ASTM C1045-97
(Practice)Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions
Standard Practice for Calculating Thermal Transmission Properties Under Steady-State Conditions
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 C 177, C 335, C 518, C 976, C 1033, C 1114 and C 1363 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 C 680.
1.4 The SI unit values used in this practice are considered 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 (21); (2) a phase change of one of the insulation system components such as a blowing gas in foam; and (3) the influence of heat flow direction and temperature difference changes for reflective insulations.
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Standards Content (Sample)
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Designation: C 1045 – 97
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
Standard Practice for
Calculating Thermal Transmission Properties Under Steady-
State Conditions
This standard is issued under the fixed designation C 1045; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope ties of Horizontal Pipe Insulations
C 518 Test Method for Steady-State Heat Flux Measure-
1.1 This practice covers requirements and guidelines for the
ments and Thermal Transmission Properties by Means of
determination of thermal transmission properties based upon
the Heat Flow Meter Apparatus
steady-state one dimensional heat transfer tests on a thermal
C 680 Practice for Determination of Heat Gain or Loss and
insulation material or system for which values of heat flux,
the Surface Temperature of Insulated Pipe and Equipment
surface or air temperatures, and specimen geometry are re-
Surfaces by the Use of a Computer Program
ported from standard test methods.
C 745 Test Method for Heat Flux Through Evacuated Insu-
1.2 The thermal transmission properties described include:
lations Using a Guarded Flat Plate Boiloff Calorimeter,
thermal conductance, thermal resistance, apparent thermal
C 976 Test Method for Steady-State Thermal Performance
conductivity, apparent thermal resistivity, surface conductance,
of Building Assemblies by Means of a Calibrated Hot Box
surface resistance, and overall thermal resistance or transmit-
C 1033 Test Method for Steady-State Heat Transfer Prop-
tance.
erties of Pipe Insulation Installed Vertically
1.3 This practice is restricted to calculation of thermal
C 1058 Practice for Selecting Temperatures for Evaluating
transmission properties from heat transfer data generated by
and Reporting Properties of Thermal Insulation
standard test methods. These methods include: (1) planar
C 1114 Test Method for Steady-State Thermal Transmission
geometries such as those used in Test Methods C 177, C 236,
Properties by Means of the Thin-Heater Apparatus
C 518, C 745, C 976, and C 1114, and (2) radial geometries
E 122 Practice for Choice of Sample Size to Estimate the
such as those used in Test Methods C 335 and C 1033.
Average Quality of a Lot or Process
1.4 This practice includes the procedure for development of
thermal conductivity as a function of temperature equation
3. Terminology
from data generated by standard test methods.
3.1 Definitions—The definitions and terminology of this
1.5 The values stated in SI units are to be regarded as the
practice are intended to be consistent with Terminology C 168.
standard.
However, because exact definitions are critical to the use of this
1.6 The attached appendixes provide discussions of the
practice, the following equations are defined here for use in the
thermal properties of thermal insulating materials, the devel-
calculations section of this practice.
opment of the basic relationships used in this practice, and
3.2 Symbols—The symbols, terms and units used in this
examples of their use.
practice are the following:
2. Referenced Documents
2.1 ASTM Standards: 2
A 5 specimen area normal to heat flux direction, m ,
C 168 Terminology Relating to Thermal Insulating Materi-
l5 thermal conductivity or apparent thermal conduc-
als
tivity, W/(m · K),
C 177 Test Method for Steady-State Heat Flux Measure-
l(T) 5 the functional relationship between thermal con-
ments and Thermal Transmission Properties by Means of
ductivity and temperature, W/(m K),
the Guarded-Hot-Plate Apparatus
l 5 the experimental thermal conductivity, W/(m K),
exp
C 236 Test Method for Steady-State Thermal Performance
l 5 mean thermal conductivity, averaged with respect
m
of Building Assemblies by Means of a Guarded Hot Box
to temperature from T to T , W/(m · K),
c h
C 335 Test Method for Steady-State Heat Transfer Proper-
C 5 thermal conductance, W/(m K),
h 5 surface coefficient, hot side, W/(m K),
h
h 5 surface coefficient, cold side, W/(m K),
c
This practice is under the jurisdiction of ASTM Committee C-16 on Thermal
l 5 metering area length in the axial direction, m,
Insulation and is the direct responsibility of Subcommittee C16.30 on Thermal
Measurements.
Current edition approved Aug. 10, 1997. Published July 1998. Originally
published as C 1045 – 85. Last previous edition C 1045 – 90.
2 3
Annual Book of ASTM Standards, Vol 04.06. Annual Book of ASTM Standards, Vol 14.02.
C 1045
q 5 one-dimensional heat flux (time rate of heat flow T 5 temperature at the outer radius.
c
through metering area divided by the apparatus
3.3.4 Apparent thermal resistivity, r, is defined in Terminol-
metering area A), W/m ,
ogy C 168.
