ASTM E2684-09

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Designation: E2684 − 09
Standard Test Method for
Measuring Heat Flux Using Surface-Mounted One-
Dimensional Flat Gages
This standard is issued under the fixed designation E2684; 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 Properties by Means of the Heat Flow Meter Apparatus
C1041Practice for In-Situ Measurements of Heat Flux in
1.1 This test method describes the measurement of the net
Industrial Thermal Insulation Using Heat Flux Transduc-
heatfluxnormaltoasurfaceusingflatgagesmountedontothe
ers
surface. Conduction heat flux is not the focus of this standard.
C1046Practice for In-Situ Measurement of Heat Flux and
Conduction applications related to insulation materials are
Temperature on Building Envelope Components
coveredbyTestMethodC518andPracticesC1041andC1046.
Thesensorscoveredbythistestmethodalluseameasurement
3. Terminology
of the temperature difference between two parallel planes
normaltothesurfacetodeterminetheheatthatisexchangedto 3.1 Definitions of Terms Specific to This Standard:
or from the surface in keeping with Fourier’s Law. The gages
3.1.1 heat flux—the heat transfer per unit area, q, with units
2 2
operate by the same principles for heat transfer in either
of W/m (Btu/ft -s). Heat transfer (or alternatively heat-
direction.
transfer rate) is the rate of thermal-energy movement across a
system boundary with units of watts (Btu/s). This usage is
1.2 Thistestmethodisquitebroadinitsfieldofapplication,
consistent with most heat-transfer books.
size and construction. Different sensor types are described in
detail in later sections as examples of the general method for 3.1.2 heat-transfer coeffıcient, (h)—an important parameter
2 2
measuring heat flux from the temperature gradient normal to a inconvectiveflowswithunitsofW/m -K(Btu/ft -s-F).Thisis
surface (1). Applications include both radiation and convec- defined in terms of the heat flux q as:
tion heat transfer. The gages have broad application from
q
h 5 (1)
aerospace to biomedical engineering with measurements rang-
∆T
ing form 0.01 to 50 kW/m . The gages are usually square or
where ∆T is a prescribed temperature difference between the
rectangular and vary in size from 1 mm to 10 cm or more on
surface and the fluid. The resulting value of h is intended to
be only a function of the fluid flow and geometry, not the
a side. The thicknesses range from 0.05 to 3 mm.
temperature difference. If the surface temperature is non-
1.3 The values stated in SI units are to be regarded as the
uniform or if there is more than a single fluid free stream
standard. The values stated in parentheses are provided for
temperature, the proper definition of ∆ T may be difficult to
information only.
specify (2). It is always important to clearly define ∆T when
calculating the heat-transfer coefficient.
1.4 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
3.1.3 surface emissivity, (ε)— the ratio of the emitted
responsibility of the user of this standard to establish appro-
thermal radiation from a surface to that of a blackbody at the
priate safety and health practices and determine the applica-
same temperature. Surfaces are assumed to be gray bodies
bility of regulatory limitations prior to use.
where the emissivity is equal to the absorptivity.
2. Referenced Documents
4. Summary of Test Method
2.1 ASTM Standards:
4.1 A schematic of the sensing technique is illustrated in
C518Test Method for Steady-State Thermal Transmission
Fig. 1. Temperature is measured on either side of a thermal
resistance layer of thickness, δ. This is the heat-flux sensing
mechanismofthistestmethod.Themeasuredheatfluxisinthe
This test method is under the jurisdiction of ASTM Committee E21 on Space
same direction as the temperature difference and is propor-
Simulation andApplications of SpaceTechnology and is the direct responsibility of
Subcommittee E21.08 on Thermal Protection.
tional to the temperature gradient through the thermal-
Current edition approved June 15, 2009. Published August 2009. DOI: 10.1520/
resistancelayer(TRL).Theresistancelayerischaracterizedby
E2684-09.
itsthickness,δ,thermalconductivity, k,andthermaldiffusivity,
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this test method. α.Thepropertiesaregenerallyaweakfunctionoftemperature.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2684 − 09
FIG. 1 Layered Heat-Flux Gage
k
5.1.1 Temperature limitations are determined by the gage
q 5 T 2 T (2)
~ !
