Abstrict An apparatus, such as, a heat flow meter instrument, for measuring
thermal properties of a specimen includes a first thermoelectric
device and a second thermoelectric device, each device being thermally
coupled to a hot plate and a cold plate, and a heat flow transducer,
thermally connectable to a specimen and constructed to measure heat
flowing through the specimen. The heat flow transducer and the specimen
are positionable in thermal contact between the hot plate of the
first thermoelectric device and the cold plate of the second thermoelectric
device. The apparatus also includes an electric power supply connected
to provide controlled amounts of electric power to the first and
second thermoelectric devices to maintain the plates at selected
temperatures, and a processor connected to receive from the heat
flow transducer a signal corresponding to the measured heat. The
processor is programmed to calculate a thermal property of the specimen
based on the temperatures and the measured heat. The apparatus includes
a closed loop heat exchange system, thermally connecting the cold
plate of the first thermoelectric device and the hot plate of the
second thermoelectric device, constructed and arranged to transfer
heat between the plates. The closed loop heat exchange system may
include a fluid pump and a first set of conduits thermally connected
to the cold plate of the first thermoelectric device and a second
set of conduits thermally connected to the hot plate of the second
thermoelectric device. The conduits convey a heat exchange fluid
in a closed loop arrangement.
Claims What is claimed is:
1. An apparatus for measuring a thermal property of a specimen
comprising:
a first thermoelectric device and a second thermoelectric device,
each said device being thermally coupled to a hot plate and a cold
plate;
a heat flow transducer, thermally connectable to a specimen, the
combination of said heat flow transducer and said specimen being
positionable in thermal contact between said hot plate of said first
thermoelectric device and said cold plate of said second thermoelectric
device, said heat flow transducer being constructed and arranged
to measure heat flowing through said specimen from said hot plate
to said cold plate;
an electric power supply connected to provide simultaneously electric
power to said first and second thermoelectric devices to maintain
said plates at selected temperatures; and
a processor connected to receive from said heat flow transducer
a signal corresponding to said measured heat; said processor being
further programmed to calculate a thermal property of said specimen
based on said temperatures and said measured heat.
2. The apparatus of claim 1 wherein said thermoelectric device
includes pairs of N-type and P-type semiconductors.
3. The apparatus of claim 1 further comprising a first temperature
sensor and a second temperature sensor located in thermal contact
with said hot plate of said first thermoelectric device and a cold
plate of said second thermoelectric device, respectively.
4. The apparatus of claim 1 further comprising:
a heat exchange system, thermally connected to said cold plate
of said first thermoelectric device or said hot plate of said second
thermoelectric device and constructed and arranged to transfer heat
to or from said plates.
5. An apparatus for measuring thermal properties of a specimen
comprising:
a first thermoelectric device and a second thermoelectric device,
each said device being thermally coupled to a hot plate and a cold
plate;
a heat flow transducer, thermally connectable to a specimen, the
combination of said heat flow transducer and said specimen being
positionable in thermal contact between said hot plate of said first
thermoelectric device and said cold plate of said second thermoelectric
device, said heat flow transducer being constructed and arranged
to measure heat flowing through said specimen from said .hot plate
to said cold plate;
at least one electric power supply connected to provide controlled
amounts of electric power to said first thermoelectric device and
said second thermoelectric device to maintain said plates at selected
temperatures;
a closed loop heat exchange system, thermally connecting said cold
plate of said first thermoelectric device and said hot plate of
said second thermoelectric device, constructed and arranged to transfer
heat between said plates; and
a processor connected to receive from said heat flow transducer
a signal corresponding to said measured heat, said processor being
further programmed to calculate a thermal property of said specimen
based on said temperatures and said measured heat.
6. The apparatus of claim 5 wherein said closed loop heat exchange
system includes a first set of conduits thermally connected to said
cold plate of said first thermoelectric device and a second set
of conduits thermally connected to said hot plate of said second
thermoelectric device, said conduits constructed to convey a heat
exchange fluid in a closed loop arrangement; and a fluid pump being
constructed to circulate said fluid.
7. The apparatus of claim 6 wherein said closed loop heat exchange
system includes a heater constructed to heat said heat exchange
fluid to a selected temperature.
8. The apparatus of claim 6 wherein said closed loop heat exchange
system includes a refrigerator constructed to cool said heat exchange
fluid to a selected temperature.
9. The apparatus of claim 1 3 4 or 5 further comprising:
a second heat flow transducer constructed to measure a flow of
heat, said first and said second heat flow transducer arranged in
thermal contact with both sides of said specimen.
10. The apparatus of claim 1 4 or 6 further comprising a thermal
guard member constructed and arranged to prevent a lateral heat
loss from said specimen.
