at each end-use condition. This solution is rather straightforward, but burdensome, and needs no other elaboration. The second is to measure each product over the entire temperature range of application conditions and to use these data to establish the thermal transmission property dependencies at the various end-use conditions. One advantage of the second approach is that once these dependencies have been established, they serve as the basis for estimating the performance for a given product at othe...
SCOPE
1.1 This practice provides the user with a uniform procedure for calculating the thermal transmission properties of a material or system from data generated by steady state, one dimensional test methods used to determine heat flux and surface temperatures. This practice is intended to eliminate the need for similar calculation sections in Test Methods C177, C335, C518, C1033, C1114 and C1363 and Practices C1043 and C1044 by permitting use of these standard calculation forms by reference.  
1.2 The thermal transmission properties described include: thermal conductance, thermal resistance, apparent thermal conductivity, apparent thermal resistivity, surface conductance, surface resistance, and overall thermal resistance or transmittance.  
1.3 This practice provides the method for developing the apparent thermal conductivity as a function of temperature relationship for a specimen from data generated by standard test methods at small or large temperature differences. This relationship can be used to characterize material for comparison to material specifications and for use in calculation programs such as Practice C680.  
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.5 This practice includes a discussion of the definitions and underlying assumptions for the calculation of thermal transmission properties. Tests to detect deviations from these assumptions are described. This practice also considers the complicating effects of uncertainties due to the measurement processes and material variability. See Section 7.  
1.6 This practice is not intended to cover all possible aspects of thermal properties data base development. For new materials, the user should investigate the variations in thermal properties seen in similar materials. The information contained in Section 7, the Appendix and the technical papers listed in the References secti...

General Information

• Status: Published
• Publication Date: 31-Mar-2019
• ICS: 17.200.10 - Heat. Calorimetry
• Technical Committee: C16 - Thermal Insulation
• Drafting Committee: C16.30 - Thermal Measurement

Relations

• Replaces: ASTM C1045-07(2013) - Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions
• Effective Date: 01-Apr-2019
• Refers: ASTM C168-24 - Standard Terminology Relating to Thermal Insulation
• Effective Date: 15-Apr-2024
• Refers: ASTM C1363-24 - Standard Test Method for Thermal Performance of Building Materials and Envelope Assemblies by Means of a Hot Box Apparatus
• Effective Date: 01-Mar-2024
• Refers: ASTM C1044-24 - Standard Practice for Using a Guarded-Hot-Plate Apparatus or Thin-Heater Apparatus in the Single-Sided Mode
• Effective Date: 01-Mar-2024
• Refers: ASTM C1043-24 - Standard Practice for Guarded-Hot-Plate Design Using Circular Line-Heat Sources
• Effective Date: 01-Mar-2024
• Refers: ASTM C680-23a - Standard Practice for Estimate of the Heat Gain or Loss and the Surface Temperatures of Insulated Flat, Cylindrical, and Spherical Systems by Use of Computer Programs
• Effective Date: 01-Nov-2023
• Refers: ASTM C1043-19 - Standard Practice for Guarded-Hot-Plate Design Using Circular Line-Heat Sources
• Effective Date: 01-Mar-2019
• Refers: ASTM C1114-06(2019) - Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Thin-Heater Apparatus
• Effective Date: 01-Mar-2019
• Refers: ASTM C168-18 - Standard Terminology Relating to Thermal Insulation
• Effective Date: 15-Apr-2018
• Refers: ASTM C168-17 - Standard Terminology Relating to Thermal Insulation
• Effective Date: 01-Jun-2017
• Refers: ASTM C1043-16 - Standard Practice for Guarded-Hot-Plate Design Using Circular Line-Heat Sources
• Effective Date: 01-Mar-2016
• Refers: ASTM C168-15a - Standard Terminology Relating to Thermal Insulation
• Effective Date: 15-Oct-2015
• Refers: ASTM C518-15 - Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus
• Effective Date: 01-Sep-2015
• Refers: ASTM C168-15 - Standard Terminology Relating to Thermal Insulation
• Effective Date: 01-Jun-2015
• Refers: ASTM C680-14 - Standard Practice for Estimate of the Heat Gain or Loss and the Surface Temperatures of Insulated Flat, Cylindrical, and Spherical Systems by Use of Computer Programs
• Effective Date: 01-Sep-2014

Overview

ASTM C1045-19 is a standard practice published by ASTM International that provides a uniform procedure for calculating the thermal transmission properties of materials and systems under steady-state conditions. Specifically, this standard offers standardized equations and methodologies for data reduction using heat flux and surface temperature data from various steady-state, one-dimensional thermal test methods. By centralizing calculation guidance, ASTM C1045-19 streamlines reporting and reduces duplicate data reduction procedures in related ASTM thermal test methods.

Key Topics

• Standardization of Data Reduction: ASTM C1045-19 is intended to be referenced within thermal test methods, allowing those methods to focus on experimental details rather than complex calculation procedures.
• Uniform Calculations: The practice establishes standardized formulas and assumptions for determining thermal transmission properties, including:
  • Thermal conductance
  • Thermal resistance
  • Apparent thermal conductivity
  • Apparent thermal resistivity
  • Surface conductance and resistance
  • Overall thermal resistance or transmittance
• Temperature Dependency: Provides methods for developing relationships between apparent thermal conductivity and temperature, based on data from tests conducted under varying conditions.
• Consideration of Uncertainties: Guidance is provided for recognizing the effects of measurement uncertainties, material variability, and deviations from ideal assumptions.
• SI Units: All calculations and reporting are standardized to SI units, ensuring consistency and global applicability.

Applications

ASTM C1045-19 is particularly valuable for professionals involved in the measurement and specification of thermal properties of insulation, building materials, piping systems, and envelope assemblies. Typical users and applications include:

• Thermal Test Laboratories: Researchers and technicians use ASTM C1045-19 to process and interpret results from standard test methods, enabling reliable comparisons between materials and conformance with product specifications.
• Building and Construction: Used for calculating the thermal performance (such as R-values or U-values) of walls, insulation panels, windows, and piping insulation. Results support energy-efficient building design and code compliance.
• Material Manufacturers: Assists in characterizing thermal properties for quality control, product development, and technical datasheets.
• Specification Writers: Helps ensure that material specifications are based on intrinsic thermal properties, promoting accurate, condition-independent characterization.
• Simulation and Engineering Software: The standardized relationships for temperature-dependent thermal conductivity support accurate modeling and simulation of heat loss, gain, and thermal performance.

Practical value lies in the reproducibility and transparency of calculations, streamlined reporting, and compatibility across multiple ASTM test standards. By referencing ASTM C1045-19, organizations can ensure consistent and reliable reporting of thermal transmission data, aiding in material selection, regulatory compliance, and performance evaluation.