Q 5 time rate of one-dimensional heat flow through the
Rectangular coordinates:
metering area of the test apparatus, W,
A ~T 2 T !
h c
r 5 radius of a hollow cylinder at the i th surface, m,
r8 5 (5)
i
QL
r8 5 thermal resistivity, K m/W,
Cylindrical coordinates:
R 5 thermal resistance, m K/W,
R 5 surface resistance, hot side, m K/W,
h
2 p l ~T 2 T !
h c
r8 5 (6)
R 5 surface resistance, cold side, m K/W,
c
Q ln ~r / r !
2 1
R 5 overall thermal resistance, m K/W,
u
NOTE 3—Thermal resistivity, r8, and the corresponding thermal con-
T 5 temperature, K,
ductivity, l, are reciprocals, that is, their product is unity. These terms
T 5 area-weighted air temperature 75 mm or more
apply to specific materials tested between two specified isothermal
from the hot side surface, K,
surfaces. For this practice, materials are considered homogeneous when
T 5 area-weighted temperature of specimen hot sur-
h
the value of the thermal conductivity or thermal resistivity is not
face, K,
significantly affected by variations in the thickness or area of the sample
T 5 area-weighted temperature of the specimen cold
c
within the normally used range of those variables.
surface, K,
3.4 Thermal Transmission Property Equations for Convec-
T 5 area-weighted air temperature 75 mm or more
tive Boundary Conditions:
from the cold side surface, K,
3.4.1 Surface resistance, R , the quantity determined by the
T 5 specimen mean temperature, average of two oppo-
i
m
temperature difference at steady-state between an isothermal
site surface temperatures, (T + T )/2, K,
h c
DT 5 temperature difference, K, surface and its surrounding air that induces a unit heat flow per
DT 5 temperature difference, surface to surface, (T − unit area to or from the surface. Typically, this parameter
s-s h
T ), K, includes the combined effects of conduction, convection, and
c
DT 5 temperature difference, air to air, (T − T ), K,
radiation. Surface resistances are calculated as follows:
a-a 1 2
U 5 thermal transmittance, W/(m K), and
A ~T 2 T !
1 h
x 5 linear dimension in the heat flow direction, m. R 5 (7)
h
Q
3.3 Thermal Transmission Property Equations:
A ~T 2 T !
c 2
3.3.1 Thermal resistance, R, is defined in Terminology
R 5 (8)
c
Q
C 168. It is not necessarily a unique function of temperature or
material, but is rather a property determined by the specific NOTE 4—Subscripts 1 and 2 are used to differentiate between the hot
and cold side air, respectively.
thickness of the specimen and by the specific range of
temperatures used to measure the thermal resistance.
3.4.2 Surface coeffıcient, h, is often called the film coeffi-
A ~T – T ! cient. These coefficients are calculated as follows:
h c
R 5 (1)
Q
Q
h 5 (9)
h
3.3.2 Thermal Conductance, C: A ~T 2 T !
1 h
Q Q
h 5 (10)
C 5 (2)
c
A ~T 2 T ! A ~T 2 T !
h c c 2
NOTE 1—Thermal resistance, R, and the corresponding thermal con- NOTE 5—The surface coeffıcient, h , and the corresponding surface
i
ductance, C, are reciprocals, that is, their product is unity. These terms resistance, R , are reciprocals, that is, their product is unity.
i
apply to specific bodies or constructions as used, either homogeneous or
3.4.3 Overall thermal resistance, R —the quantity deter-
u
heterogeneous, between two specified isothermal surfaces.
mined by the temperature difference at steady-state between
NOTE 2—Subscripts h and c are used to differentiate between hot side
the air temperatures on the two sides of a body or assembly that
and cold side surfaces.
induces a unit time rate of heat flow per unit area through the
3.3.3 Apparent thermal conductivity, l, is defined in Termi-
body. It is the sum of the resistances of the body or assembly
nology C 168.
and of the two surface resistances and may be calculated as
Rectangular coordinates:
follows:
QL
A ~T 2 T !
l5 (3) 1 2
A ~T 2 T ! R 5 (11)
h c u
Q
Cylindrical coordinates:
5 R 1 R 1 R
c h
Q ln~r /r !
2 1
3.4.4 Thermal transmittance, U (sometimes called overall
l5 (4)
2 p l ~T 2 T !
h c
coefficient of heat transfer), is calculated as follows:
Q
where:
U 5 (12)
A T – T !
r 5 inner radius, ~
1 2
T 5 temperature at the inner radius,
h
The transmittance can be calculated from the thermal con-
r 5 outer radius, and
ductance and the surface coefficients as follows:
C 1045
1/U 5 ~1/h ! 1 ~1/C! 1 ~1/h ! (13) R ) to be calculated from the test results.
h c
u
5.3 Calculate the thermal property of interest using the data
NOTE 6—Thermal transmittance, U, and the corresponding overall
from the test as described in 5.1, and the appropriate equation
thermal resistance, R , are reciprocals, that is, their product is unity.
u
in 3.3 or 3.4.
