Department of Mechanical and Aerospace Engineering

5

University of Florida

Department of Mechanical and Aerospace Engineering

Title of Experiment

EML 4147C – Thermal/HeatDesign and Lab

Prepared by: Nicholas Stiesi

Date: 4/08/08

ABSTRACT

The purpose of this experiment was to characterize the performance of a Moll's Thermopile. Most importantly, the question to be answered is if the thermopile intercepts all incident radiation, or if it effectively ignores radiation from the surroundings and reads only radiation incident from a direct target. To test this, a rig was set up consisting of the thermopile and an oven, which were pointed directly at each other with a known distance in between. Readings from the thermopile were taken and compared to theoretical calculations. These calculations predicted amounts of radiation incident from the oven as well as the surroundings. After this analysis, it was found the the thermopile is, in fact, directional. The experimental data for incoming radiation matched the calculated values of incident radiation from the oven alone. In fact, when the surroundings were taken into account in the theoretical calculation, the results were counterintuitive. The thermopile, being heated by the oven, actually resided at a higher temperature than the surroundings, and would in theory be radiating energy to the surroundings, rather than accepting radiation from the environment.

OBJECTIVE

The purpose of this experiment was to predict the behavior of an unknown Moll's thermopile. The unit was obtained with limited documentation as to performance. Therefore, it was of interest to know if the unit intercepts radiation from all directions, or if it absorbs in a directional manner. It was also of interest to know the approximate accuracy of the unit compared to theoretical estimations.

APPARATUS/PROCEDURE

The rig used to carry out this experiment consisted of the Moll's Thermopile, and a 200 Watt oven. The oven body was shielded by a water cooled radiation shield with a 2cm aperture through which radiation is to escape. The thermopile consisted of a metal housing that contained 16 thermocouples which output voltage to a data acquisition system. The thermopile housing featured a 2.5cm aperture through which radiation was to be absorbed. The unit was attached to an adjustable mount which slid along a track which was graduated in units of centimeters. This allowed for knowing the exact distance between the thermopile and the oven.

Figure 1: Geographic arrangement of the test rig

The procedure for the experiment consisted simply of warming the oven to approximately 900°F. Once the oven temperature stabilized, the thermopile was moved to a linear distance of 10cm from the oven. The voltage reading from the thermopile was taken, and the distance was increased by 5cm. This process was repeated for distances up to 50cm.

TECHNICAL APPROACH

Experimentally, the technical approach to this experiment consisted of calculating thermopile power and temperature values from output voltage and the unit's appropriate calibration figures. First, from the output voltage, the intercepted power can be found by:

The thermopile temperature can be calculated by:

Much more rigorous calculations are necessary to calculate the predicted radiant power intercepted by the thermopile. Starting with the thermopile’s intercepted radiation based on the oven only, one would first need to find the view factor for the pair. This dimensionless number can be thought of as the fraction of radiation leaving the oven that is actually intercepted by the thermopile. The oven and thermopile apertures can be thought of as coaxial parallel disks, meaning their view factor is well defined, and given by:

From here, one could now calculate qoven->thermopile, or the net rate at which the thermopile intercepts radiation that is emitted by the oven:

The next exercise would be to calculate the amount of radiation intercepted by the thermopile that originated from the surroundings. To do this, it is best to think of the entire rig as an enclosure. Said enclosure would look like conic solid; a cylinder with different diameters at either end. In this case, the circular surfaces would be the thermopile and oven apertures, and the remaining surface of the solid would be the area of the surroundings. Also, the surroundings could also be approximated as a black body, since the material of the surroundings is air, and should reflect only negligible amounts of incident radiation. That being said, there is no well defined method of finding the view factor of a conic solid surface with respect to the perpendicular disk. However, the summation rule of view factors states that in an enclosure, the sum of all view factors with respect to a given surface are equal to 1. So, in the assumed enclosure that is the experimental rig, there are only 3 surfaces: oven, thermopile, and surroundings. Since the view factor of the oven with respect to the thermopile is already known, it follows that:

(note that since the thermopile aperture is a plane surface, it does not “see” itself, so

Fthermopile->thermopile is equal to zero).

With the view factor known, the area of the surroundings is a simple geometric exercise. This allows for the calculation of the net radiation gained by the thermopile due to the surroundings:

RESULTS

Below are some tabulated results for this experiment. (a full spreadsheet of results can be found in the appendix).

Table 1: Experimental results

The above table shows the data for both intercepted radiation and temperature for the thermopile based on the output voltage readings. As expected, the amount of radiation intercepted by, as well as the temperature of the thermopile decrease as the distance from the oven increases.

Table 2: Predicted and theoretical results

This table shows the theoretical values of net radiation to the thermopile due to the individual contributions of the oven and the surroundings. Also shown is the percent error between the experimental data and the theoretically calculated radiation flux due to the oven alone. These errors are a measure of the unit’s accuracy, as well as it’s resistance to the effects of the surroundings. Also, notice the sign on the values of the surroundings contributions to net radiation. The negative numbers indicate that the thermopile would actually be radiating TO the surroundings, not the inverse. This result makes sense because the driving potential for radiation exchange between black bodies is temperature differential. Since the oven is effectively heating the thermopile to temperature higher than ambient, the thermopile would then radiate to the surroundings. However, for the purpose of this experiment, these values are more than likely inflated. They were calculated using the absolute room temperature, and do not take into account the temperature gradients that exist in the air around the test rig.

Now, if the contributions of the surroundings were to be taken into account, the % error as shown above would be inflated by orders of magnitude, and the radiation curve for the thermopile would not even show itself on the graph below. This would be due to the net radiation gained by the thermopile being negative, which is due to the fact that the radiation loss to the surroundings is actually greater in magnitude than the gain from the oven. However, experimental data dictates that this isn’t the case, and the thermopile is actually quite ignorant of ambient conditions.

Figure 2: Incident radiation to the thermopile vs. distance for both experimental and theoretical data.

CONCLUSION

In conclusion, the thermopile in question is a solid unit, but should not be used in situations where tight constrictions are made on accuracy. The unit proved to be accurate to about 11% on average, but also exhibited deviations from the theoretical calculations as high as 20%. However, other factors could have influenced those errors besides unit accuracy (including the effects of the surroundings), so further and perhaps more controlled accuracy testing is recommended. For the question of surrounding radiation, though, this unit proved to be very efficient in blocking out the effects of the surroundings. Theoretically, this unit should have been losing radiation to the ambient faster than it could gain from the oven, but experimental data proved that this is not the case. Therefore, the conclusion can be drawn that the thermopile effectively does not “see” the surrounds, and this unit could be confidently pointed at a dime-sized target in order to read the emitted radiation from the target only.