Related Standards

ASTM C1045-19 is closely related to several other ASTM standards, which provide the test methods from which data are derived or support specific applications. Key referenced standards include:

• ASTM C168: Terminology Relating to Thermal Insulation
• ASTM C177: Steady-State Heat Flux Measurements by Guarded-Hot-Plate Apparatus
• ASTM C335: Steady-State Heat Transfer Properties of Pipe Insulation
• ASTM C518: Heat Flow Meter Apparatus
• ASTM C680: Calculation of Heat Gain or Loss and Surface Temperatures of Insulated Systems
• ASTM C1033, C1114, C1199, C1363: Various test methods for insulation and building envelope assemblies
• ASTM C1043, C1044: Practices for apparatus operation in single-sided and guarded-hot-plate configurations
• ASTM C1058: Guide for selecting test temperatures for evaluating and reporting thermal properties
• ASTM E122: Guidance on estimating sample size for statistical confidence

Keywords: thermal transmission, thermal conductivity, steady-state, heat flux, surface temperature, thermal resistance, thermal insulation, ASTM C1045-19, calculation procedure, building materials, data reduction, energy efficiency, material testing

By integrating ASTM C1045-19 into laboratory workflows and material specification documents, organizations ensure accurate, uniform, and internationally recognized thermal property assessments.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C1045 − 19
Standard Practice for
Calculating Thermal Transmission Properties Under Steady-
State Conditions
This standard is issued under the fixed designation C1045; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope propertiesseeninsimilarmaterials.Theinformationcontained
inSection7,theAppendixandthetechnicalpaperslistedinthe
1.1 Thispracticeprovidestheuserwithauniformprocedure
Referencessectionofthispracticemaybehelpfulindetermin-
forcalculatingthethermaltransmissionpropertiesofamaterial
ing whether the material under study has thermal properties
orsystemfromdatageneratedbysteadystate,onedimensional
that can be described by equations using this practice. Some
test methods used to determine heat flux and surface tempera-
examples where this method has limited application include:
tures.Thispracticeisintendedtoeliminatetheneedforsimilar
(1) the onset of convection in insulation as described in
calculation sections in Test Methods C177, C335, C518,
Reference (1);(2) while a phase change is taking place in one
C1033, C1114 and C1363 and Practices C1043 and C1044 by
of the insulation components causing an unsteady-state condi-
permitting use of these standard calculation forms by refer-
tion; and (3) the influence of heat flow direction and tempera-
ence.
ture difference changes for reflective insulations.
1.2 The thermal transmission properties described include:
1.7 This international standard was developed in accor-
thermal conductance, thermal resistance, apparent thermal
dance with internationally recognized principles on standard-
conductivity,apparentthermalresistivity,surfaceconductance,
ization established in the Decision on Principles for the
surface resistance, and overall thermal resistance or transmit-
Development of International Standards, Guides and Recom-
tance.
mendations issued by the World Trade Organization Technical
1.3 This practice provides the method for developing the
Barriers to Trade (TBT) Committee.
apparent thermal conductivity as a function of temperature
relationship for a specimen from data generated by standard 2. Referenced Documents
test methods at small or large temperature differences. This
2.1 ASTM Standards:
relationship can be used to characterize material for compari-
C168Terminology Relating to Thermal Insulation
son to material specifications and for use in calculation
C177Test Method for Steady-State Heat Flux Measure-
programs such as Practice C680.
ments and Thermal Transmission Properties by Means of
1.4 The values stated in SI units are to be regarded as the Guarded-Hot-Plate Apparatus
standard. No other units of measurement are included in this C335TestMethodforSteady-StateHeatTransferProperties
standard. of Pipe Insulation
C518Test Method for Steady-State Thermal Transmission
1.5 Thispracticeincludesadiscussionofthedefinitionsand
Properties by Means of the Heat Flow Meter Apparatus
underlying assumptions for the calculation of thermal trans-
C680Practice for Estimate of the Heat Gain or Loss and the
mission properties. Tests to detect deviations from these
Surface Temperatures of Insulated Flat, Cylindrical, and
assumptions are described. This practice also considers the
Spherical Systems by Use of Computer Programs
complicating effects of uncertainties due to the measurement
C1033Test Method for Steady-State Heat Transfer Proper-
processes and material variability. See Section 7.
ties of Pipe Insulation Installed Vertically (Withdrawn
1.6 Thispracticeisnotintendedtocoverallpossibleaspects
2003)
of thermal properties data base development. For new
C1043Practice for Guarded-Hot-Plate Design Using Circu-
materials, the user should investigate the variations in thermal
lar Line-Heat Sources
1 2
This practice is under the jurisdiction of ASTM Committee C16 on Thermal For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Insulation and is the direct responsibility of Subcommittee C16.30 on Thermal contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Measurement. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved April 1, 2019. Published May 2019. Originally the ASTM website.
approved in 1985. Last previous edition approved in 2013 as C1045–07 (2013). The last approved version of this historical standard is referenced on
DOI: 10.1520/C1045-19. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1045 − 19
C1044Practice for Using a Guarded-Hot-PlateApparatus or
∆T = temperature difference, air to air, (T − T ), K,
a-a 1 2
Thin-Heater Apparatus in the Single-Sided Mode
∆T = temperature difference, surface to surface,
s-s
C1058Practice for Selecting Temperatures for Evaluating
(T − T ), K,
h c
and Reporting Thermal Properties of Thermal Insulation U = thermal transmittance, W/(m ·K), and
C1114Test Method for Steady-State Thermal Transmission x = linear dimension in the heat flow direction, m,
λ = thermal conductivity, W/(m·K),
Properties by Means of the Thin-Heater Apparatus
λ = apparent thermal conductivity, W/(m·K),
C1199TestMethodforMeasuringtheSteady-StateThermal
a
λ(T) = functional relationship between thermal conductiv-
Transmittance of Fenestration Systems Using Hot Box
ity and temperature, W/(m·K),
Methods
λ = experimental thermal conductivity, W/(m·K),
exp
C1363Test Method for Thermal Performance of Building
λ = meanthermal conductivity, averagedwithrespect to
m
Materials and Envelope Assemblies by Means of a Hot
temperature from T to T , W/(m·K), (see sections
c h
Box Apparatus
6.4.1 and Appendix X3).
E122PracticeforCalculatingSampleSizetoEstimate,With
NOTE 1—Subscripts h and c are used to differentiate between hot side
Specified Precision, the Average for a Characteristic of a
and cold side surfaces.
Lot or Process
3.3 Thermal Transmission Property Equations:
3. Terminology
3.3.1 Thermal Resistance, R, is defined in Terminology
C168. It is not necessarily a unique function of temperature or
3.1 Definitions— The definitions and terminology of this
material, but is rather a property determined by the specific
practice are intended to be consistent with Terminology C168.
thickness of the specimen and by the specific set of hot-side
However,becauseexactdefinitionsarecriticaltotheuseofthis
and cold-side temperatures used to measure the thermal resis-
practice,thefollowingequationsaredefinedhereforuseinthe
tance.
calculations section of this practice.
A ~T 2 T !
h c
3.2 Symbols—The symbols, terms and units used in this
R 5 (1)
Q
practice are the following:
3.3.2 Thermal Conductance, C:
A = specimen area normal to heat flux direction, m ,
Q 1
C = thermal conductance, W/(m ·K),
C 5 5 (2)
h = surface heat transfer coefficient, cold side, A T 2 T R
~ h c!
c
NOTE 2—Thermal resistance, R, and the corresponding thermal
W/(m ·K),
conductance,C,arereciprocals;thatis,theirproductisunity.Theseterms
h = surface heat transfer coefficient, hot side,
h
2 apply to specific bodies or constructions as used, either homogeneous or
W/(m ·K),
heterogeneous, between two specified isothermal surfaces.
L = thickness of a slab in heat transfer direction, m,
