ASTM E457-96

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Designation: E 457 – 96
Standard Test Method for
Measuring Heat-Transfer Rate Using a Thermal Capacitance
(Slug) Calorimeter
This standard is issued under the fixed designation E 457; 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 multiplying the density, specific heat, and length of the slug by
the slope of the temperature–time curve obtained by the data
1.1 This test method describes the measurement of heat
acquisition system (see Eq 1).
transfer rate using a thermal capacitance-type calorimeter
3.3 The technique for measuring heat transfer rate by the
which assumes one-dimensional heat conduction into a cylin-
thermal capacitance method is illustrated schematically in Fig.
drical piece of material (slug) with known physical properties.
1. The apparatus shown is a typical slug calorimeter which, for
1.2 This standard does not purport to address all of the
example, can be used to determine both stagnation region heat
safety concerns, if any, associated with its use. It is the
transfer rate and side-wall or afterbody heat transfer rate
responsibility of the user of this standard to establish appro-
values. The annular insulator serves the purpose of minimizing
priate safety and health practices and determine the applica-
heat transfer to or from the body of the calorimeter, thus
bility of regulatory limitations prior to use.
approximating one-dimensional heat flow. The body of the
1.3 The values stated in SI units are to be regarded as the
calorimeter is configured to establish flow and should have the
standard.
same size and shape as that used for ablation models or test
NOTE 1—For information see Test Methods E 285, E 422, E 458,
specimens.
E 459, and E 511.
3.3.1 For the control volume specified in this test method, a
thermal energy balance during the period of initial linear
2. Referenced Documents
temperature response can be stated as follows:
2.1 ASTM Standards:
Energy Received by the Calorimeter ~front face! (1)
E 285 Test Method for Oxyacetylene Ablation Testing of
Thermal Insulation Materials 5 Energy Conducted Axially Into the Slug
E 422 Test Method for Measuring Heat Flux Using a
q 5rC l DT/Dt 5 MC /A DT/Dt
~ ! ~ ! ~ !
c p p
Water-Cooled Calorimeter
where:
E 458 Test Method for Heat of Ablation
q˙ 5 calorimeter heat transfer rate, W/m ,
E 459 Test Method for Measuring Heat Transfer Rate Using c
r5 density of slug material, kg/m ,
a Thin-Skin Calorimeter
C 5 average specific heat of slug material during the
p
E 511 Test Method for Measuring Heat Flux Using a
2 temperature rise (DT), J/kg·K,
Copper-Constantan Circular Foil, Heat-Flux Gage
l 5 length or axial distance from front face of slug to
the thermocouple location (back-face), m,
3. Summary of Test Method
DT 5 (T − T ) 5 calorimeter slug temperature rise dur-
f i
3.1 The measurement of heat transfer rate to a slug or
ing exposure to heat source (linear part of curve),
thermal capacitance type calorimeter may be determined from
K,
the following data:
Dt 5 (t − t ) 5 time period corresponding to DT tem-
f i
3.1.1 Density and specific heat of the slug material,
perature rise, s,
3.1.2 Length or axial distance from the front face of the
M 5 mass of the cylindrical slug, kg,
cylindrical slug to the back-face thermocouple, 2
A 5 cross-sectional area of slug, m .
3.1.3 Slope of the temperature—time curve generated by
In order to determine the steady-state heat transfer rate with
the back-face thermocouple, and
a thermal capacitance-type calorimeter, Eq 1 must be solved by
3.1.4 Calorimeter temperature history.
using the known properties of the slug material (for example,
3.2 The heat transfer rate is thus determined numerically by
density and specific heat)—the length of the slug, and the slope
(linear portion) of the temperature–time curve obtained during
This test method is under the jurisdiction of ASTM Committee E-21 on Space
Simulation and Applications of Space Technology and is the direct responsibility of
Subcommittee E21.08 on Thermal Protection.
Current edition approved Oct. 10, 1996. Published December 1996. Originally “Thermophysical Properties of High Temperature Solid Materials,” TPRC,
published as E 457 – 72. Last previous edition E 457 – 72 (1990)e . Purdue University, or “Handbook of Thermophysical Properties,” Tolukian and
Annual Book of ASTM Standards, Vol 15.03. Goldsmith, MacMillan Press, 1961.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
E 457
FIG. 1 Schematic of a Thermal Capacitance (Slug) Calorimeter
the exposure to a heat source. The initial and final temperature if severe pressure variations exist across the face of the
transient effects must be eliminated by using the initial linear calorimeter, side heating caused by flow into or out of the
portion of the curve (see Fig. 2). insulation gap would be minimized. Depending on the size of
3.3.2 In order to calculate the initial response time for a the calorimeter surface, variations in heat transfer rate may
given slug, Eq 2 may be used. exist across the face of the calorimeter; therefore, the measured
heat transfer rate represents an average heat transfer rate over
l rC 2
p
t 5 ln (2) the surface of the slug.
R 2
q indicated
kp
S D
1 2
3.5 Since interpretation of the data obtained by this test
q input
method is not within the scope of this discussion, such effects
where: as surface recombination and thermo-chemical boundary layer
k 5 thermal conductivity of slug material, W/m·K
reactions are not considered in this test method.
3.3.3 For maximum linear test time (temperature–time
3.6 If the thermal capacitance calorimeter is used to mea-
curve) within an allowed surface temperature limit, the relation
sure only radiative heat transfer rate or combined convective/
shown as Eq 3 may be used for a calorimeter which is insulated
radiative heat transfer rate values, the surface reflectivity of the
by a gap at the back face.
calorimeter should be measured over the wavelength region of
interest (depending on the source of radiant energy).
t 5 0.48 rlC ~DT /q˙! (3)
max,opt. p frontface
where:
4. Significance and Use
DT 5 the calorimeter final front face tempera-
front face
4.1 The purpose of this test method is to measure the rate of
ture minus the initial front face (ambi-
thermal energy per unit area transferred into a known piece of
ent) temperature, T .
o
material (slug) for purposes of calibrating the thermal environ-
3.3.4 Eq 3 is based on the optimum length of the slug which
ment into which test specimens are placed for evaluation. The
can be obtained by applying Eq 4 as follows:
calorimeter and holder size and shape should be identical to
l 5 3 k DT /5q˙ (4)
opt. front face c
that of the test specimen. In this manner, the measured heat
transfer rate to the calorimeter can be related to that experi-
3.4 To minimize side heating or side heat losses, the body is
separated physically from the calorimeter slug by means of an enced by the test specimen.
insulating gap or a low thermal diffusivity material, or both. 4.2 The slug calorimeter is one of many calorimeter con-
The insulating gap that is employed should be small, and cepts used to measure heat transfer rate. This type of calorim-
recommended to be no more than 0.05 mm on the radius. Thus, eter is simple to fabricate, inexpensive, and readily installed
since it is not water-cooled. The primary disadvantages are its
short lifetime and relatively long cool-down time after expo-
sure to the thermal environment. In measuring the heat transfer
Ledford, R. L., Smotherman, W. E., and Kidd, C. T., “Recent Developments in
Heat-Transfer Rate, Pressure, and Force Measurements for Hotshot Tunnels,”
rate to the calorimeter, accurate measurement of the rate of rise
AEDC-TR-66-228 (AD645764), January 1967.
in back-face temperature is imperative.
Kirchhoff, R. H., “Calorimetric Heating-Rate Probe for Maximum-Response-
4.3 In the evaluation of high-temperature materials, slug
Time Interval,” American Institute of Aeronautics and Astronautics Journal, AIAJA,
Vol 2, No. 5,
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