11. The apparatus of claim 10 wherein said thermal guard member
includes a set of conduits connected to said closed loop heat exchange
system and constructed to convey said heat exchange fluid.
12. The apparatus of claim 1 wherein said electric power supply
is a current supply constructed to deliver DC current to said first
thermoelectric device and said second thermoelectric device connected
in series.
13. The apparatus of claim 1 wherein said electric power supply
is a voltage source connected to deliver DC voltage to said first
thermoelectric device and said second thermoelectric device.
14. The apparatus of claim 1 or 5 further comprising a potentiometer
constructed and arranged to provide a signal corresponding to the
thickness of said specimen.
15. The apparatus of claim 1 or 5 wherein said processor is further
arranged to calculate said thermal property under steady-state thermal
conditions.
16. The apparatus of claim 1 or 5 wherein said processor is further
arranged to calculate a predicted steady-state value of said thermal
property under transient thermal conditions.
17. The apparatus of claim 16 wherein said processor is further
arranged to employ a selected equation predicting thermal behavior
of said specimen under said transient thermal conditions.
18. An apparatus for measuring a thermal property of a specimen
comprising:
a first heat generating device thermally coupled to a hot plate
and a second heat generating device thermally coupled to a cold
plate;
a first temperature sensor and a second temperature sensor located
in thermal contact with said hot plate and said cold plate, respectively;
a heat flow transducer, thermally connectable to a specimen, constructed
and arranged to measure heat flowing through said specimen before
reaching steady-state thermal conditions, the combination of said
heat flow transducer and said specimen being positionable in thermal
contact between said hot plate and said cold plate;
at least one electric power supply connected to provide controlled
amounts of electric power to said first device and said second device
to maintain said plates at selected temperatures; and
a processor connected to receive from said heat flow transducer
a signal corresponding to said measured heat, said processor being
further programmed to calculate a predicted steady-state value of
a thermal property of said specimen under transient thermal conditions
based on said measured heat and said temperatures.
19. The apparatus of claim 18 further comprising at least one heat
exchange system, thermally connected to said cold plate and said
hot plate, constructed and arranged to maintain said plates at said
selected temperatures.
20. A method of measuring a thermal property of a specimen comprising:
providing a first thermoelectric device and a second thermoelectric
device, each said device being thermally coupled to a hot plate
and a cold plate, said thermoelectric devices being connected to
an electric power supply;
positioning a specimen, thermally coupled to a heat flow transducer,
in thermal contact between said hot plate of said first thermoelectric
device and said cold plate of second thermoelectric device;
establishing selected temperatures of said hot plates and said
cold plates by providing simultaneously electric power from said
power supply to said first thermoelectric device and said second
thermoelectric device;
measuring heat flowing through said specimen from said hot plate
of said first thermoelectric device to said cold plate of said second
thermoelectric device by utilizing said heat flow transducer; and
calculating a thermal property of said specimen based on said measured
heat and said temperatures.
21. The method of claim 20 further comprising:
providing a closed loop heat exchange system thermally connected
to said cold plate of said first thermoelectric device and said
hot plate of said second thermoelectric device; and
transferring heat between said cold plate of said first thermoelectric
device and said hot plate of said second thermoelectric device.
22. The method of claim 21 wherein said heat transferring step
includes circulating a heat exchange fluid in a closed loop arrangement.
23. The method of claim 22 further including preventing lateral
heat loss from said specimen.
24. The method of claim 23 wherein said preventing step includes
circulating said heat exchange fluid in a thermal guard member disposed
around said specimen.
25. The method of claim 22 further including heating said circulating
fluid to a selected temperature.
26. The method of claim 22 further including cooling said circulating
fluid to a selected temperature.
27. The method of claim 20 21 or 22 further providing a second
heat flow transducer, and the method further comprising positioning
said first and said second heat flow transducer in thermal contact
with both sides of said specimen, and determining heat flowing through
said specimen by utilizing said second heat flow transducer.
28. The method of claim 20 further providing first temperature
sensor and a second temperature sensor, and the method further comprising
positioning said first and said second temperature sensor in thermal
contact with said hot plate of said first thermoelectric device
and said cold plate of said second thermoelectric device, respectively,
and measuring temperatures of said hot plate and said cold plate.
29. The method of claim 20 wherein said establishing step includes
providing a selected amount of current to said first thermoelectric
device and said second thermoelectric device.
30. The method of claim 20 wherein said establishing step includes
maintaining a selected voltage across said first thermoelectric
device and said second thermoelectric device.
31. The method of claim 20 further including measuring the thickness
of said specimen.
32. The method of claim 20 further including calculating said thermal
property under steady-state thermal conditions.
33. The method of claim 20 further including calculating a predicted
steady-state value of said thermal property under transient thermal
conditions.