3.3.3 Eq 1, Eq 2, Eq 3, Eq 5and Eq 7-13 are for rectangular
L = metering area length in the axial direction, m,
p
q = one-dimensional heat flux (time rate of heat flow coordinate systems only. Similar equations for resistance, etc.
canbedevelopedforacylindricalcoordinatesystemproviding
through metering area divided by the apparatus
metering area A), W/m , the difference in areas is considered. (See Eq 4 and Eq 6.) In
Q = time rate of one-dimensional heat flow through the practice, for cylindrical systems such as piping runs, the
metering area of the test apparatus, W,
thermalresistanceshallbebaseduponthepipeexternalsurface
r = thermal resistivity, K·m⁄K,
area since that area does not change with different insulation
r = apparent thermal resistivity, K·m⁄K,
a thickness
r = inside radius of a hollow cylinder, m,
in 3.3.4 Apparent–Thermal conductivity, λ , is defined in Ter-
a
r = outside radius of a hollow cylinder, m,
out minology C168.
R = thermal resistance, m ·K⁄W,
Rectangular coordinates:
R = surface thermal resistance, cold side, m ·K⁄W,
c
QL
R = surface thermal resistance, hot side, m ·K⁄W,
h
λ 5 (3)
2 a
A ~T 2 T !
R = overall thermal resistance, m ·K⁄W,
h c
u
T = temperature, K,
Cylindrical coordinates:
T = area-weighted air temperature 75 mm or more from
Qln r /r
the hot side surface, K, ~ out in!
λ 5 (4)
a
T = area-weighted air temperature 75 mm or more from 2 π L T 2 T
~ !
2 p in out
the cold side surface, K,
3.3.5 Apparent Thermal Resistivity, r , is defined in Termi-
a
T = area-weighted temperature of the specimen cold
c
nology C168.
surface, K,
Rectangular Coordinates:
T = area-weighted temperature of specimen hot surface,
h
K, A T 2 T 1
~ !
h c
r 5 5 (5)
a
T = temperature at the inner radius, K,
QL λ
in
a
T = specimen mean temperature, average of two oppo-
m
Cylindrical Coordinates:
site surface temperatures, (T + T )/2, K,
h c
T = temperature at the outer radius, K,
2 π L T 2 T
out p ~ in out!
r 5 5 (6)
∆T = temperature difference, K, a
Qln r /r λ
~ !
out in a
C1045 − 19
NOTE 3—The apparent thermal resistivity, r , and the corresponding
results.Asaresult,manyusersfinditdifficulttolocatethedata
a
thermal conductivity, λ , are reciprocals, that is, their product is unity.
a
reduction details necessary to reduce the data obtained from
These terms apply to specific materials tested between two specified
these tests. This practice is designed to be referenced in the
isothermal surfaces. For this practice, materials are considered homoge-
thermal test methods, thus allowing those test methods to
neous when the value of the thermal conductivity or thermal resistivity is
concentrate on experimental details rather than data reduction.
not significantly affected by variations in the thickness or area of the
sample within the normally used range of those variables.
4.2 This practice is intended to provide the user with a
3.4 Transmission Property Equations for Convective
uniform procedure for calculating the thermal transmission
Boundary Conditions:
properties of a material or system from standard test methods
3.4.1 Surface Thermal Resistance, R, the quantity deter-
i used to determine heat flux and surface temperatures. This
minedbythetemperaturedifferenceatsteady-statebetweenan
practiceisintendedtoeliminatetheneedforsimilarcalculation
isothermal surface and its surrounding air that induces a unit
sections in the ASTM Test Methods (C177, C335, C518,
heat flow rate per unit area to or from the surface. Typically,
C1033, C1114, C1199, and C1363) by permitting use of these
this parameter includes the combined effects of conduction,
standard calculation forms by reference.
convection,andradiation.Surfaceresistancesarecalculatedas
4.3 This practice provides the method for developing the
follows:
thermal conductivity as a function of temperature for a
A ~T 2 T !
1 h specimen from data taken at small or large temperature
R 5 (7)
h
Q
differences. This relationship can be used to characterize
material for comparison to material specifications and for use
A T 2 T
~ !
c 2
R 5 (8)
c
in calculations programs such as Practice C680.
Q
4.4 Two general solutions to the problem of establishing
3.4.2 Surface Heat Transfer Coeffıcient, h, is often called
i
thermal transmission properties for application to end-use
the film coefficient. These coefficients are calculated as fol-
conditions are outlined in Practice C1058. (Practice C1058
lows:
should be reviewed prior to use of this practice.) One is to
Q 1
measure each product at each end-use condition. This solution
h 5 5 (9)
h
A T 2 T R
~ !
1 h h
is rather straightforward, but burdensome, and needs no other
Q 1
elaboration. The second is to measure each product over the
h 5 5 (10)
c
A ~T 2 T ! R
c 2 c entire temperature range of application conditions and to use
NOTE4—Thesurfaceheattransfercoefficient,h,andthecorresponding
i
these data to establish the thermal transmission property
surface thermal resistance, R, are reciprocals, that is, their product is
i
dependenciesatthevariousend-useconditions.Oneadvantage
unity.Thesepropertiesaremeasuredataspecificsetofambientconditions
of the second approach is that once these dependencies have
and are therefore only correct for the specified conditions of the test.
been established, they serve as the basis for estimating the
3.4.3 Overall Thermal Resistance, R —The quantity deter-
u
performance for a given product at other conditions.
mined by the temperature difference, at steady-state, between
Warning—Theuseofathermalconductivitycurvedeveloped
theairtemperaturesonthetwosidesofabodyorassemblythat
in Section 6 must be limited to a temperature range that does
induces a unit time rate of heat flow per unit area through the
not extend beyond the range of highest and lowest test surface
body. It is the sum of the resistance of the body or assembly
temperatures in the test data set used to generate the curve.
and of the two surface resistances and may be calculated as
follows:
5. Determination of Thermal Transmission Properties for
a Specific Set of Temperature Conditions
A ~T 2 T !
1 2
R 5 (11)
u
Q
5.1 Choose the thermal test parameter (λ or r, R or C, U or
R ) to be calculated from the test results. List any additional
u
5 R 1R1R
c h
information required by that calculation i.e. heat flux,
temperatures, dimensions. Recall that the selected test param-
3.4.4 Thermal Transmittance, U (sometimes called overall
etermightlimittheselectionofthethermaltestmethodusedin
coefficient of thermal transfer), is calculated as follows:
5.2.
Q 1
U 5 5 (12)
5.2 Select the appropriate test method that provides the
A T 2 T R
~ !
1 2 u
thermal test data required to determine the thermal transmis-
The transmittance can be calculated from the thermal con-
sion property of interest for the sample material being studied.
ductance and the surface coefficients as follows:
(See referenced papers and Appendix X1 for help with this
1/U 5 1/h 1 1/C 1 1/h (13)
~ ! ~ ! ~ ! determination.
h c
NOTE 5—Thermal transmittance, U, and the corresponding overall
5.3 Using that test method, determine the required steady-
thermalresistance,R ,arereciprocals;thatis,theirproductisunity.These
u
state heat flux and temperature data at the selected test
properties are measured at a specific set of ambient conditions and are
therefore only correct for the specified conditions of the test.
condition.
NOTE 6—The calculation of specific thermal transmission properties
requires that: (1) the thermal insulation specimen is homogeneous, as
4. Significance and Use
defined in Terminology C168 or, as a minimum, appears uniform across
4.1 ASTM thermal test method descriptions are complex
the test area; (2) the measurements are taken only after steady-state has
becauseofaddedapparatusdetailsnecessarytoensureaccurate beenestablished;(3)theheatflowsinadirectionnormaltotheisothermal
C1045 − 19
surfaces of the specimen; (4) the rate of flow of heat is known; (5) the thermal conductivity, λ , and the thermal conductivity at the mean
m
specimen dimensions, that is, heat flow path length parallel to heat flow, temperature, λ (T ), are equal only in the special case where λ (T)isa
m
and area perpendicular to heat flow, are known; and (6) both specimen constant or linear function of temperature (2); that is, when there is no
surface temperatures (and equivalently, the temperature difference across curvature (nonlinearity) in the conductivity-temperature relation. In all
