1. University of California,
Merced
Engr 135: Heat Transfer
Lab #5: Intro to Thermal Radiation
Jonathan Ramirez, Derek Brigham, Eduardo Rojas-Flores
Section 05L
April 29, 2016
2. Abstract: The objectives of this experiment were to become familiar with the
Inverse Square Law and to understand radiation properties from multiple surfaces. Two
different setups were used in order to test these objectives. One involved a thermal
radiation cube and the other a Stefan-Boltzmann lamp. The results of the lab were
conclusive and in agreement with thermal radiation theory. It was found that different
surfaces have different radiative properties and that the Inverse Square Law does indeed
hold. Overall, the laboratory experiment was successful in completing its objectives and
effectively demonstrated the principles of radiative heat transfer.
Introduction: The objectives of this experiment were to become familiar with the
Inverse Square Law and to understand radiation properties from multiple surfaces. The
lab involved thermal radiation, which is a method of heat transfer composed largely of
infrared radiation. Thermal radiation occurs between two surfaces with differing
temperatures and some separation of distance. Radiation does not require matter between
the two surfaces, and thus will occur even in a vacuum. The mechanism which thermal
radiation happens by is usually viewed as the propagation of electromagnetic waves.
Radiation has four parameters of note: distance, intensity, emissivity, and
absorptivity. Distance affects the intensity of the radiation according to the Inverse
Square Law:
𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 =
𝐼
𝐷2
(𝑬𝒒. 𝟏)
where I is the density of the light and D is the distance between the emitting body
and the absorbing body.
Emissivity is defined as the ratio of the radiation emitted by the surface to the
radiation emitted by a blackbody of the same temperature. Note that a blackbody is an
idealized concept denoting a surface which emits no radiation, thereby absorbing
everything. This leads into the definition of absorptivity, which is a property that
determines the fraction of the irradiation absorbed by a surface.
In this experiment, the physical implementations for testing radiation properties
from multiple surfaces and the Inverse Square Law were as depicted in Figures 1 and 2
below. Figure 1 shows a thermal cube, a radiation sensor, and two multimeters
(ohmmeter and millivoltmeter). The Stefan-Boltzmann Lamp was used to test radiation
properties from the different surfaces by taking readings with the radiation sensor. Figure
2 shows the setup for testing the Inverse Square Law. It depicts a meter stick, multimeter,
power supply, and Stefan-Boltzmann lamp. The Inverse Square Law was tested by
moving the light bulb filament further and further away.
3. Figure 1: Radiation properties from multiple surfaces.
Figure 2: Testing the Inverse Square Law.
Procedure: To begin the experiment, reproduce the set up shown in Figure 1,
connect a multimeter (mV) to a sensor and the other multimeter (Ω) to the cube shown
above. Turn on the cube dial to HIGH setting and wait for the resistance to drop to
40,000 Ω then set the power to 5.0. The thermal resistance of the cube will fluctuate, but
wait until equilibrium is reached. Use the sensor to make contact with the face surface of
the cube and ensure that both prongs are fully pressed to the surface. Record the data for
all four face surfaces, then repeat the whole process for power settings of 6.5, 8.0 and
HIGH.
4. For the second part of the experiment, configure the millivolt meter and power
supply as shown in Figure 2. Ensure that the radiation sensor and the Stefan-Boltzman
lamp are the same height and directly across from each other. Starting from the initial
point of 10cm, record the voltage values at increments of 10cm and then take the ambient
radiation level. Turn the power to 10V and record the voltage readings starting from
10cm to 100cm. The power should not exceed a value of 13V. Doing so will invalidate
the data collected and potentially cause physical harm.
Results/Discussion: Upon completing the two experiments and collecting the
data, Tables 1, 2 and Graph 1 below were made that reflects the values based off the
experimental procedures.
Power Setting
5.0
Power Setting
6.5
Power Setting
8.0
Power Setting
HIGH
Thermal
Resistance
19.7kΩ Thermal
Resistance
9.6kΩ Thermal
Resistance
5.4kΩ Thermal
Resistance
5.1kΩ
Temperatu
re
63.5 ℃ Temperatu
re
83.5℃ Temperatu
re
101℃ Temperatu
re
102.5
℃
Surface
Sensor
Readi
ng
(mV)
Surface
Sensor
Readi
ng
(mV)
Surface
Sensor
Readi
ng
(mV)
Surface
Sensor
Readi
ng
(mV)
Black 7.2 Black 10.5 Black 17 Black 17.2
White 7.1 White 10.7 White 16.5 White 16.7
Polished
Aluminum
0.5 Polished
Aluminum
0.8 Polished
Aluminum
1.1 Polished
Aluminum
1.1
Dull
Aluminum
2.1 Dull
Aluminum
5.9 Dull
Aluminum
5.1 Dull
Aluminum
5.4
Table 1: Thermal resistance, temperature and sensor readings for the four different
power settings.