34. The method of claim 33 wherein said calculating step includes
employing a selected equation that predicts thermal behavior of
said specimen under transient thermal conditions.
35. A method of measuring a thermal property of a specimen comprising:
providing a first heat generating device thermally coupled to a
hot plate and a second heat generating device thermally coupled
to a cold plate; a first temperature sensor and a second temperature
sensor located in thermal contact with said hot plate and said cold
plate, respectively, said devices being connected to at least one
electric power supply;
positioning a specimen, thermally coupled to a heat flow transducer,
in thermal contact between said hot plate and said cold plate;
establishing selected temperatures of said hot and cold plates
by providing electric power to said first device and said second
device;
measuring heat flowing through said specimen by utilizing said
heat flow transducer before reaching steady-state thermal conditions;
and
calculating a predicted steady-state value of a thermal property
of said specimen under transient thermal conditions based on said
measured heat and said temperatures.
36. The method of claim 35 further comprising:
providing at least one heat exchange system thermally connected
to said cold plate and said hot plate; and
transferring heat to or from said plates to maintain said plates
at said selected temperatures.
Description BACKGROUND OF THE INVENTION
The present invention relates to heat flow meter instruments for
testing thermal properties of materials including thermal conductivity
and heat capacity. More particularly, the invention relates to a
closed loop heat flow meter instrument that utilizes thermoelectric
devices for controlling temperature.
Thermal properties, such as thermal conductivity and heat capacity,
are important physical properties of solids. Heat flows through
a solid that has a temperature gradient across its volume. The thermal
conductivity of a specimen can be measured directly by measuring
the heat flux resulting from a known temperature gradient across
a known thickness. A one-dimensional form of the Fourier heat flow
relation is frequently used to calculate thermal conductivity under
steady-state conditions: ##EQU1## wherein k is thermal conductivity,
Q is a heat flow per a unit surface area (heat flux), .DELTA.T is
a temperature difference over the thickness .DELTA.X. A standard
instrument measures the thermal conductivity of a specimen located
between two flat plates by maintaining the plates at known, but
different temperatures. As heat flows through the specimen from
the hot side to the cold side, a heat flux transducer measures the
amount of heat transferred. A thermocouple measures the temperature
of each plate.
In some instruments, the two plates are heated (or cooled) separately.
Usually, each plate is heated by an electric heater, such as an
etched foil heater or a wire heater, powered by an electric power
supply. The plate may also be thermally connected to a heat sink
with a circulating coolant. The desired plate temperature is reached
by balancing the action of the heater and the cooling system. The
balancing commonly causes pulsation of the temperature, and thus
the plate provides pulsating amounts of heat to the specimen. To
reduce the pulsating effect, a thermal buffer is frequently placed
between the plate and the heat flux transducer. Therefore, it may
take a relatively long time to achieve a thermal equilibrium at
a desired temperature. Alternatively, each plate may be heated or
cooled by regulating temperature of the fluid circulating in the
heat sinks. This type of temperature regulation may increase the
cost of operation. In either case, the output of the heat flux transducer
and of the thermocouples is monitored until variations in temperature
subside and steady-state heat conditions exist. Then, the instrument
measures the thermal conductivity. The measurements are usually
performed according to standard testing methods, such as, C 518
or C 1045 methods published in Annual Book of ASTM Standards.
Furthermore, a conventional electric heater may introduce a significant
error to the measured data. Some instruments use a heater powered
by an AC power supply. The AC signal introduces AC noise into the
system. This noise affects detection of the sensor signals since
they are at the microvolt levels. Therefore, to provide accurate
data, the sensors may need AC shielding.
There are other methods that do not require the steady-state conditions.
The thermal conductivity coefficient may be measured by so called
thermal diffusivity methods and quasi-stationary methods. The thermal
diffusivity methods (e.g., hot wire method, flash method) determine
the thermal conductivity coefficient by indirectly measuring the
time of flight of a heat pulse across a layer of the specimen. The
thermal diffusivity is the ratio of the thermal conductivity, at
an average temperature of the specimen, and the heat capacity. The
quasi-stationary method measures usually the sum of temperature
differences between the two flat surfaces of the specimen, as the
heat is conducted toward the colder plate. This method assumes a
linear temperature distribution inside the specimen which is an
approximation of the actual behavior.
There is a need for a fast, efficient and highly accurate heat
flow meter instrument, which has a relatively small size.
SUMMARY OF THE INVENTION
In general, the instrument of the present invention is a fast,
efficient and highly accurate heat flow meter (HFM). The HFM instrument
is constructed and arranged to control precisely temperature of
a high temperature plate and a low temperature plate surrounding
a specimen. Each plate includes one or more thermoelectric devices,
consisting of pairs of an N-type semiconductor and a P-type semiconductor.