the specimen) are known; and in the case of a hot box systems test, both other cases, the conductivity, λ , as determined by Eq 3 is not simply a
exp
air curtain temperatures must be known. functionofmeantemperature,butdependsonthevaluesofbothT andT .
h c
Thisisthereasontheexperimentalvalue,λ ,ofthermalconductivityfor
exp
5.4 Calculatethethermalpropertyusingthedatagatheredin
a large temperature difference is not, in general, the same as that for a
5.2 and 5.3, and the appropriate equation in 3.3 or 3.4 above.
small difference at the same mean temperature. The discrepancy between
The user of this practice is responsible for insuring that the the mean thermal conductivity and the thermal conductivity at the mean
temperature increases as ∆T increases. Treatment of these differences is
input data from the tests conducted are consistent with the
discussed in Section 6.
defined properties of the test parameter prior to parameter
5.6.3 When ∆T is so large that the mean (experimental)
calculation.Areview of the information in Section 7 will help
thermal conductivity differs from the thermal conductivity at
in this evaluation. For example, data must be examined for
the mean specimen temperature by more than 1%, the derived
consistency in such areas as heat flow stability, heat flow
thermalconductivity(Eq3)shallbeidentifiedasameanvalue,
orientation, metering area, geometry limits, surface tempera-
λ , over the range from T to T . For example, for the
ture definition and others.
m c h
insulationmaterialpresentedinX3.4,the1%limitisexceeded
5.5 Using the data from the test as described in 5.3,
fortemperaturedifferencesgreaterthan125Katatemperature
determinethetestmeantemperatureforthethermalpropertyof
of475K.Reference (2)describesamethodforestablishingthe
5.4 using Eq 14:
actual λ versus T dependency from mean thermal conductivity
T 5 T 1T /2 (14)
~ ! measurements. Proofs of the above statements, along with
m h c
NOTE 7—The thermal transmission properties determined in 5.4 are
some illustrative examples, are given in Appendix X3.
applicable only for the conditions of the test. Further analysis is required
using data from multiple tests if the relationship for the thermal transmis-
6. Determination of the Thermal Conductivity
sion property variation with temperature is to be determined. If this
Relationship for a Temperature Range
relationshipisrequired,theanalysistobefollowedispresentedinSection
6.
6.1 Consult Practice C1058 for the selection of appropriate
5.6 An Example: Computation of Thermal Conductivity
testtemperatures.Usingtheappropriatetestmethodofinterest,
Measured in a Two-Sided Guarded Hot Plate: determine the steady-state heat flux and temperature data for
5.6.1 For a guarded hot plate apparatus in the normal, each test covering the temperature range of interest.
double-sided mode of operation, the heat developed in the
6.2 When Temperature Differences are Small—The use of
metered area heater passes through two specimens. To reflect
Eq 3 or Eq 4 is valid for determining the thermal conductivity
this fact, Eq 3 for the operational definition of the mean
versus temperature only if the temperature difference between
thermalconductivityofthepairofspecimensmustbemodified
the hot and cold surfaces is small. For the purpose of this
to read:
practice, experience with most insulation materials at tempera-
Q turesaboveambientshowsthatthemaximum∆Tshouldbe25
λ 5 (15)
exp
A ∆T /L 1 ∆T /L Kor5%ofthemeantemperature(K),whicheverisgreater.At
@~ ! ~ ! #
s2s 1 s2s 2
temperaturesbelowambient,thetemperaturedifferenceshould
where:
be less than 10 percent of the absolute mean temperature. (See
(∆/T /L) = the ratio of surface-to-surface temperature dif-
s-s 1
Reference (2)). The procedure given in section 6.2.1 is fol-
ference to thickness for Specimen 1. A similar
lowed only when these temperature difference conditions are
expression is used for Specimen 2.
met. The procedure of section 6.3 is valid for all test data
reduction.
5.6.2 In many experimental situations, the two temperature
differences are very nearly equal (within well under 1%), and
NOTE 9—One exception to this temperature difference conditions is
the two thicknesses are also nearly equal (within 1%), so that
testing of insulation materials exhibiting inflection points due to the
Eq 15 may be well approximated by a simpler form: change of state of insulating gases. For these materials, testing shall be
conducted with sufficiently small temperature differences and at closely
QL
average
spaced mean temperatures.The selection of test temperatures will depend
λ 5 (16)
exp
2A ∆T
on the vapor pressure versus temperature relationship of the gases
average
involved and the ability of the test apparatus to provide accurate
where:
measurements at low temperature differences. Another exception occurs
∆T = the mean temperature difference, with the onset of convection within the specimen. At this point, the
average
thermal conductivity of the specimen is no longer defined at these
((∆T ) +(∆ T ) )/2,
s-s 1 s-s 2
conditions and the thermal parameter of choice to be calculated is either
L =(L +L )/2 is the mean of the two specimen
average 1 2
thermal resistance or thermal conductance.
thicknesses, and
6.2.1 The quantities on the right-hand side of Eq 3 are
2 A = occurs because the metered power flows out
known for each data point; from these quantities λ(T) may be
throughtwosurfacesofthemeteredareaforthis
calculated if ∆T is sufficiently small (see 6.2), for normal
apparatus. For clarity in later discussions, use of
insulation applications. The value of λ (T) so obtained is an
this simpler form, Eq 16, will be assumed.
approximation, its accuracy depends on the curvature (non-
NOTE8—Themeanthermalconductivity,λ ,isusuallynotthesameas
m
the thermal conductivity, λ (T ), at the mean temperature T . The mean linearity) of the thermal conductivity-temperature relationship
m m
C1045 − 19
(2). It is conventional to associate the value of λ obtained 6.4.1 Integrate the selected thermal conductivity function
exp
from Eq 16 with the mean temperature T at the given data with respect to temperature. For example, if the selected
m
point. For data obtained at a number of mean temperatures, a function λ(T) were a polynomial function of the form
functional dependence of λ with T may be obtained, with n m
λ T 5 a 1a T 1a T , (19)
~ !
o n m
functionalcoefficientstobedeterminedfromthedata.Inorder
then,fromEq18,thetemperature-averagedthermalconduc-
toapplyaleastsquaresfittothedata,thenumberofdatapoints
tivity would be:
shall be greater than the number of coefficients in the function
n11 n11 m11 m11
toobtainthefunctionaldependenceofthethermalconductivity
a T 2 T a T 2 T
~ ! ~ !
n h c m h c
λ 5 a 1 1 (20)
m o
λ T on temperature, T. The accuracy of the coefficients thus
~n11!~T 2 T ! ~m11!~T 2 T !
h c h c
obtained depend not only on the experimental imprecision, but
6.4.2 Bymeansofanystandardleast-squaresfittingroutine,
also on the extent to which the thermal conductivity-
the right-hand side of Eq 20 is fitted against the values of
temperaturerelationshipdepartsfromthetruerelationshipover
experimentalthermalconductivity,λ .Thisfitdeterminesthe
exp
the temperature range defined by the isothermal boundaries of
coefficients (a , a , a ) for the selected n and m in the thermal
o n m
the specimen during the tests.
conductivity function, Eq 19 in this case.
6.3 Computation of Thermal Conductivity When Tempera-
6.4.3 Use the coefficients obtained in 6.4.2 to describe the
tureDifferencesareLarge—Thefollowingsectionsapplytoall
assumedthermalconductivityfunction,Eq19.Eachdatapoint
testing results and are specifically required when the tempera-
is then conventionally plotted at the corresponding mean
ture difference exceeds the limits stated in 6.2. This situation
specimentemperature.Whenthefunctionisplotted,itmaynot
typically occurs during measurements of thermal transmission
pass exactly through the data points.This is because each data
in pipe insulation,Test Method C335, but may also occur with
point represents mean conductivity, λ , and this is not equal to
m
measurements using other apparatus. Eq 17 and 18 are devel-
the value of the thermal conductivity, λ (T ), at the mean
m
oped in Appendix X2, but are presented here for continuity of
temperature. The offset between a data point and the fitted
this practice.
curve depends on the size of test ∆T and on the nonlinearity of
the thermal conductivity function.
6.3.1 The dependence of λ on T for flat-slab geometry is:
