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Thermal Radiation
Engineering lab 1 (Universiti Tun Hussein Onn Malaysia)
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AEROSPACE ENGINEERING LAB 1 (MECH 2128)
SECTION 1
LAB REPORT : HEAT TRANSFER
GROUP 4
LECTURER : DR. MUHAMMAD HANAFI BIN AZAMI
GROUP MEMBERS :
1. MUHAMMAD IQHWAN BIN ZABIDI
1814949
2. AINA SOFEA BINTI FAHIZAL
1911420
3. NAJIHAH FARIZSHA BINTI AHMAD RIZAL 1815388
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1.0 ABSTRACT
For this part of experiment 3, it is subdivided into three parts which are part A, part B
and part C. In part A, the power we consume remains constant, while the distance between
the radiometer and the heat source changes. During part B, the distance between the
radiometer and the heat source is constant, but the power varies between low, medium, and
maximum. Whilst for part C, we varied the angle of incidence while consuming constant
power. The outcome of part A shows that the intensity of the radiometer is inversely
proportional to the distance between the radiometer and the heat source. This demonstrates
that the distance influences the radiometer's intensity reading. In part B, we can observe that
the radiometer's intensity increases as the power increases, causing the temperature to rise.
This demonstrates that the power used to adjust the two temperatures influences the
radiometer's intensity. Whilst in part C, we can genuinely observe that the result of the
luxmeter reading accordingly to the increasing angle does show a decreasing value indicating
the cosine graph when plotted. As the result of this experiment deviates somewhat from the
theoretical value, both random and systematic error does occur during the test and is
accounted for.
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2.0 INTRODUCTION
Thermal radiation is a transfer of heat energy by electromagnetic waves with its related
laws being differently applied to those for conduction and convection. No medium of transfer
is needed as exemplified by the energy of the sun reaching the earth and all bodies at
temperatures above absolute zero emit thermal radiation. Some of the important physical laws
on thermal and optical radiation are Stefan Boltzmann’s and Lambert’s distance laws.
As commonly known as heat transfer due to temperature difference. Heat can be
transferred in three distinct ways, which are commonly known as conduction, convection, and
radiation. Any source that is hot and gives off light emits thermal radiation. As the temperature
of the object increases, it emits higher energies. In general, the net rate of energy transfer by
thermal radiation between two surfaces involves complicated relationships among the
properties of the surface, their orientations among each other, to the extent which the
intervening medium scatters, emits and absorbs thermal radiation and other factors.
In these experiments, some fundamental laws were used and related to radiation. Heat
radiation differs from conduction and convection in that thermal radiation needs the presence
of an intervening medium, whereas conduction and convection need not. In comparison to
conduction and convection, thermal radiation is substantially quicker. For part A, the Inverse
square law of heat, the total energy dQ from an element dA can be imagined flowing through
a hemisphere of radius r. A surface element on this hemisphere ⅆ𝐴1 lies on the line making an
angle 𝜙 with the normal and the solid angle subtended by ⅆ𝐴1 at dA is dw =
ⅆ𝐴1
𝑟2
.If the rate
flow of energy through ⅆ𝐴1 is dQ 𝜙 then dQ 𝜙 = 𝑖𝜙 ⅆ𝑤ⅆ𝐴, where i 𝜙 is the intensity of
radiation in the 𝜙 direction.
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Figure 1 : Solid Angle.
For part B, the Stefan Boltzmann Law experiment, thermal radiation occurs because of
radiation released by bodies because of their temperature. As a result, everything with a
temperature greater than zero will experience thermal radiation. According to the StefanBoltzmann Law, the thermal energy emitted by a blackbody radiator per second per unit
area is proportional to the absolute temperature to the fourth power. Given, 𝑞̇ 𝑏 =
𝑎(𝑇𝑠 4 − 𝑇𝑎4 ), where;
𝑞̇ 𝑏 = Energy emitted by unit area of a black body surface (Wm-2)
𝑎 = Stefan-Boltzmann constant equal to 5.67 × 10-8 (Wm-2K-4)
𝑇𝑠 = Temperature of black plate (K)
𝑇𝑎 = Temperature of the radiometer and surroundings (K)
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3.0 OBJECTIVE
The experiment aims to demonstrates the most important physical laws on thermal
and optical radiation.