The thermoelectric devices are powered by one or more power supplies.
The heat sinks of the two thermoelectric devices are thermally connected
by a closed loop heat exchange system with a circulating medium.
Thus the heat rejected by the heat sink at a higher temperature
can be transferred to the heat sink at a lower temperature. The
heat exchange system includes a separate heater or a refrigerator
used to regulate the temperature of the circulating medium, which,
in turn, controls the mean temperature of the specimen. This arrangement
creates an efficient and thermally stable system with relatively
small heat losses. The present invention has a wide range of applications
in systems that pump heat across a slab of material having its surfaces
at selected temperatures.
In another aspect, an apparatus (e.g., a heat flow meter instrument)
for measuring thermal properties of a specimen includes a first
thermoelectric device and a second thermoelectric device, each device
being thermally coupled to a hot plate and a cold plate, and a heat
flow transducer, thermally connectable to a specimen, constructed
and arranged to measure heat flowing through the specimen. The heat
flow transducer and the specimen are positionable in thermal contact
between the hot plate of the first thermoelectric device and the
cold plate of the second thermoelectric device. The apparatus also
includes an electric power supply connected to provide controlled
amounts of electric power to the first and second thermoelectric
devices to maintain the plates at selected temperatures, and a processor
connected to receive from the heat flow transducer a signal corresponding
to the measured heat. The processor is programmed to calculate a
thermal property of the specimen based on the temperatures and the
measured heat.
In another aspect, an apparatus for measuring thermal properties
of a specimen includes a first thermoelectric device and a second
thermoelectric device, each device being thermally coupled to a
hot plate and a cold plate, and a heat flow transducer, thermally
connectable to a specimen, constructed and arranged to measure heat
flowing through the specimen. The heat flow transducer and the specimen
are positionable in thermal contact between the hot plate of the
first thermoelectric device and the cold plate of the second thermoelectric
device. The apparatus also includes electric power means (e.g.,
one or more electric power supplies) connected to provide controlled
amounts of electric power to the first thermoelectric device and
the second thermoelectric device to maintain the plates at selected
temperatures, a heat exchange system, thermally connecting the cold
plate of the first thermoelectric device and the hot plate of the
second thermoelectric device, constructed and arranged to transfer
heat between the plates, and a processor connected to receive from
the heat flow transducer a signal corresponding to the measured
heat. The processor is further programmed to calculate a thermal
property of the specimen based on the temperatures and the measured
heat.
In another aspect, an apparatus for measuring thermal properties
of a specimen includes a first heat generating device thermally
coupled to a hot plate and a second heat generating device thermally
coupled to a cold plate, a first temperature sensor and a second
temperature sensor located in thermal contact with the hot plate
and the cold plate, respectively, and a heat flow transducer, thermally
connectable to a specimen, constructed and arranged to measure heat
flowing through the specimen. The heat flow transducer and the specimen
are positionable in thermal contact between the hot plate and the
cold plate. The apparatus further includes at least one electric
power supply connected to provide controlled amounts of electric
power to the first device and the second device to maintain the
plates at selected temperatures, and a processor connected to receive
from the heat flow transducer a signal corresponding to the measured
heat. The processor is further programmed to calculate a predicted
steady-state value of a thermal property of the specimen under transient
thermal conditions based on the measured heat and the temperatures.
Embodiments of the apparatus may include one or more of the following
features. The thermoelectric device includes pairs of N-type and
P-type semiconductors.
The apparatus may include a first temperature sensor and a second
temperature sensor located in thermal contact with the hot plate
of the first thermoelectric device and a cold plate of the second
thermoelectric device, respectively.
The apparatus may include a heat exchange system (a closed loop
system or an open loop system), thermally connected to the cold
plate of the first thermoelectric device and the hot plate of the
second thermoelectric device.
The apparatus may include at least one heat exchange system for
providing heat to or removing heat from the cold plate thermally
coupled to the specimen or the hot plate thermally coupled to the
specimen.
A closed loop heat exchange system may include a first set of conduits
thermally connected to the cold plate of the first thermoelectric
device and a second set of conduits thermally connected to the hot
plate of the second thermoelectric device, the conduits being constructed
to convey a heat exchange fluid in a closed loop arrangement, and
a fluid pump constructed to circulate the fluid.
The closed loop heat exchange system may further include a heater
constructed to heat the heat exchange fluid to a selected temperature.
The closed loop heat exchange system may further include a refrigerator
constructed to cool the heat exchange fluid to a selected temperature.
The apparatus may further include a second heat flow transducer
constructed to measure a flow of heat, the first and the second
heat flow transducer being arranged in thermal contact with both
sides of the specimen.
