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System Design and Measurement Procedure
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.
Figure 3.1; The experimental set up used at the students laboratory at the Vrije Universiteit Amsterdam
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.
Figure 3.2; The sensor array consisting of 32 temperature-sensitive resistors, mounted on a printed circuit board.
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.
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.
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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