According to Table 1 in ranking the absorptivity amount from highest to lowest,
the black side of the cube was the highest in absorptivity with the white side being
second, the dull aluminum side was third, and the polished aluminum was the lowest. The
absorptivity of a material is directly correlated to the reflectivity, because if the material
has a high reflection value, it will not take in a high amount of radiant energy. If the
thermal resistance is low, then the absorptivity of the material will be greater meaning it
will take in more radiant energy. Additionally, as the temperature rises from the increase
in the power settings value, the higher the intensity of radiant energy will be given off
which will also increase the absorptivity of the material.
In relation to the cube, the black and white sides had very high absorptivity and
relatively low reflectivity. Since the black side had no reflection, it was able to take in all
the intensity of the radiation and based off the sensor readings, it was the highest in
almost all the power settings saving the power settings at 6.5, where the white side was
slightly higher. For the white side, it had a small amount of reflectivity in which it
5. accounted for slightly lower values than the black side in all the power setting trials.
Since these two have almost no reflectivity, it is more on absorbing the radiant energy
because these materials have a high thermal conductivity, meaning as the intensity of the
radiation increases with the temperature increase, heat transfer along the material will
happen a lot quicker which will cause the material to absorb almost all the intensity given
off.
For the other two sides with lower values, the dull aluminum and polished
aluminum both have high reflectivity but low absorptivity. The sensor readings of dull
aluminum for all the trials were much higher than that of the polished aluminum. The
reason for this is that dull aluminum has a tampered surface which decreased the
reflectivity of the material and makes it more susceptible to absorbing radiant energy.
From this the dull aluminum has a fairly balanced mix of reflectivity and absorptivity,
hence the sensor reading values for the material being half of that for the black and white
sides. For polished aluminum, its surface is highly reflective which makes it unable to
absorb radiant energy and due to this, the sensor readings found for the material were
very low compared to the other three sides of the cube. For both dull and polished
aluminum, they both have a fairly low conductivity with the dull aluminum being higher
and due to this, heat transfer occurs slowly if not at all through both materials.
The power settings affect radiation absorption because by increasing the value of
the power settings, it increases the intensity of the radiant energy given off. It also
accounts for a temperature increases and a lower thermal resistance. By increasing the
power settings, more radiation intensity is being applied to the material which will absorb
a higher amount of it because there is a greater amount of it in its surroundings. This is
true based on the trend of the values in the table in which as the power settings are
increased, the values for each of the materials (sensor readings and temperature) increase
while thermal resistance decreases.
7. Graph 1: Intensity vs. Distance from Table 2 values.
In Table 2, the radiation was measured with increasing distance values and
intensity was correlated as well. From the data analyzed in the experiment, Graph 2 was
made which relates the intensity of the radiation with the distance between the sensor and
the lamp.
Based on the experiment, intensity is related to distance in a way where if the
distance between the sensor and the heated object is increased, the intensity will decrease
because the heat transfer occurring between the sensor and the heated object will get
smaller due to an increase in ambient space between them. The trend in Table 2 and
Graph 1 makes sense because as the distance increases, the intensity will decrease
because the temperature will slowly reach to ambient conditions and away from the
temperature of the heated lamp in the experiment.
In relation to Eq. 1 which was used to create Graph 1, it is valid for all points of
the data because the trend decreases exponentially and eventually reach zero because the
distance which is in the denominator is increasing and multiplied by an exponent of 2.
Due to this, the denominator is greater than 1 which is in the numerator and eventually
the result becomes smaller until it reaches ambient conditions where the intensity
becomes zero at this point. Eq. 1 only holds if the decrease in intensity is proportional to
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120
Intensity(mV)
Distance (cm)
Intensity vs. Distance
8. the increases in distance; if the intensity increases while the distance increases and/or the
trend values become linear where the graph resembles a line, then Eq. 1 does not hold.
Conclusion: This laboratory experiment successfully demonstrated the principles
of radiative heat transfer. The specific objectives of this experiment were the absorptivity
and reflectivity of different surfaces and the Inverse Square Law. Part 1 of the experiment
revealed the radiation properties of multiple surfaces. The data clearly showed that
different surfaces have different absorptivity and reflectivity. Part 2 of the experiment
demonstrated the Inverse Square Law by use of the Stefan-Boltzmann lamp. Graph 1,
which shows the data from part 2, clearly depicts a decreasing exponential relationship,
in agreement with Equation 1. Overall, the laboratory experiment was successful in
completing its objectives and effectively demonstrated the principles of radiative heat
transfer.