The apparatus may further include a thermal guard member constructed
and arranged to prevent a lateral heat loss from the sample. The
thermal guard member may include a set of conduits connected to
the closed loop heat exchange system and constructed to convey the
heat exchange fluid.
The electric power supply of the apparatus is a current supply
constructed to deliver DC current to the first thermoelectric device
and the second thermoelectric device connected in series. Alternatively,
the electric power supply is a voltage source connected to deliver
DC voltage to the first thermoelectric device and the second thermoelectric
device.
The apparatus may further include a potentiometer constructed and
arranged to provide a signal corresponding to the thickness of the
specimen.
The processor of the apparatus may be further arranged to calculate
the thermal property under steady-state thermal conditions.
The processor may be further arranged to calculate a predicted
steady-state value of the thermal property under transient thermal
conditions. The processor may employ a selected equation predicting
thermal behavior of the specimen under the transient thermal conditions.
The apparatus operates in the temperature range of about 263 K
to 393 K, and can characterize different materials, such as, fiberglass,
cellular foams, rubber polymers, composite materials, ceramics,
or glasses. The tested materials have thermal resistances (R values)
in the range of about 0.5 to 40 m.sup.2 .multidot.K/W. The apparatus
has a reproducibility better than .+-.0.2% between different tests.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1 and 1A depict a schematic representation of a heat flow
meter instrument for measuring thermal properties of a specimen.
FIG. 2 depicts schematically an upper thermoelectric unit and a
lower thermoelectric unit employed in the heat flow meter instrument.
FIGS. 3A and 3B depict schematically a closed loop and an open
loop arrangement for controlling power supplied to the thermoelectric
units.
FIGS. 3C and 3D depict schematically heat exchange systems for
controlling the mean temperature of the instrument.
FIG. 4 depicts schematically data acquisition hardware of the heat
flow meter instrument.
FIG. 5 is a flowchart of data acquisition and reduction.
FIG. 6 is a flowchart of an algorithm for determining thermal equilibrium
of the instrument.
FIGS. 7A and 7B depict schematically embodiments of the test section
of a guarded heat flow meter instrument.
FIGS. 8A and 8B depict a measured functional dependence of the
calibration factor and its deviation from the steady state value
under transient temperature conditions, respectively.
FIG. 9 is a flowchart of a predictive algorithm employed in a transient
temperature mode.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 depicts a heat flow meter (HFM) instrument 1 for measuring
thermal conductivity of a material specimen 2. HFM instrument 1
is mounted on a frame that includes an upper frame plate 3 a lower
frame plate 4 and four stationary threaded rods 5A, 5B, 5C and
5D (5D is not shown). Specimen 2 is sandwitched between a lower
plate assembly 6 and an upper plate assembly 7 connected to an upper
support plate 8. Four stepper motors 9A, 9B, 9C and 9D (9D is not
shown), connected to upper support plate 8 by sliding pins 10 ride
up and down on the four stationary threaded rods. As the upper plate
assembly is lowered and comes into contact with specimen 2 the
sliding pins enable the four motors to continue in the downward
motion so that upper plate assembly 7 contacts by gravity specimen
2. (The motors are, for example, linear actuators model ZB17GBKN-10-9
made by Eastern Air Devices, Dover, N.H.) Upper plate assembly 7
and a lower plate assembly 6 are thermally connected by a heat exchange
system to create a closed thermal loop.
Also referring to FIG. 1A, upper plate assembly 7 is made of an
upper heat flux transducer 14 thermally coupled to an upper surface
plate 16 made of a material with high thermal conductivity, and
thermocouples 18 and 20. Upper surface plate 16 is thermally coupled
to an upper thermoelectric unit 30 which is thermally connected
to an upper heat sink 32. Heat sink 32 is a flat plate with a set
of conduits constructed to carry a circulating fluid. The fluid
circulates in a closed fluid circuit between upper heat sink 32
and a lower heat sink 54. Similarly, the lower module includes a
lower heat flux transducer 42 which is in thermal contact with
specimen 2 and is thermally coupled to lower surface plate 44 made
of a material with high thermal conductivity. Both heat flux transducers
14 and 42 are ITI type "A" transducers commercially available
from International Thermal Instruments, Del Mar, Calif. (Other heat
flux transducers can also be used, such as, transducers made by
RDF Corporation of Hudson, N.H.) Thermocouples 46 and 48 measure
the temperature of lower surface plate 44. Surface plate 44 is thermally
coupled to a lower thermoelectric unit 50 which in turn is thermally
coupled to lower heat sink 54. Lower heat sink 54 similarly as
upper heat sink 32 includes a set of conduits for carrying a circulating
fluid. (Instead of the thermocouples, the instrument may use a thermistor,
such as, a 10 k.OMEGA. precision thermistor model YSI 44016 made
by YSI Inc., Yellow Springs, Ohio, a temperature transducer AD 590
made by Analog Devices Inc., Norwood, Mass., or any other device
that can measure temperature.)