1 2
δ material properties and the method of application to the
surface. The range of heat flux that can be measured and the
From this point the different gages may vary substantially
time response are limited by the gage design and construction
in how the temperature difference T − T is measured and
2 2
1 2
details. Measurements from 10W/m to above 100 kW/m are
the thickness of the thermal resistance layer used. These as-
easily obtained with current sensors. Time constants as low as
pects of each different type of sensor are discussed along
10 ms are possible, while thicker sensors may have response
with the implications for measurements.
timesgreaterthan1s.Itisimportanttochoosethesensorstyle
4.2 Heat-flux gages using this test method generally use
andcharacteristicstomatchtherangeandtimeresponseofthe
either thermocouple elements or resistance-temperature ele-
required application.
ments to measure the required temperatures.
4.2.1 Resistance temperature detectors (RTDs) generally
5.2 The measured heat flux is based on one-dimensional
havegreatersensitivitytotemperaturethanthermocouples,but
analysis with a uniform heat flux over the surface of the gage
require separate temperature measurements on each side of the
surface. Because of the thermal disruption caused by the
thermal-resistance layer. The temperature difference must then
placement of the gage on the surface, this may not be true.
be calculated as the small difference between two relatively
Wesley (3) and Baba et al. (4) have analyzed the effect of the
large values of temperature.
gage on the thermal field and heat transfer within the surface
4.2.2 Thermocouples can be arranged in series across the
substrate and determined that the one-dimensional assumption
thermal-resistance layer as differential thermocouple pairs that
is valid when:
measure the temperature difference directly.The pairs can also
δk
beputinseriestoformadifferentialthermopiletoincreasethe .1 (4)
Rk
s
sensitivity to heat flux.
where:
E Nσ δ
T
S 5 5 (3)
k = the thermal conductivity of the substrate material,
q k s
R = the effective radius of the gage,
δ = the combined thickness, and
Here N represents the number of thermocouple pairs form-
ing the differential thermopile and σ is the effective tem- k = the effective thermal conductivity of the gage and
T
perature sensitivity (Seebeck coefficient) of the two thermo-
adhesive layers.
couple materials. Although the voltage output is directly
5.3 Measurements of convective heat flux are particularly
proportional to the heat flux, the sensitivity may be a func-
tion of the gage temperature.
sensitive to disturbances of the temperature of the surface.
Because the heat transfer coefficient is also affected by any
5. Significance and Use
non-uniformities of the surface temperature, the effect of a
small temperature change with location is further amplified, as
5.1 Thistestmethodwillprovideguidanceforthemeasure-
explained by Moffat et al. (2) and Diller (5). Moreover, the
ment of the net heat flux to or from a surface location. To
smaller the gage surface area, the larger is the effect on the
determine the radiant energy component the emissivity or
heat-transfer coefficient of any surface temperature non-
absorptivity of the gage surface coating is required and should
uniformity. Therefore, surface temperature disruptions caused
be matched with the surrounding surface. The potential physi-
by the gage should be kept much smaller than the surface to
cal and thermal disruptions of the surface due to the presence
environment temperature difference causing the heat flux.This
of the gage should be minimized and characterized. For the
necessitates a good thermal path between the gage and the
case of convection and low source temperature radiation to or
surface onto which it is mounted.
fromthesurfaceitisimportanttoconsiderhowthepresenceof
the gage alters the surface heat flux. The desired quantity is 5.3.1 Fig. 2 shows a heat-flux gage mounted onto a plate
usually the heat flux at the surface location without the with the surface temperature of the gage of T and the surface
s
presence of the gage. temperature of the surrounding plate of T .The goal is to keep
p
E2684 − 09
FIG. 2 Diagram of an Installed Surface-Mounted Heat-Flux Gage
the gage surface temperature as close as possbible to the plate bottom temperature sensors simply need to be at a uniform
temperature to minimize the thermal disruption of the gage. temperature and the top temperature sensors need to be at a
Thisrequiresthethermalresistanceofthegageandadhesiveto
temperature dictated by the heat flux perpendicular to the
be minimized along the thermal pathway from T and T . surface. This can be accomplished on a high-conductivity
s p
5.3.2 Another method to avoid the surface temperature
substrate by separate thermal-resistance pads for the top
disruption problem is to cover the entire surface with the temperature measurements. Several examples are given of the
heat-flux gage material. This effectively ensures that the
thermopile and RTD based types of gages.