4. Significance and Use
5.4 Using the data from the test as described in 5.1,
4.1 ASTM thermal test methods are complex because of
determine the test mean temperature for the thermal property of
added apparatus details necessary to ensure accurate results. As 5.3 using the following equation:
a result, many users find it difficult to locate the data reduction
T 5 ~T 1 T !/2 (14)
m h c
details necessary to reduce the data obtained from these tests.
NOTE 8—The thermal transmission properties determined in 5.3 are
This practice is designed to be referenced in the thermal test
applicable only for the conditions of the test. Further analysis is required
methods, thus allowing them to concentrate on experimental
using data from multiple tests if the relationship for the thermal property
details rather than data reduction.
variation with mean test temperature is to be determined. If this relation-
4.2 This practice is intended to provide the user with a
ship is required, the analysis to be followed is presented in Section 6.
uniform procedure for calculating the thermal transmission
5.5 An Example of a Computation of Thermal Conductivity
properties of a material or system from standard test methods
Measured in a Two-Sided Guarded Hot Plate:
used to determine heat flux and surface temperatures. This
5.5.1 For a guarded hot plate apparatus in the normal,
practice is intended to replace the similar calculation sections
double-sided mode of operation, the heat developed in the
of Test Methods C 177, C 236, C 335, C 518, C 745, C 976,
metered area heater passes through two specimens. To reflect
C 1033, and C 1114.
this fact, Eq 3 for the operational definition of the mean
4.3 This practice provides the method for developing the
thermal conductivity of the pair of specimens must be modified
thermal conductivity as a function of temperature for a
to read:
specimen from data taken at small or large temperature
Q
differences. This relationship can be used to characterize
l 5 (15)
exp
A @~DT/L! 1~DT/L! #
1 2
material for comparison to material specifications and for use
in calculations programs such as Practice C 680.
where:
4.4 Two general solutions to the problem of establishing
(D/T /L) 5 the ratio of surface to surface temperature
ss 1
thermal transmission properties for application to end-use
difference to thickness for Specimen 1. A
conditions are outlined in Practice C 1058. (Practice C 1058
similar expression is used for Specimen 2.
should be reviewed prior to use of this practice.) One is to
5.5.2 In many experimental situations, the two temperature
measure each product for each end-use condition. This solution
differences are very nearly equal (within well under 1 %), and
is rather straightforward and needs no other elaboration. The
the two thicknesses are also nearly equal (within 1 %), so that
second is to measure each product over the entire temperature
Eq 15 may be well approximated by a simpler form:
range of application conditions and to use these data to
QL
average
establish the thermal-transmission property dependencies on
l 5 (16)
exp
2A DT
average
the various end-use conditions. One advantage of the second
approach is that once these dependencies have been estab-
where:
lished, they serve as the basis for estimating the performance
DT 5 the arithmetic mean temperature difference
average
for a given product to other conditions.
(DT +DT )/2,
1 2
4.5 Precaution—The use of thermal curves developed in L 5 (L +L )/2 is the arithmetic mean of the two
average 1 2
Section 6 must be limited to a temperature range that does not specimen thicknesses, and
2A 5 occurs because the metered power flows out
extend to less than the lowest surface temperature or higher
than the highest surface temperature for the test data set used through two surfaces of the metered area for
this apparatus. For clarity in later discussions,
to generate the curves.
use of this simpler form, Eq 16, will be
5. Determination of Thermal Transmission Properties for
assumed.
a Specific Temperature
NOTE 9—The mean thermal conductivity, l , is usually not the same as
5.1 Using the appropriate test method of interest, determine m
the thermal conductivity, l (T ), at the mean temperature T . The mean
m m
the steady-state heat flux and temperature data for the test.
thermal conductivity, l , and the thermal conductivity at the mean
m
NOTE 7—The calculation of thermal properties requires that: (1) the temperature, l (T ), are equal only in the special case where l (T)isa
m
thermal insulation specimen is homogeneous, as defined in Terminology constant or linear function of temperature (1), that is, when there is no
C 168 or, as a minimum, appears uniform across the test area; (2) the curvature (nonlinearity) in the conductivity-temperature relation. In all
measurements are taken only after steady-state has been established; (3) other cases, the conductivity, l , as determined by Eq 3 is not simply a
exp
the heat flows in a direction normal to the isothermal surfaces of the function of mean temperature, but depends on the values of both T and T .
h c
specime
...
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