Also referring to FIG. 2 DC power supply 60 provides electric
power to upper thermoelectric unit 30 and lower thermoelectric unit
50 connected in series. Both thermoelectric units 30 and 50 include
several identical thermoelectric devices each consisting of pairs
of an N-type semiconductor and a P-type semiconductor located between
two ceramic substrates (a cold face and a hot face). Identical thermoelectric
devices 30A, 30B, 30C, 30D, . . . , are wired in parallel and thermally
coupled to a hot face 28 and a cold face 29. Similarly, identical
thermoelectric devices 50A, 50B, 50C, 50D, . . . , are electrically
connected in parallel and thermally coupled to a cold face 51 and
a hot face 52. The DC power supply (e.g., a Vicor power supply,
model VI-LF; Sorenson or Lambda power supplies) has an adjustable
output to regulate the temperature of the devices. Since power supply
60 provides a DC current to the two thermoelectric units connected
in series, approximately the same amount of heat is delivered to
specimen 2 by hot face 28 as is taken out of the other side of specimen
2 by cold face 51. The precise amounts of heat added and removed,
including the losses, depend also on the operating temperatures
of the thermoelectric units.
The HFM instrument is constructed to control the temperature across
surface plate 16 and 44 in a closed loop, as shown in FIG. 3A, or
in an open loop arrangement, as shown in FIG. 3B. The instrument
includes at least four K-type (chromel-alumel) thermocouples 18
20 46 and 48 which provide the surface plate temperatures for
monitoring and controlling purposes. Thermocouples 20 and 48 are
connected together in a differential mode, wherein the alumel leads
are joined together and the differential temperature (T.sub.Delta)
is measured across the chromel leads. The chromel leads (62A, 62B)
are connected to a controller 64. Controller 64 receives a temperature
set point either manually or via a computer interface and provides
a voltage output signal (V.sub.Delta) to power supply 60. Power
supply 60 provides the corresponding DC current (66) to thermoelectric
units 30 and 50. In the open loop arrangement, a scaled output controller
65 provides the control voltage signal (V.sub.Delta) solely based
on the temperature set point. Power supply 60 provides a DC current
(67) that may be trimmed (63) to regulate the temperature difference
across thermoelectric units 30 and 50. Alternatively, thermocouples
18 and 46 may be replaced by a set of thermocouples distributed
over the area of the plates to measure a temperature profile of
the surface plates.
The closed thermal loop, which connects upper heat sink 32 and
lower heat sink 54 via conduits 34 and 38 enables stable and efficient
thermal operation of the HFM instrument. A circulating pump 40 circulates
a ethylene glycol/water mixture (or another fluid such as oil or
water) between heat sink 54 which is in thermal contact with hot
face 52 and heat sink 32 thermally connected to cold face 29.
Pump 40 may be a dual head pump MARCH Model 802 (made by March Manufacturing
Inc., Glenview, Ill.) One or more thermocouples (37) are used to
measure the temperature of the circulating fluid. Heat exchange
system 36 is constructed to control the temperature of the fluid
(T.sub.Mean) The temperature control is achieved by either a closed
loop arrangement or an open loop control arrangement. At stable
conditions, the circulating fluid is maintained at a constant temperature
T.sub.Mean so that the surface plate temperatures will be controlled
at approximately (T.sub.Mean +1/2T.sub.Delta) and (T.sub.Mean -1/2T.sub.Delta).
Basically, power supply 60 achieves the desired temperature differential
(T.sub.Delta) across the specimen, and heat exchange system 36 establishes
the mean temperature (T.sub.Mean).
Referring to FIG. 3C, depending on the temperature range of the
instrument, a heat exchange system 36A may include a simple electrical
heater connected to a controller in a closed loop arrangement 35.
Referring to FIG. 3D, alternatively, the temperature of the fluid
(T.sub.Mean) is regulated by a heat exchange system 36B. Heat exchange
system 36B includes a thermoelectric heat exchanger 70 with a first
face 70A thermally connected to conduits 34 and 38 and a second
face 70B thermally connected to an internal thermal loop 74. Thermal
loop 74 includes a pump 76 and a radiator 78 cooled, for example,
by ambient air. A simplified heat exchange system 36B may have the
second face coupled directly to a finned heat sink that provides
the heat exchange. A fan may be used to blow air to the finned heat
sink. Such a simplified design eliminates the need for internal
thermal loop 74 radiator 78 and pump 76.