1 T
NOTE 10—Many equation forms other than Eq 19 can be used to
h
λ 5 λ~T! δT
*
m
represent the thermal conductivity function. If possible, the equation
T
∆T
c
chosen to represent the thermal conductivity versus temperature relation-
ship should be easily integrated with respect to temperature. However, in
or;
some instances it may be desirable to choose a form for λ(T) that is not
λ 5 QL/@2 A ~T 2 T !# (17)
m h c easilyintegrated.Suchequationsmaybefoundtofitthedataoveramuch
wider range of temperature. Also, the user is not restricted to the use of
The quantities T,T,Q, and (L/2A) on the right-hand side
h c polynomial equations to represent λ(T), but only to equation forms that
are known for each data point obtained by the user.
can be integrated either analytically or numerically. In cases where direct
integration is not possible, one can carry out the same procedure using
6.3.2 The dependence of λ on T for cylindrical geometry is:
numerical integration.
1 T
in
6.5 TCI Method—A Summary—The thermal conductivity
λ 5 λ T δT
* ~ !
m
∆T T
out
integral method of analysis is summarized in the following
steps:
or;
6.5.1 Measureseveralsetsofλ ,T ,andT overarangeof
exp h c
Qln r /r
~ !
out in
temperatures.
λ 5 (18)
m
2 π L T 2 T
~ !
p in out
6.5.2 Select a functional form for λ( T)asin Eq 19, and
integrateitwithrespecttotemperaturetoobtaintheequivalent
The quantities T , T , Q, 1n (r /r ) and 2π L on the
in out out in p
of Eq 20.
right-hand side, are known for each data point obtained by the
6.5.3 Perform a least-squares fit to the experimental data of
user.
the integral of the functional form obtained in 6.5.2 to obtain
6.4 Thermal Conductivity Integral (TCI) Method—To ob-
the best values of the coefficients.
tain the dependence of thermal conductivity on temperature
6.5.4 Usethesecoefficientstocompletetheλ(T)equationas
from Eq 17 or Eq 18, a specific functional dependence to
defined in 6.5.2. Remember that the thermal conductivity
represent the conductivity-temperature relation must first be
equation derived herein is good only over the range of
chosen. This Practice recommends that the functional form of
temperatures encompassed by the test data. Extrapolation of
the describing equation closely describe the physical phenom-
the test results to a temperature range not covered by the data
enagoverningtheheattransferthroughthesample.Inaddition,
is not acceptable.
this functional form must be continuous over the temperature
range of use. This will avoid potential problems during data
7. Consideration of Test Result Significance
fitting and integration. (See Note 10.) While not absolutely
necessary, choosing the physically correct equation form can 7.1 A final step in the analysis and reporting of test results
provide better understanding of the physical forces governing requires that the data be reviewed for significance and accu-
the heat flow behavior. After the form of the thermal conduc- racy. It is not the intent of this practice to cover all aspects of
tivity equation is chosen, steps 6.4.1 – 6.4.3 are followed to the strategy of experimental design, but only to identify areas
determine the coefficients for that equation. of concern. Some additional information is provided in the
C1045 − 19
Appendix but the interested reader is referred to the reference coefficients,themethodofdataanalysisandregression,andthe
section for more detailed information. The following areas range of temperatures that were used to determine the coeffi-
should be considered in the evaluation of the test results cients.
produced using a Practice C1045 analysis.
8.6 The temperature range of usefulness for the equation
coefficients shall be specified. For example, using the data of
7.2 Assessment of Apparatus Uncertainty—The determina-
tion of apparatus uncertainty should be performed as required Table X3.1 yields a temperature range of usefulness of the
coefficients of 286 K to 707 K.
by the appropriate apparatus test method.
8.7 Unlessotherwisespecified,thecalculationandreporting
7.3 Material Inhomogeneity—The uncertainty caused by
of C1045 results shall be in SI units.
specimen inhomogeneity can seriously alter the measured
dependencies. To establish the possible consequences of ma-
9. Using C1045 in Specifications
terial inhomogeneity on the interpretation of the results, the
usershallmeasureanadequatefractionoftheproductoverthe 9.1 Material specifications can benefit from the use of
entire range of product manufacture variations. If possible, C1045 in specifying the apparent thermal conductivity rela-
several specimens shall be measured to sample a sufficient tionship desired. It is important that the material be specified
portion of the product. The resultant mean value of the byintrinsicpropertiesthatareindependentoftestconditionsto
measurements is representative of the product to within the insurethatthemethodoftest,ortheconditionsusedduringthe
uncertainty of the mean, while the range of the results is test do not influence the results. Practice C1045 provides a
indicative of the product i
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: C1045 − 07 (Reapproved 2013) C1045 − 19
Standard Practice for
Calculating Thermal Transmission Properties Under Steady-
State Conditions
This standard is issued under the fixed designation C1045; 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.
1. Scope
1.1 This practice provides the user with a uniform procedure for calculating the thermal transmission properties of a material
or system from data generated by steady state, one dimensional test methods used to determine heat flux and surface temperatures.
This practice is intended to eliminate the need for similar calculation sections in Test Methods C177, C335, C518, C1033, C1114
and C1363 and Practices C1043 and C1044 by permitting use of these standard calculation forms by reference.
1.2 The thermal transmission properties described include: thermal conductance, thermal resistance, apparent thermal
conductivity, apparent thermal resistivity, surface conductance, surface resistance, and overall thermal resistance or transmittance.
1.3 This practice provides the method for developing the apparent thermal conductivity as a function of temperature relationship
for a specimen from data generated by standard test methods at small or large temperature differences. This relationship can be
used to characterize material for comparison to material specifications and for use in calculation programs such as Practice C680.
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.5 This practice includes a discussion of the definitions and underlying assumptions for the calculation of thermal transmission
properties. Tests to detect deviations from these assumptions are described. This practice also considers the complicating effects
of uncertainties due to the measurement processes and material variability. See Section 7.
1.6 This practice is not intended to cover all possible aspects of thermal properties data base development. For new materials,
the user should investigate the variations in thermal properties seen in similar materials. The information contained in Section 7,
the Appendix and the technical papers listed in the References section of this practice may be helpful in determining whether the
material under study has thermal properties that can be described by equations using this practice. Some examples where this
method has limited application include: (1) the onset of convection in insulation as described in Reference (1); (2) while a phase
change of is taking place in one of the insulation system components such as a blowing gas in foam; components causing an
unsteady-state condition; and (3) the influence of heat flow direction and temperature difference changes for reflective insulations.
1.7 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
C168 Terminology Relating to Thermal Insulation
C177 Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the
Guarded-Hot-Plate Apparatus
C335 Test Method for Steady-State Heat Transfer Properties of Pipe Insulation
C518 Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus
C680 Practice for Estimate of the Heat Gain or Loss and the Surface Temperatures of Insulated Flat, Cylindrical, and Spherical
Systems by Use of Computer Programs
C1033 Test Method for Steady-State Heat Transfer Properties of Pipe Insulation Installed Vertically (Withdrawn 2003)
