Radiation Heat Transfer Lab

The objective of this laboratory experiment is to investigate the radiation laws (Lambert’s Distance, Cosine Law and Stefan-Boltzmann Law) using thermal and optical radiation.

This experiment was carried out with the assistance of the Thermal Radiation Apparatus which consists of a heat source (that provides the heat for the verification of the Stefan-Boltzmann Law), a thermopile (that assists in detecting the temperature), a luxmeter (that assists in measuring the luminous intensity for the verification of Lambert’s Distance & Cosine Law), absorption plates that detect any radiance incident upon them, a swivelling light source (that assists in provides luminous radiation for the verification of Lambert’s Cosine Law) and finally measuring amplifier that detects he amount of irradiance incident upon the measuring plates and provides an electronic output in the form of a reading.

Lambert’s Distance Law states the as the separation distance between the point source of radiation and the detector plates is increased, the irradiance detected will decrease. This law was proved to be precise since the irradiance and the distance have a negative slope of -1.584 on Figure #1.

Lambert’s Cosine Law, which constitutes that the radiant intensity, I, of the radiation emitted by a flat source is same from any direction but the irradiance, E, decreases with the increase of cosine of the angle of incidence. This law was also proved to be accurate as it can be seen from Table #2 that as the angle of incidence increased, the irradiance decreased.

The Stefan-Boltzmann Law was also verified. It was observed that the irradiance of a blackbody was proportional to the fourth power of the absolute temperature.

The main source error in the lab experiment was that the laboratory room was not completely dark and caused the measuring plates to detect ambient light radiation and giving untrue readings.

PROCEDURE

The procedure outlaid in the lab manual was followed to precision. The procedure steps were carried out in a safe manner for Lambert’s Distance Law, Lambert’s Cosine Law and Stefan-Boltzmann Law. [2]

RESULTS

Lambert’s Distance Law:

Please refer to Table #1, Figure #1 and Figure #2 in Appendix A – Tables and Figures for the Results of the experiment conducted to observe Lambert’s Distance Law.

Lambert’s Cosine Law:

Please refer to Table #2, Table #3, Figure #3 and Figure #4 in Appendix A – Tables and Figures for the Results of the experiment conducted to observe Lambert’s Cosine Law.

Stefan-Boltzmann Law:

Please refer to Table #4, Table #5 and Figure #5 in Appendix A – Tables and Figures for the Results of the experiment conducted to observe Stefan-Boltzmann Law.

DISCUSSION

Lambert’s Distance Law:

Theoretically it is believed that Lambert’s Distance Law correlates to the fact that the irradiance of the radiation emitted perpendicularly towards a surface from a point source is inversely proportional to the square of the distance separating the illuminated surface and the source. [2] From the experiment it was observed that as the distance between the illuminated surface and the source of radiation increased, the irradiance decreased; as an individual can notice that at a separation distance of 100 mm the irradiance was observed to be 1069 W/m2 and at the separation distance of 800 mm the irradiance reduced to a 126 W/m2. From Figure #1 (Lambert’s Distance Law plotted on a Log-Log scale) and Figure #2 (Lambert’s Distance Law plotted on a normal scale), it can be discerned that the irradiance diminishes as the separation distance between the source of radiation and the illumination surface increases.

Lambert’s Cosine Law:

Lambert’s Cosine Law states that the radiant intensity, I, emitted by a flat source is the same from any direction, however the irradiance, E, decreases with the cosine of the angle of direction. [2] This law essentially dictates that the direction of illuminance is irrelevant since the radiance from the surface at any angle is exactly the same to the human eye; this happens due to the fact that as the angle of direction of the rays increases relative to the normal (0� – angle of direction), the area of incidence for the radiation decreases. Another theoretical observation that can be made from the law stated above is that the maximum irradiance will occur at the angle of zero degrees.

It can be perceived from Figure #3, in which the relationship between angle and light intensity on blackbody in a radian measure is shown, the blue circles represent the angle from the center of the unit circle that correspond to the respective normalized illuminance value. From Table #2 it can be noted that as the angle of incidence is increased the illuminance decreases; this corroborates Lambert’s Cosine Law even further.

Stefan-Boltzmann Law:

This law situates that the total irradiance of a blackbody radiator is proportional to the fourth power of the absolute temperature. [1] This can be stated mathematically, as , where ? is the Boltzmann constant with a value of 5.67*10-8 W/m2*K4; although this law applies solely to blackbodies. From Figure #4 it can observed that a linear relationship develops between the temperature and the irradiance, with a positive slope of 2078.1; when the temperature climbs the measuring amplifier detects a higher amount of irradiance.

The theoretical irradiance values were calculated, since the only variable parameters in the equation for the irradiance are the temperatures that are detected. From Table #5 it can be discerned that the theoretical values had a percent error of approximately 76% when compared to the experimental values. This is a very high percent error and can be explained by that fact that not all of the radiation emitted by the source reaches the measuring plates and the majority of the radiation is lost to the environment.

Errors:

The main source error in the lab experiment was confronted during the second part of the lab; during which the Cosine Law was being detected. This room needs to be completely dark and only the radiance from the source must reach the measuring plates so as to provide the most accurate results. This was not achieved as the room was not completely dark and ambient radiation was allowed to be incident upon the measuring plates causing an error.

Experimental errors were caused due to the measuring ruler for the distances of separation and the error in the readings for the irradiance.

Another source of error may be that all sources of radiance during the lab experiment were assumed to be point sources; this is untrue as radiance was incident upon the measuring plates from reflection off the surfaces present in the laboratory room.

CONCLUSION

From the laboratory experiment conducted the Lambert’s Distance Law was proved to be true as it was observed that an inversely proportional relationship developed between the distance and the irradiance detected by the measuring amplifier. Similarly, the Cosine Law was also proved to be correct, as an inversely proportional relationship was also detected between the angle of incidence and the illuminance measured. The last law to be confirmed was the Stefan-Boltzmann Law, which was observed when the total irradiance of the blackbody radiator was proportional to the fourth power of the absolute temperature.

Overall a firm understanding of Lambert’s Distance & Cosine Laws and Stefan-Boltzmann Law and radiation transfer were gained.