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System Design
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Set Up
For the solution suggested in the section
theory to be applicable, a steady state temperature profile for
cylindrical geometry is to be generated. As suggested this can
be arranged by placing a long coil in some conducting medium.
The conducting medium should be a solid with low emissivity at
temperatures of relevance. Such a medium then does not allow
for heat transport through convection and hardly any through
radiation. At the student's lab at the Vrije Universiteit Amsterdam,
sand was used since it behaves conform these conditions and is
easy in use. As shown in figure 3.1 a bucket was filled
with sand, with the coil in the center.
In the section on theory the coil was assumed to be infinitely
long. This condition ensures that only the radial coordinates
of the equation of heat transfer in cylindrical coordinates are
to be evaluated. If no infinitely long coil is used, heat is
lost also in the axial direction. This effect becomes larger
the closer the point of observation is near the tip of the rod.
To minimize these axial heat losses, two plates of insulating
material were placed at the bottom and on top of the bucket.
The thermal conductivity of this material is 0.038 W / m K
whereas the conductivity of sand is in the order 0.25 1.0 W / m K
so that the time scales of the heat penetration in the insulation
differ heavily from heat penetration in the sand.
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3.1; The experimental set up used at the students laboratory
at the Vrije Universiteit Amsterdam |
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For measurement of a temperature profile in the sand one may
use a probe with a sensor at the tip and measure the profile
at various locations. This unit is particularly useful for the
monitoring of the temperature profile in the axial direction.
For the measurement of the temperature
in the axial direction however this instrument yields relatively
large uncertainties. Therefore a second instrument was developed
at the Vrije Universiteit. For the measurement of a spatial temperature
profile an array of sensors was constructed (see fig. 3.2).
The array consists of 32 temperature-sensitive resistors, mounted
on a printed circuit board. The sensors are controlled using
a multiplexer, set to scan the array over some specified period
of time. Using an automated control, the system can be set up
to measure the temperature profile periodically in time, so that
the development of the spatial temperature profile can be monitored
and eventually the steady state profile is measured.
The resistances that are used in the sensor
array depend linearly on temperature for the range between 233 K
and 398 K. Their accuracy is limited to some ± 2 K
at room temperature, but it may increase for the rest of the
operational range, up to a maximum of some ± 4 K.
To improve the accuracy, additional calibration on top of the
factory calibration is called for.
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Figure
3.2; The sensor array consisting of 32 temperature-sensitive
resistors, mounted on a printed circuit board. |
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Calibration Chamber
The calibration of the sensors within
the range of linear behavior basically comes down to the measurement
of the voltage output for two, known and differing temperatures.
The achievement of a single stationary and uniform temperature
over the whole of the sensor array is not self-evident. The sensors
are highly sensitive to spatial temperature variations on scales
smaller than dimensions of the sensors. Small convective currents
can already degrade the quality of the calibration severely.
Therefore a calibration chamber was developed at the Vrije Universiteit
Amsterdam. The calibration chamber is formed by a small container
with relatively walls. Furthermore it is constructed of highly
conducting material, in this particular case aluminum. If heated
using a simple stove and given some time to rest, the aluminum
container will be of virtually uniform temperature as will the
inner volume. If the array of sensors is placed within the box
a uniform temperature distribution over the whole array is more
or less ensured. Temperature differences may still occur however
since the sensors are highly sensitive to point loads and small
scale convective eddies. Therefore the inner volume of the calibration
chamber was filled with sand, so that neither point loads nor
convection can interfere.
Finally the second calibration temperature
should not be higher than about 320 K since the electronic
components other than the sensors on the measurement array may
be quite sensitive to temperatures like these. Non-linear behavior
and strong noise interference in the second calibration measurement
may therefore lead to erroneous results. A calibration measurement
like that is easily recognized when the the calibration chamber
does not show to be of uniform temperature while cooling.
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Figure
3.2; The calibration chamber consists of an alluminum container
with thick walls. The various elements that form the container
are attached using a large amount of bolts to optimize thermal
contact. A nearly uniform temperature can be established within
the calibration chamber. |
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Procedure
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The procedure to perform a measurement consists of the subsequent
steps:
- Identify relevant parameters with their
uncertainties
- Calibrate sensors
- Check calibration
- Start measurement cycle with long periods
and many measurements (be sure the total measurement time covers
the time needed to obtain a steady state)
- Calculate the relevant variables on basis
of these data
- Perform an error analysis
- Graph or tabulate the relevant data and
their respective uncertainties
- Draw conclusions
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