This practice is under the jurisdiction of ASTM Committee C16 on Thermal Insulation and is the direct responsibility of Subcommittee C16.30 on Thermal Measurement.
Current edition approved Sept. 1, 2013April 1, 2019. Published January 2014May 2019. Originally approved in 1985. Last previous edition approved in 20072013 as
C1045 – 07.C1045 – 07 (2013). DOI: 10.1520/C1045-07R13.10.1520/C1045-19.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1045 − 19
C1043 Practice for Guarded-Hot-Plate Design Using Circular Line-Heat Sources
C1044 Practice for Using a Guarded-Hot-Plate Apparatus or Thin-Heater Apparatus in the Single-Sided Mode
C1058 Practice for Selecting Temperatures for Evaluating and Reporting Thermal Properties of Thermal Insulation
C1114 Test Method for Steady-State Thermal Transmission Properties by Means of the Thin-Heater Apparatus
C1199 Test Method for Measuring the Steady-State Thermal Transmittance of Fenestration Systems Using Hot Box Methods
C1363 Test Method for Thermal Performance of Building Materials and Envelope Assemblies by Means of a Hot Box Apparatus
E122 Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or
Process
3. Terminology
3.1 Definitions— The definitions and terminology of this practice are intended to be consistent with Terminology C168.
However, because exact definitions are critical to the use of this practice, the following equations are defined here for use in the
calculations section of this practice.
3.2 Symbols—The symbols, terms and units used in this practice are the following:
A = specimen area normal to heat flux direction, m ,
C = thermal conductance, W/(m · K),
h = surface heat transfer coefficient, cold side,
c
W/(m · K),
h = surface heat transfer coefficient, hot side,
h
W/(m · K),
L = thickness of a slab in heat transfer direction, m,
L = metering area length in the axial direction, m,
p
q = one-dimensional heat flux (time rate of heat flow through metering area divided by the apparatus metering area A),
W/m ,
Q = time rate of one-dimensional heat flow through the metering area of the test apparatus, W,
r = thermal resistivity, K · m ⁄K,
r = apparent thermal resistivity, K · m ⁄K,
a
r = inside radius of a hollow cylinder, m,
in
r = outside radius of a hollow cylinder, m,
out
R = thermal resistance, m · K ⁄W,
R = surface thermal resistance, cold side, m · K ⁄W,
c
R = surface thermal resistance, hot side, m · K ⁄W,
h
R = overall thermal resistance, m · K ⁄W,
u
T = temperature, K,
T = area-weighted air temperature 75 mm or more from the hot side surface, K,
T = area-weighted air temperature 75 mm or more from the cold side surface, K,
T = area-weighted temperature of the specimen cold surface, K,
c
T = area-weighted temperature of specimen hot surface, K,
h
T = temperature at the inner radius, K,
in
T = specimen mean temperature, average of two opposite surface temperatures, (T + T )/2, K,
m h c
T = temperature at the outer radius, K,
out
ΔT = temperature difference, K,
ΔT = temperature difference, air to air, (T − T ), K,
a-a 1 2
ΔT = temperature difference, surface to surface,
s-s
(T − T ), K,
h c
U = thermal transmittance, W/(m · K), and
x = linear dimension in the heat flow direction, m,
λ = thermal conductivity, W/(m · K),
λ = apparent thermal conductivity, W/(m · K),
a
λ(T) = functional relationship between thermal conductivity and temperature, W/(m · K),
λ = experimental thermal conductivity, W/(m · K),
exp
λ = mean thermal conductivity, averaged with respect to temperature from T to T , W/(m · K), (see sections 6.4.1 and
m c h
Appendix X3).
NOTE 1—Subscripts h and c are used to differentiate between hot side and cold side surfaces.
3.3 Thermal Transmission Property Equations:
3.3.1 Thermal Resistance, R, is defined in Terminology C168. It is not necessarily a unique function of temperature or material,
but is rather a property determined by the specific thickness of the specimen and by the specific set of hot-side and cold-side
temperatures used to measure the thermal resistance.
C1045 − 19
A T 2 T
~ !
h c
R 5 (1)
Q
3.3.2 Thermal Conductance, C:
Q 1
C 5 5 (2)
A T 2 T R
~ h c!
NOTE 2—Thermal resistance, R, and the corresponding thermal conductance, C, are reciprocals; that is, their product is unity. These terms apply to
specific bodies or constructions as used, either homogeneous or heterogeneous, between two specified isothermal surfaces.
3.3.3 Eq 1, Eq 2, Eq 3, Eq 5and Eq 7-13 are for rectangular coordinate systems only. Similar equations for resistance, etc. can
be developed for a cylindrical coordinate system providing the difference in areas is considered. (See Eq 4 and Eq 6.) In practice,
for cylindrical systems such as piping runs, the thermal resistance shall be based upon the pipe external surface area since that area
does not change with different insulation thickness
3.3.4 Apparent–Thermal conductivity, λ , is defined in Terminology C168.
a
Rectangular coordinates:
Q L
λ 5 (3)
a
A T 2 T
~ !
h c
Cylindrical coordinates:
Qln r /r
~ !
out in
λ 5 (4)
a
2 π L T 2 T
~ !
p in out
3.3.5 Apparent Thermal Resistivity, r , is defined in Terminology C168.
a
Rectangular Coordinates:
A ~T 2 T ! 1
h c
r 5 5 (5)
a
Q L λ
a
Cylindrical Coordinates:
2 π L T 2 T
~ ! 1
p in out
r 5 5 (6)
a
Qln r /r λ
~ !
out in a
NOTE 3—The apparent thermal resistivity, r , and the corresponding thermal conductivity, λ , are reciprocals, that is, their product is unity. These terms
a a
apply to specific materials tested between two specified isothermal surfaces. For this practice, materials are considered homogeneous when the value of
the thermal conductivity or thermal resistivity is not significantly affected by variations in the thickness or area of the sample within the normally used
range of those variables.
3.4 Transmission Property Equations for Convective Boundary Conditions:
3.4.1 Surface Thermal Resistance, R , the quantity determined by the temperature difference at steady-state between an
i
isothermal surface and its surrounding air that induces a unit heat 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 as follows:
A ~T 2 T !
1 h
R 5 (7)
h
Q
A T 2 T
~ !
c 2
R 5 (8)
c
Q
3.4.2 Surface Heat Transfer Coeffıcient, h , is often called the film coefficient. These coefficients are calculated as follows:
i
Q 1
h 5 5 (9)
h
A T 2 T R
~ !
1 h h
Q 1
h 5 5 (10)
c
A ~T 2 T ! R
c 2 c
NOTE 4—The surface heat transfer coefficient, h , and the corresponding surface thermal resistance, R , are reciprocals, that is, their product is unity.
i i
These properties are measured at a specific set of ambient conditions and are therefore only correct for the specified conditions of the test.
3.4.3 Overall Thermal Resistance, R —The quantity determined by the temperature difference, at steady-state, between the air
u
temperatures on the two sides of a body or assembly that induces a unit time rate of heat flow per unit area through the body. It
is the sum of the resistance of the body or assembly and of the two surface resistances and may be calculated as follows:
A T 2 T
~ !
1 2
R 5 (11)
u
Q
5 R 1R1R
c h
3.4.4 Thermal Transmittance, U (sometimes called overall coefficient of thermal transfer), is calculated as follows:
C1045 − 19
Q 1
U 5 5 (12)
A ~T 2 T ! R
1 2 u
The transmittance can be calculated from the thermal conductance and the surface coefficients as follows:
1/U 5 1/h 1 1/C 1 1/h (13)
~ ! ~ ! ~ !
h c
NOTE 5—Thermal transmittance, U, and the corresponding overall thermal resistance, R , are reciprocals; that is, their product is unity. These properties
u
are measured at a specific set of ambient conditions and are therefore only correct for the specified conditions of the test.
4. Significance and Use
4.1 ASTM thermal test method descriptions are complex because of added apparatus details necessary to ensure accurate
results. As a result, many users find it difficult to locate the data reduction details necessary to reduce the data obtained from these
tests. This practice is designed to be referenced in the thermal test methods, thus allowing those test methods to concentrate on
experimental details rather than data reduction.
4.2 This practice is intended to provide the user with a uniform procedure for calculating the thermal transmission properties
of a material or system from standard test methods used to determine heat flux and surface temperatures. This practice is intended
to eliminate the need for similar calculation sections in the ASTM Test Methods (C177, C335, C518, C1033, C1114, C1199, and