When the fluid circulating in conduits 34 and 38 is being cooled,
a DC power supply 72 provides current to maintain face 70A as a
cold face and face 70B as a hot face. Then the heat from hot face
70B is dissipated by thermal loop 74. Alternatively, by reversing
the current DC power supply 72 can maintain face 70A as a hot face
and face 70B as a cold face. Then the hot face will supply a controlled
amount of heat to the fluid circulating in conduits 34 and 38.
The HFM instrument has a test area constructed to accommodate a
12".times.12" specimen up to 4" in thickness prepared
by standard techniques. (The instrument may have a test area that
accommodates a 24".times.24" specimen up to 8" in
thickness.) The specimen is placed on the top of lower plate assembly
6 in thermal contact with lower heat flux transducer 42. When upper
plate assembly 7 is lowered to the specimen surface, the described
mechanism allows upper heat flux transducer 14 to conform with the
specimen surface. The thickness of the specimen is measured by a
linear potentiometer LX-PA-4.7 (made by Unimeasure, Inc., Corvallis,
Oreg.). The linear potentiometer (not shown in FIG. 1) connects
the center of plate 8 and the center of the moving upper plate assembly
7 and thus measures the distance between plate 8 and plate assembly
7. This distance corresponds to an average thickness of specimen
2. (Alternatively, a linear potentiometer may be connected to each
corner of plate assembly 7. The average thickness is then calculated
from the data measured by the four potentiometers.)
Referring to FIG. 4 the operation of the HFM instrument is controlled
by an embedded PC-104 system 80 connected to a control console 82.
(A standalone 486 or 586 personal computer may be used instead.)
Computer 70 is connected to a data acquisition board 84 via an RS
232 serial interface. Board 84 is a Lawson model 202 (24 bit Data
Acquisition Board), which is connected to a amplifier/multiplexer
system 86 (Lawson, model 20b, made by Lawson Labs., Inc., Kalispell,
Mont.). The system receives sensor values T.sub.u and T.sub.l measured
by thermocouples 18 and 46 respectively, T.sub.Delta measured across
the chromel leads of thermocouples 20 and 48 and T.sub.Mean measured
by thermocouple 37. The system also acquires values Q.sub.u and
Q.sub.l from heat flux transducers 14 and 42 respectively, and
the thickness value from the linear potentiometer.
Computer 80 runs an automation software, which enables automatic
data acquisition and temperature control. Based on a control algorithm,
computer 80 sends control signals to the Lawson 202 board (control
64 of FIG. 3A for differential temperature control), which, in turn,
sends analog (0-5 Volt) control signals 88 and 89 to DC power supply
60 and heat exchange system 36 respectively.
Referring to FIG. 5 the software performs the data acquisition
and evaluation as follows. In steps 92 through 95 the processor
reads values T.sub.u, T.sub.l, Q.sub.u, and Q.sub.l. Depending on
the heat flux transducer employed (step 96), the computer assigns
the specimen heat, Q=Q.sub.u (step 98 if only the upper heat flux
transducer is used), Q=Q.sub.l (step 100 if only the lower heat
flux transducer is used), or Q=1/2 (Q.sub.l +Q.sub.u) (step 102
if both the upper and lower heat flux transducers are used). The
computer reads values T.sub.Mean and T.sub.Delta in steps 104 and
106. Values of T.sub.Mean and T.sub.Delta are used as dedicated
feedback sensors in the control algorithm. These values are compared
to 1/2 (T.sub.l +T.sub.u) and (T.sub.u -T.sub.l), respectively,
when adjusting the set points of T.sub.Mean and T.sub.Delta.
In a calibration procedure, a reference sample with known thermal
conductivity is measured to calibrate the instrument. The computer
first recalls the thermal conductivity value (k) corresponding to
the reference sample at the 1/2(T.sub.l +T.sub.u) temperature (step
110). Next, the computer calculates the heat flux transducer calibration
factor, N, based on Eq. 2 (step 112). ##EQU2##
In a measurement procedure that characterizes a specimen, the computer
first recalls the calibration factor (N) corresponding to the calibration
temperature 1/2(T.sub.l +T.sub.u) of the instrument (step 114).
Next, the computer calculates the thermal conductivity value, k
(step 116), as follows: ##EQU3## All data can be displayed on the
screen and printed on a printer (steps 124 or 126).
Also referring to FIG. 6 when the instrument operates in a steady
state mode, the computer checks the thermal equilibrium by employing
an algorithm 118. The operator can control the level of thermal
equilibrium by initially selecting "rough" and "fine"
deviation values for N or k. For example, during the calibration
procedure, the computer recalls ten most recent values of N (field
130), calculates their average, Avg(i) (step 132) and stores Avg(i)
in field 144. Then, the computer tests "rough equilibrium"
(step 134). If any of the measured value (N.sub.i) of the ten most
recent values stored in field 130 is outside the selected "rough"
deviation value (135), the instrument performs a new scan (136)
and stores the calculated value N (Equation 2) in field 130. If
the ten most recent values (N.sub.i+j) are within the selected "rough"
deviation value (137), the computer calculates the average of the
current "fine" block, i.e., Result(i) in step 138. In
step 140 the computer evaluates whether all of the last ten values
stored in field 144 are within the selected "fine" deviation
value. If each value is within the "fine" deviation value,
the system has reached thermal equilibrium, and the last calculated
value, Result(i), is the final value. Otherwise, the instrument
performs a new scan (142). The same equilibrium algorithm is performed
during the measurement run for k values.
