Radiation and Convection
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System Design and Measurement Procedure
The measurement system consists of three components. In the first place a hot object is needed as the radiating body. This object will need to be located within some enclosure called the experimentation chamber. Finally the system will need to be monitored under conditions that approximate vacuum, so that the experimentation chamber is placed in a vacuum chamber. Each of these components will now be discussed in more detail.
A small metal cylinder at the center of the system is used as the 'hot object'. At the core of the cylinder a heating element is located, connected to a variable feed. Depending on the metal the cylinder can be heated up to some maximum value. Above that value the material may melt, and it should be realized that the melting point is lower than the melting point at atmospheric pressure. In the case of the set up used at the Vrije Universiteit Amsterdam, the cylinder used consists of copper and it should not be heated above some 900 K. Finally the cylinder is painted grey and it is assumed to behave like a grey body.
As suggested before, a measurement involving radiation only is to take place in a vacuum chamber, since no heat transfer through either conduction or convection is possible under these conditions. The measurements are performed in a cylindrical vacuum chamber as discussed in the next subsection.
Within a vacuum chamber a smaller cylindrical chamber, the experimentation chamber (see fig. 3.1), is located. The walls of the experimentation chamber are cooled using a cooling circuit. The temperature of the cooling water flowing into the walls of the experimentation chamber is stabilized using a Lauda bath and continually compared to the temperature of the water flowing out of the wall of the vacuum chamber using a constantan-copper, type T thermocouple. Since the flow velocity is monitored as well, using a flow meter, one is able to monitor the total amount of heat absorbed from the system.
Furthermore the inner side of the experimentation chamber consists of a removable cylindrical copper element. If various of the elements are constructed and painted in differing colors, the emissivity e of the inner surface of the experimentation chamber can be changed. A silicon temperature sensor KTY-10 is attached to the inner surface.
Finally, at the center of the experimentation chamber a small metal cylinder, containing a heating element, is hung. Again several of these cylinders may be constructed and painted in differing colors so that the emissivity e of the cylinder can be varied. The temperature of the hot object can be monitored by mounting a temperature sensor on the cylinder, which in the case of the set up presented here was a PT-100.
A set up like this allows for the measurement of heat transfer through radiation, according to eq. (2.7). If the cylinder at the center is heated at a constant rate the system will stabilize after some time so that a steady state is reached. The heat produced in the cylinder by dissipation is than equal to the heat removed from the system by the cooling circuit. Both can be monitored, since the power supplied to the heating element is known and the heat removed by the cooling circuit can be deduced on the basis of the measurements of the thermocouple.
The temperatures of the heating element and the inner surface of the experimentation chamber are known as well so that the emissivity may found. For more accurate results the emissivity e may be determined by changing the amounts of power supplied to the heating element.
Figure 3.1: The set up used at the Vrije Universiteit Amsterdam. The experimentation chamber is located within a vacuum chamber, and cooled with a cooling circuit. Within the experimentation chamber the 'hot object', a small metal cylinder, is hung.
The Vacuum Chamber
The pressure in the vacuum chamber is controlled through use of a vacuum control unit (see fig. 3.2). It consists of a pump A, a turbo-pump B and a valve C. Its connection to the vacuum chamber is determined by the main gate D.
To create low pressures in the vacuum chamber a series of steps is to be followed that is typical to the set up as described here:
- The system needs to be airtight. This implies that the bell, the casing of the vacuum chamber, needs to rest nicely on the rubber ring on the bottom of the vacuum chamber.
- The main gate D should be opened, so that the pumps A and B and the vacuum chamber are connected.
- The valve C in the vacuum control unit should be closed.
- The cooling circuit should be up and running.
- If the previous conditions are fulfilled one may start the pump.
- After one minute the pressure in the experimentation chamber (i.e. the pressure as indicated by pressure sensor TPR 250) should be smaller than 0.2 Torr (1 Torr = 1 mm/Hg = 1,33 102 Pa). If this is not the case, some problem has occurred and the pump should be switched off immediately so that the first steps can be rechecked. It should be noted that apart from to possibility that the procedure has not been followed it may also be possible that the cool water circuit is leaking. In that case the pressure can only become as low as the vapor pressure of water. At room temperature the vapor pressure of water is about 0.25 Torr.
- If no problem occurs, the pressure in the experimentation chamber becomes about 0.1 Torr after some five minutes. At this point one may switch on the turbo-pump. This high performance pump outperforms the regular pump so that the pressure in the chamber between the to pumps (see pressure sensor V1) may increase shortly. The pressure in this chamber should remain lower than 0.2 Torr and if not, one is to switch off the turbo-pump.
- After some ten minutes the pressure in the experimentation room will be lower than 10-4 Torr. At this point pressure is lowest and the system is in dynamic equilibrium, such that the inlet through small leaks equals the amount of air that is removed from the system by the pumps.
It should be mentioned here that the pressure can be stabilized at higher levels by opening valve C slightly so that the inlet through the 'leaks' is increased slightly. With that the equilibrium is shifted towards higher pressures. In this respect it is important to realize that the turbo-pump is build to maintain pressures between 10 -5 and 10-1 Torr. Above these levels the turbo-pump will suffer mechanical distortion. The regular pump however is well able to maintain pressures between 10-1 and 750 Torr so that there is no need for the turbo-pump in this pressure regime.
Figure 3.2: The vacuum control unit allows for control of the pressure in the vacuum chamber.
The procedure for the measurement of the emissivity is given by the following steps;
- Identify relevant parameters with their uncertainties
- Prepare the vacuum chamber
- Measure the temperature of the heating element and casing of the experimentation chamber for different amounts of power supplied to the heating element
- 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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