C1363) by permitting use of these standard calculation forms by reference.
4.3 This practice provides the method for developing the thermal conductivity as a function of temperature for a specimen from
data taken at small or large temperature differences. This relationship can be used to characterize material for comparison to
material specifications and for use in calculations programs such as Practice C680.
4.4 Two general solutions to the problem of establishing thermal transmission properties for application to end-use conditions
are outlined in Practice C1058. (Practice C1058 should be reviewed prior to use of this practice.) One is to measure each product
at each end-use condition. This solution is rather straightforward, but burdensome, and needs no other elaboration. The second is
to measure each product over the entire temperature range of application conditions and to use these data to establish the thermal
transmission property dependencies at the various end-use conditions. One advantage of the second approach is that once these
dependencies have been established, they serve as the basis for estimating the performance for a given product at other conditions.
Warning— The use of a thermal conductivity curve developed in Section 6 must be limited to a temperature range that does not
extend beyond the range of highest and lowest test surface temperatures in the test data set used to generate the curve.
5. Determination of Thermal Transmission Properties for a Specific Set of Temperature Conditions
5.1 Choose the thermal test parameter (λ or r, R or C, U or R ) to be calculated from the test results. List any additional
u
information required by that calculation i.e. heat flux, temperatures, dimensions. Recall that the selected test parameter might limit
the selection of the thermal test method used in 5.2.
5.2 Select the appropriate test method that provides the thermal test data required to determine the thermal transmission property
of interest for the sample material being studied. (See referenced papers and Appendix X1 for help with this determination.
5.3 Using that test method, determine the required steady-state heat flux and temperature data at the selected test condition.
NOTE 6—The calculation of specific thermal transmission properties requires that: (1) the thermal insulation specimen is homogeneous, as defined in
Terminology C168 or, as a minimum, appears uniform across the test area; (2) the measurements are taken only after steady-state has been established;
( 3) the heat flows in a direction normal to the isothermal surfaces of the specimen; (4) the rate of flow of heat is known; (5) the specimen dimensions,
that is, heat flow path length parallel to heat flow, and area perpendicular to heat flow, are known; and (6) both specimen surface temperatures (and
equivalently, the temperature difference across the specimen) are known; and in the case of a hot box systems test, both air curtain temperatures must
be known.
5.4 Calculate the thermal property using the data gathered in 5.2 and 5.3, and the appropriate equation in 3.3 or 3.4 above. The
user of this practice is responsible for insuring that the input data from the tests conducted are consistent with the defined properties
of the test parameter prior to parameter calculation. A review of the information in Section 7 will help in this evaluation. For
example, data must be examined for consistency in such areas as heat flow stability, heat flow orientation, metering area, geometry
limits, surface temperature definition and others.
5.5 Using the data from the test as described in 5.3, determine the test mean temperature for the thermal property of 5.4 using
Eq 14:
T 5 T 1T /2 (14)
~ !
m h c
NOTE 7—The thermal transmission properties determined in 5.4 are applicable only for the conditions of the test. Further analysis is required using
data from multiple tests if the relationship for the thermal transmission property variation with temperature is to be determined. If this relationship is
required, the analysis to be followed is presented in Section 6.
5.6 An Example: Computation of Thermal Conductivity Measured in a Two-Sided Guarded Hot Plate:
5.6.1 For a guarded hot plate apparatus in the normal, double-sided mode of operation, the heat developed in the metered area
heater passes through two specimens. To reflect this fact, Eq 3 for the operational definition of the mean thermal conductivity of
the pair of specimens must be modified to read:
C1045 − 19
Q
λ 5 (15)
exp
A @~ΔT /L! 1~ΔT /L! #
s2s s2s
1 2
where:
(Δ/T /L) = the ratio of surface-to-surface temperature difference to thickness for Specimen 1. A similar expression is used for
s-s 1
Specimen 2.
5.6.2 In many experimental situations, the two temperature differences are very nearly equal (within well under 1 %), and the
two thicknesses are also nearly equal (within 1 %), so that Eq 15 may be well approximated by a simpler form:
Q L
average
λ 5 (16)
exp
2A ΔT
average
where:
ΔT = the mean temperature difference,
average
((ΔT ) + (Δ T ) )/2,
s-s 1 s-s 2
L = (L +L )/2 is the mean of the two specimen thicknesses, and
average 1 2
2 A = occurs because the metered power flows out through two surfaces of the metered area for this apparatus. For clarity
in later discussions, use of this simpler form, Eq 16, will be assumed.
NOTE 8—The mean thermal conductivity, λ , is usually not the same as the thermal conductivity, λ (T ), at the mean temperature T . The mean thermal
m m m
conductivity, λ , and the thermal conductivity at the mean temperature, λ (T ), are equal only in the special case where λ (T) is a constant or linear
m m
function of temperature (2); that is, when there is no curvature (nonlinearity) in the conductivity-temperature relation. In all other cases, the conductivity,
λ , as determined by Eq 3 is not simply a function of mean temperature, but depends on the values of both T and T . This is the reason the experimental
exp h c
value, λ , of thermal conductivity for a large temperature difference is not, in general, the same as that for a small difference at the same mean
exp
temperature. The discrepancy between the mean thermal conductivity and the thermal conductivity at the mean temperature increases as ΔT increases.
Treatment of these differences is discussed in Section 6.
5.6.3 When ΔT is so large that the mean (experimental) thermal conductivity differs from the thermal conductivity at the mean
specimen temperature by more than 1 %, the derived thermal conductivity (Eq 3) shall be identified as a mean value, λ , over the
m
range from T to T . For example, for the insulation material presented in X3.4, the 1 % limit is exceeded for temperature
c h
differences greater than 125 K at a temperature of 475 K. Reference (2) describes a method for establishing the actual λ versus
T dependency from mean thermal conductivity measurements. Proofs of the above statements, along with some illustrative
examples, are given in Appendix X3.
6. Determination of the Thermal Conductivity Relationship for a Temperature Range
6.1 Consult Practice C1058 for the selection of appropriate test temperatures. Using the appropriate test method of interest,
determine the steady-state heat flux and temperature data for each test covering the temperature range of interest.
6.2 When Temperature Differences are Small—The use of Eq 3 or Eq 4 is valid for determining the thermal conductivity versus
temperature only if the temperature difference between the hot and cold surfaces is small. For the purpose of this practice,
experience with most insulation materials at temperatures above ambient shows that the maximum Δ T should be 25 K or 5 % of
the mean temperature (K), whichever is greater. At temperatures below ambient, the temperature difference should be less than 10
percent of the absolute mean temperature. (See Reference (2)). The procedure given in section 6.2.1 is followed only when these
temperature difference conditions are met. The procedure of section 6.3 is valid for all test data reduction.
NOTE 9—One exception to this temperature difference conditions is testing of insulation materials exhibiting inflection points due to the change of state
of insulating gases. For these materials, testing shall be conducted with sufficiently small temperature differences and at closely spaced mean temperatures.
The selection of test temperatures will depend on the vapor pressure versus temperature relationship of the gases involved and the ability of the test
