ASTM C1045-07(2013)
(Practice)Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions
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 ot...
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...
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Standards Content (Sample)
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Designation: C1045 − 07 (Reapproved 2013)
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) a phase change of one of the insulation
C1033, C1114 and C1363 and Practices C1043 and C1044 by
system components such as a blowing gas in foam; and (3) the
permitting use of these standard calculation forms by refer-
influence of heat flow direction and temperature difference
ence.
changes for reflective insulations.
1.2 The thermal transmission properties described include:
thermal conductance, thermal resistance, apparent thermal
2. Referenced Documents
conductivity,apparentthermalresistivity,surfaceconductance,
2.1 ASTM Standards:
surface resistance, and overall thermal resistance or transmit-
C168Terminology Relating to Thermal Insulation
tance.
C177Test Method for Steady-State Heat Flux Measure-
1.3 This practice provides the method for developing the
ments and Thermal Transmission Properties by Means of
apparent thermal conductivity as a function of temperature
the Guarded-Hot-Plate Apparatus
relationship for a specimen from data generated by standard
C335TestMethodforSteady-StateHeatTransferProperties
test methods at small or large temperature differences. This
of Pipe Insulation
relationship can be used to characterize material for compari-
C518Test Method for Steady-State Thermal Transmission
son to material specifications and for use in calculation
Properties by Means of the Heat Flow Meter Apparatus
programs such as Practice C680.
C680Practice for Estimate of the Heat Gain or Loss and the
Surface Temperatures of Insulated Flat, Cylindrical, and
1.4 The values stated in SI units are to be regarded as
Spherical Systems by Use of Computer Programs
standard. No other units of measurement are included in this
C1033Test Method for Steady-State Heat Transfer Proper-
standard.
ties of Pipe Insulation Installed Vertically (Withdrawn
1.5 Thispracticeincludesadiscussionofthedefinitionsand
2003)
underlying assumptions for the calculation of thermal trans-
C1043Practice for Guarded-Hot-Plate Design Using Circu-
mission properties. Tests to detect deviations from these
lar Line-Heat Sources
assumptions are described. This practice also considers the
C1044Practice for Using a Guarded-Hot-PlateApparatus or
complicating effects of uncertainties due to the measurement
Thin-Heater Apparatus in the Single-Sided Mode
processes and material variability. See Section 7.
C1058Practice for Selecting Temperatures for Evaluating
1.6 Thispracticeisnotintendedtocoverallpossibleaspects
and Reporting Thermal Properties of Thermal Insulation
of thermal properties data base development. For new
C1114Test Method for Steady-State Thermal Transmission
materials, the user should investigate the variations in thermal
Properties by Means of the Thin-Heater Apparatus
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 service@astm.org. For Annual Book of ASTM
Measurement. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Sept. 1, 2013. Published January 2014. Originally the ASTM website.
approved in 1985. Last previous edition approved in 2007 as C1045–07. DOI: The last approved version of this historical standard is referenced on
10.1520/C1045-07R13. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1045 − 07 (2013)
C1199TestMethodforMeasuringtheSteady-StateThermal
λ = apparent thermal conductivity, W/(m·K),
a
Transmittance of Fenestration Systems Using Hot Box
λ(T) = functional relationship between thermal conductiv-
Methods
ity and temperature, W/(m·K),
C1363Test Method for Thermal Performance of Building λ = experimental thermal conductivity, W/(m·K),
exp
Materials and Envelope Assemblies by Means of a Hot λ = meanthermal conductivity, averagedwithrespect to
m
temperature from T to T , W/(m·K), (see sections
Box Apparatus
c h
E122PracticeforCalculatingSampleSizetoEstimate,With 6.4.1 and Appendix X3).
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
the difference in areas is considered. (See Eq 4 and Eq 6.) In
metering area A), W/m ,
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,
thickness
a
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
2 π L T 2 T
T = area-weighted air temperature 75 mm or more from
~ !
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
~ ! 1
out p in out
r 5 5 (6)
a
∆T = temperature difference, K,
Qln r /r λ
~ out in! a
∆T = temperature difference, air to air, (T − T ), K,
a-a 1 2 NOTE 3—The apparent thermal resistivity, r , and the corresponding
a
∆T = temperature difference, surface to surface,
thermal conductivity, λ , are reciprocals, that is, their product is unity.
s-s
a
These terms apply to specific materials tested between two specified
(T − T ), K,
h c
isothermal surfaces. For this practice, materials are considered homoge-
U = thermal transmittance, W/(m ·K), and
neous when the value of the thermal conductivity or thermal resistivity is
x = linear dimension in the heat flow direction, m,
not significantly affected by variations in the thickness or area of the
λ = thermal conductivity, W/(m·K),
sample within the normally used range of those variables.
C1045 − 07 (2013)
3.4 Transmission Property Equations for Convective 4.2 This practice is intended to provide the user with a
Boundary Conditions: uniform procedure for calculating the thermal transmission
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
follows:
4.3 This practice provides the method for developing the
thermal conductivity as a function of temperature for a
A ~T 2 T !
1 h
R 5 (7)
h
specimen from data taken at small or large temperature
Q
differences. This relationship can be used to characterize
A T 2 T
~ !
c 2
R 5 (8) material for comparison to material specifications and for use
c
Q
in calculations programs such as Practice C680.
3.4.2 Surface Heat Transfer Coeffıcient, h, is often called
i
4.4 Two general solutions to the problem of establishing
the film coefficient. These coefficients are calculated as fol-
thermal transmission properties for application to end-use
lows:
conditions are outlined in Practice C1058. (Practice C1058
should be reviewed prior to use of this practice.) One is to
Q 1
h 5 5 (9)
h
A T 2 T R measure each product at each end-use condition. This solution
~ !
1 h h
is rather straightforward, but burdensome, and needs no other
Q 1
h 5 5 (10)
elaboration. The second is to measure each product over the
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
unity.Thesepropertiesaremeasuredataspecificsetofambientconditions dependenciesatthevariousend-useconditions.Oneadvantage
and are therefore only correct for the specified conditions of the test.
of the second approach is that once these dependencies have
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 ~T 2 T !
1 2
a Specific Set of Temperature Conditions
R 5 (11)
u
Q
5.1 Choose the thermal test parameter (λ or r, R or C, U or
5 R 1R1R R ) to be calculated from the test results. List any additional
c h u
information required by that calculation i.e. heat flux,
3.4.4 Thermal Transmittance, U (sometimes called overall
temperatures, dimensions. Recall that the selected test param-
coefficient of thermal transfer), is calculated as follows:
etermightlimittheselectionofthethermaltestmethodusedin
Q 1 5.2.
U 5 5 (12)
A T 2 T R
~ !
1 2 u
5.2 Select the appropriate test method that provides the
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)
~ ! ~ ! ~ !
h c
determination.
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
properties are measured at a specific set of ambient conditions and are
state heat flux and temperature data at the selected test
therefore only correct for the specified conditions of the test.
condition.
NOTE 6—The calculation of specific thermal transmission properties
4. Significance and Use
requires that: (1) the thermal insulation specimen is homogeneous, as
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
surfaces of the specimen; (4) the rate of flow of heat is known; (
...
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