thermalresistancethroughthegageismatchedwiththatofthe
6.2 Thermopile Gages—Thermopile gages are based on
surrounding plate. It is important to have independent mea-
thermocouples forming multiple junctions on either side of the
sures of the substrate surface temperature and the surface
TRL.Ifproperlymountedanddesignedfortheapplication,the
temperatureofthegage.Thegagesurfacetemperaturemustbe
operation of these heat-flux gages is simple. There is no
used for defining the value of the heat-transfer coefficient.
activation current or energy required for the thermocouple
When the gage material does not cover the entire surface, the
sensor units. The output voltage is continuously generated by
temperature measurements are needed to ensure that the gage
the gage in proportion to the number of thermocouple pairs
does indeed provide a small thermal disruption.
wired in series. The output can be directly connected to an
5.4 Thetimeresponseoftheheat-fluxgagecanbeestimated
appropriate differential amplifier and voltage readout device.
analytically if the thermal properties of the thermal-resistance
6.2.1 An early report of the layered sensor (6) used a single
layer are well known. The time required for 98 % response to
thermocouple pair across the resistance layer. Ortolano and
a step input (6) based on a one-dimensional analysis is:
Hines (10) used a number of thermocouple pairs as described
1.5δ by Eq 3 to give a larger voltage output.The thermocouples are
t 5 (5)
α placed as foils around a Kapton thermal-resistance layer and
butt welded on either side, as illustrated in Fig. 3. Kapton
where α is the thermal diffusivity of the TRL. Covering or
sheetsareusedaroundthegageforencasementandprotection.
encapsulation layers must also be included in the analysis.
The resulting Micro-Foil gage is 75 to 400 µm thick and
Uncertainties in the gage dimensions and properties require a
flexible for easy attachment to surfaces, but the low conduc-
direct experimental verification of the time response. If the
tivity (high thermal resistance) of the materials must be
gage is designed to absorb radiation, a pulsed laser or opti-
considered when used for convection measurements. The
cally switched Bragg cell can be used to give rise times of
less than 1 µs (7,8). However, a mechanical wheel with slits sensors are limited to temperatures below (250°C) and heat
can be used with a light to give rise times on the order of 1 fluxes less than 100 kW/m . The time response can be as fast
ms (9), which is generally sufficient. as 20 ms, but transient signals may be attenuated unless the
frequency of the disturbance is less than a few hertz.
5.4.1 Because the response of these sensors is close to an
6.2.2 Terrell (11) describes a gage design (Episensor) made
exponentialrise,ameasureofthetimeconstantτforthesensor
with screen printing techniques of conductive inks. A copper/
can be obtained by matching the experimental response to step
nickel thermocouple pair is used with a dielectric ink for the
changes in heat flux with exponential curves.
thermal-resistance layer. The inks are printed onto anodized
2t/τ
q 5 q ~1 2 e ! (6)
ss aluminum shim stock for the substrate. Although the entire
package is 350 µm thick, the thermal resistance is low because
The value of the step change in imposed heat flux is repre-
of the high thermal conductivity of all of the materials.
sented by q . The resulting time constant characterizes the
ss
Because of the large number of thermocouple pairs (up to
first-order sensor response.
10,000), sensitivities are sufficient to measure heat fluxes as
6. Apparatus-Sensor Construction
lowas0.1W/m .Thethermaltimeconstantisabout1sandthe
upper temperature limit is approximately 150°C. The alumi-
6.1 Temperature sensors are mounted or deposited on either
num base allows some limited conformance to a surface.
side of the thermal-resistance layer (TRL), which is usually a
thin material which can be mounted on the test object. The 6.2.3 The thermopile connections can also be made through
method of construction and details of operation varies for each small holes in theTRL. Plating of copper and nickel is used to
different type of gage. Although most of the gages place the create such a gage (BF Heat Flux Transducer) from 1 cm
temperature sensors directly over top of each other across the square to 32 cm square with a high density of junctions per
TRL, it is not a requirement for proper measurement. The area. The thickness is 200 µm which gives a time constant of
E2684 − 09
FIG. 3 Micro-Foil Heat-Flux Gage
approximately1s.Ithaslimitedflexibilityandhasamaximum across the silicone monoxide. A bridge circuit is used with a
operating temperature of 150°C. one volt excitation across the two resistances to provide two
6.2.4 Another
...