apparatus to provide accurate measurements at low temperature differences. Another exception occurs with the onset of convection within the specimen.
At this point, the thermal conductivity of the specimen is no longer defined at these conditions and the thermal parameter of choice to be calculated is
either thermal resistance or thermal conductance.
6.2.1 The quantities on the right-hand side of Eq 3 are known for each data point; from these quantities λ(T) may be calculated
if ΔT is sufficiently small (see 6.2), for normal insulation applications. The value of λ (T) so obtained is an approximation, its
accuracy depends on the curvature (non-linearity) of the thermal conductivity-temperature relationship (2). It is conventional to
associate the value of λ obtained from Eq 16 with the mean temperature T at the given data point. For data obtained at a number
exp m
of mean temperatures, a functional dependence of λ with T may be obtained, with functional coefficients to be determined from
the data. In order to apply a least squares fit to the data, the number of data points shall be greater than the number of coefficients
in the function to obtain the functional dependence of the thermal conductivity λ T on temperature, T. The accuracy of the
coefficients thus obtained depend not only on the experimental imprecision, but also on the extent to which the thermal
conductivity-temperature relationship departs from the true relationship over the temperature range defined by the isothermal
boundaries of the specimen during the tests.
6.3 Computation of Thermal Conductivity When Temperature Differences are Large—The following sections apply to all testing
results and are specifically required when the temperature difference exceeds the limits stated in 6.2. This situation typically occurs
C1045 − 19
during measurements of thermal transmission in pipe insulation, Test Method C335, but may also occur with measurements using
other apparatus. Eq 17 and 18 are developed in Appendix X2, but are presented here for continuity of this practice.
6.3.1 The dependence of λ on T for flat-slab geometry is:
1 T
h
λ 5 λ T δT
* ~ !
m
ΔT T
c
or;
λ 5 QL/ 2 A T 2 T (17)
@ ~ !#
m h c
The quantities T , T , Q, and (L/2A) on the right-hand side are known for each data point obtained by the user.
h c
6.3.2 The dependence of λ on T for cylindrical geometry is:
1 T
in
λ 5 λ~T! δT
*
m
T
ΔT
out
or;
Qln r /r
~ !
out in
λ 5 (18)
m
2 π L T 2 T
~ !
p in out
The quantities T ,T ,Q, 1n (r /r ) and 2π L on the right-hand side, are known for each data point obtained by the user.
in out out in p
6.4 Thermal Conductivity Integral (TCI) Method—To obtain the dependence of thermal conductivity on temperature from Eq
17 or Eq 18, a specific functional dependence to represent the conductivity-temperature relation must first be chosen. This Practice
recommends that the functional form of the describing equation closely describe the physical phenomena governing the heat
transfer through the sample. In addition, this functional form must be continuous over the temperature range of use. This will avoid
potential problems during data fitting and integration. (See Note 10.) While not absolutely necessary, choosing the physically
correct equation form can provide better understanding of the physical forces governing the heat flow behavior. After the form of
the thermal conductivity equation is chosen, steps 6.4.1 – 6.4.3 are followed to determine the coefficients for that equation.
6.4.1 Integrate the selected thermal conductivity function with respect to temperature. For example, if the selected function λ(T)
were a polynomial function of the form
n m
λ T 5 a 1a T 1a T , (19)
~ !
o n m
then, from Eq 18, the temperature-averaged thermal conductivity would be:
n11 n11 m11 m11
a T 2 T a T 2 T
~ ! ~ !
n h c m h c
λ 5 a 1 1 (20)
m o
n11 T 2 T m11 T 2 T
~ ! ~ ! ~ ! ~ !
h c h c
6.4.2 By means of any standard least-squares fitting routine, the right-hand side of Eq 20 is fitted against the values of
experimental thermal conductivity, λ . This fit determines the coefficients (a ,a ,a ) for the selected n and m in the thermal
exp o n m
conductivity function, Eq 19 in this case.
6.4.3 Use the coefficients obtained in 6.4.2 to describe the assumed thermal conductivity function, Eq 19. Each data point is then
conventionally plotted at the corresponding mean specimen temperature. When the function is plotted, it may not pass exactly
through the data points. This is because each data point represents mean conductivity, λ , and this is not equal to the value of the
m
thermal conductivity, λ (T ), at the mean temperature. The offset between a data point and the fitted curve depends on the size of
m
test ΔT and on the nonlinearity of the thermal conductivity function.
NOTE 10—Many equation forms other than Eq 19 can be used to represent the thermal conductivity function. If possible, the equation chosen to
represent the thermal conductivity versus temperature relationship should be easily integrated with respect to temperature. However, in some instances
it may be desirable to choose a form for λ(T) that is not easily integrated. Such equations may be found to fit the data over a much wider range of
temperature. Also, the user is not restricted to the use of polynomial equations to represent λ(T), but only to equation forms that can be integrated either
analytically or numerically. In cases where direct integration is not possible, one can carry out the same procedure using numerical integration.
6.5 TCI Method—A Summary—The thermal conductivity integral method of analysis is summarized in the following steps:
6.5.1 Measure several sets of λ , T , and T over a range of temperatures.
exp h c
6.5.2 Select a functional form for λ( T) as in Eq 19, and integrate it with respect to temperature to obtain the equivalent of Eq
20.
6.5.3 Perform a least-squares fit to the experimental data of the integral of the functional form obtained in 6.5.2 to obtain the
best values of the coefficients.
6.5.4 Use these coefficients to complete the λ(T) equation as defined in 6.5.2. Remember that the thermal conductivity equation
derived herein is good only over the range of temperatures encompassed by the test data. Extrapolation of the test results to a
temperature range not covered by the data is not acceptable.
7. Consideration of Test Result Significance
7.1 A final step in the analysis and reporting of test results requires that the data be reviewed for significance and accuracy. It
is not the intent of this practice to cover all aspects of the strategy of experimental design, but only to identify areas of concern.
C1045 − 19
Some additional information is provided in the Appendix but the interested reader is referred to the reference section for more
detailed information. The following areas should be considered in the evaluation of the test results produced using a Practice C1045
analysis.
7.2 Assessment of Apparatus Uncertainty—The determination of apparatus uncertainty should be performed as required by the
appropriate apparatus test method.
7.3 Material Inhomogeneity—The uncertainty caused by specimen inhomogeneity can seriously alter the measured dependen-
cies. To establish the possible consequences of material inhomogeneity on the interpretation of the results, the user shall measure
an adequate fraction of the product over the entire range of product manufacture variations. If possible, several specimens shall
be measured to sample a sufficient portion of the product. The resultant mean value of the measurements is representative of the
product to within the uncertainty of the mean, while the range of the results is indicative of the product inhomogeneity. Additional
information regarding sampling procedures can be found in Practice E122.
7.4 Test Grid—The thermal transmission properties determined for an insulation are dependent on several variables, including
product classification, temperature, density, plate emittance, fill-gas pressure, temperature difference, and fill-gas species. The
effect of the insulation material variability (inhomogeneity) is an important parameter in asessing the significance of results and
their application to design or quality control. A complete characterization of these dependencies would require the measurement
of thermal transmission for all possible combinations of these variables. Analysis of this magn
...