Referring to FIGS. 7A and 7B, in another embodiment, the HFM instrument
is a guarded heat flow meter. The test section (150A or 150B) of
the instrument is constructed to limit lateral heat loss from specimen
2. Test section 150A includes four heat guards 154A, 154B, 154C,
and 154D thermally connected to conduits 154. Conduits 154 circulate
the fluid maintained at T.sub.Mean. During the measurement, the
heat guards surround specimen 2 sandwiched between upper surface
plate 16 and lower surface plate 44 and thus limit the lateral
heat loss from the specimen. Alternatively, test section 150B includes
a single heat guard 158 with an opening 157 made to fit specimen
2. Heat guard 158 again includes a set of conduits 158 for the circulating
fluid. (This instrument can operate according to the F 433 standard
testing method, published in the Annual Book of ASTM Standards.)
The test section is constructed for a quick exchange of the specimen
to be measured either by the above-described, steady state method
or a transient temperature method.
In another embodiment, the instrument operates in a transient temperature
mode. This transient temperature mode may be used with HFM instrument
1 described above or with any standard heat flow meter instrument.
The transient temperature mode is employed in a quick measurement
of the thermal conductivity without waiting until the system reaches
the steady state. For example, when performing quality control on
a production line of thermal insulation materials, the on line testing
related to process control requires a relatively short measurement
time. Thus the computer does not execute algorithm 118 (of FIG.
6), but executes a predictive algorithm 170 (of FIG. 9). During
the predictive algorithm, the instrument measures a transient data
response over a relatively short time period and calculates the
expected steady-state value of thermal conductivity (k), which is
a characteristic of the tested material.
When a new specimen is loaded into the test section with plates
16 and 44 at the selected temperatures, the specimen undergoes a
step function change in its surface temperatures. The thermal behavior
of the specimen can be approximated by an electric RC circuit connected
to a DC voltage, wherein R.sub.th is a modeled thermal resistance
and C.sub.th is a modeled thermal capacitance of the specimen. Using
the well known relationship of a charging capacitance in a serial
RC circuit, the thermal conductivity k can be approximated as follows:
##EQU4## wherein k(t) is an instantaneous value at time t after
loading the specimen, k.sub.final is the steady state value, and
.tau. is the product R.sub.th .times.C.sub.th. The same relationship
can be used for the calibration factor (N) during the calibration
procedure as is confirmed in FIG. 8A. FIG. 8A shows instantaneous
values of the calibration factor N(t) measured on a 12".times.12".times.1"
Styrofoam.RTM. sample (triangles) and the predicted RC functional
dependance (N(t) calculated from the Equation 4 type relationship).
FIG. 8B shows a time dependence (162) of the percent error of the
predicted final value relative to the steady-state value of k. After
about one minute, the predicted value is within 1% of the steady-state
value.
Referring to FIG. 9 in the transient temperature mode, the computer
executes predictive algorithm 170 instead of the equilibrium algorithm
(shown as step 118 in FIG. 5). The computer calculates an instantaneous
thermal conductivity k(t) (step 116). In step 174 the computer
recalls the value of .tau. from the memory. Then, the computer calculates
the predicted value k.sub.final using Equation 5 (step 172).
wherein .tau.=R.sub.th .times.C.sub.th, t(0) is the time the specimen
was exposed to the temperatures of lower plate assembly 6 and upper
plate assembly 7 prior to starting the test, and t is the elapsed
test time at which data was collected. Values R.sub.th and C.sub.th
are determined for each material by measuring the time dependance
of k until the steady state of the specimen is achieved (see FIG.
8A). Both R.sub.th and C.sub.th depend on the type of material and
on the specimen size.
In step 176 the computer may check for variations in the predicted
value. If two subsequent values k.sub.final are within a selected
limit (178), the transient temperature run is completed. If the
values k.sub.final are outside of a selected limit (180), the instrument
reads new values T.sub.u, T.sub.l, Q.sub.u, and Q.sub.l and repeats
the calculation cycle. Therefore, the transient temperature mode
permits rapid evaluation of tested samples.
Other embodiments of the HFM instrument may include different combinations
of the features suggested above and features described in prior
art. Additional embodiments are within the following claims. |