1. To investigate the relationship between the distance of radiometer and the heat source
and the radiometer reading.
2. To investigate the relationship between the angle between light source and luxmeter
and luxmeter reading.
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4.0 EXPERIMENTAL DESIGN
4.1 MATERIALS
Figure 2 : Thermal Radiation apparatus.
4.2 METHOD
On a flat table, a thermal radiation device is positioned. As the temperature rises,
the switch is turned to the ‘ON' position, as shown by the temperature measurement. The
temperature reading will be regulated at a set level over time. We also keep an eye on the
radiometer data as the temperature rises. To prevent the radiometer from heating up, it is
protected by a rubber cover. The distance between the radiometer and the heat source is
shown by a scale on the track. To avoid parallax mistake, the distance is measured parallel
to the eyes' level. To eliminate radiometer reading error, the experiment is conducted from
the farthest to the closest distance between the radiometer and the heat source.
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4.3 PROCEDURE
Part A : Inverse Square Law of Heat
1. Place the radiometer at 1000mm from the heat source.
2. Switch on the radiometer and observe and record the background readings i.e.
radiation and temperature. (Ensure that the load is switched on)
3. Switch on the load switch and set the power regulator to 5.
4. Wait for a steady temperature. Record the radiometer reading and the distance
from the heat source of the radiometer along the horizontal track for ten
radiometer positions.
Part B : Stefan-Boltzmann Law
1. Place the radiometer 150mm and the black plate 50mm from the heat source.
2. Record the black plate temperature and the radiometer reading at room
temperature.
3. Then record the readings for selected increments of increasing temperature up to
100°c. Both readings should be calculated simultaneously at any given point.
Part C : Lambert’s Direct Law (Cosine Law)
1. Mount the luxmeter at a separation of L = 400mm from the light source. Ensure
that the luxmeter is connected to the measuring amplifier.
2. Switch on the measuring amplifier and note the background readings.
3. Mount the light source in position 𝜑 = 0°, switch it on and turn the power
regulator to setting no 9.
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4. Record the illuminance, E in Lux and repeat the procedure with increasing angle
of incidence, 𝜑 in steps of 10° (0° to 90°).
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5.0 RESULTS AND DISCUSSION
5.1 DATA TABULATION
Part A : Inverse Square Law of Heat
Table 1 : Radiometer Reading and Distance from Heat Source, X.
Distance (mm)
Radiometer Reading, R (W𝑚2 )
1000
44
900
56
800
75
700
104
600
144
500
211
400
318
300
477
200
606
100
632
Part B : Stefan-Boltzmann Law
Table 2 : Radiometer Reading and Temperature.
Temperature
Radiometer Reading, R
(°𝑘)
(W𝑚−2 )
60
333
139
70
343
166
80
353
219
90
363
278
Temperature (°𝐶)
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100
373
343
Part C : Lambert’s Direct Law (Cosine Law)
Table 3 : Luxmeter Reading, Angles and Normal Irradiance.
Angle ( φ)
Luxmeter Reading, Eφ
0
181
10
148
20
84
30
45
40
33
50
20
60
13
70
10
80
7
90
6
(Lux)
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5.2 SAMPLE CALCULATIONS
Part A : Inverse Square Law of Heat
Table 4 : Logarithm Values for X and R from data taken.
log10 X
log10 𝑅
3.00
2.95
2.90
2.85
2.78
2.70
2.60
2.48
2.30
2.00
1.64
1.75
1.88
2.02
2.16
2.32
2.50
2.68
2.78
2.80
Figure 3: Graph of Radiometer Reading, R vs Distance, X.
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Figure 4 : Graph of log10 𝑅 vs log10 𝑋.
For manual calculation ;
We can take the formula m = (y2-y1) / (x2 – x1) ;
(3.00 – 2.60 )/ (1.64 – 2.5) = - 0.465
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Part B : Stefan-Boltzmann Law
Table 5 : Table of Source Temperature, Ambient Temperature, Radiometer Reading and
Energy Emitted
Readings
Calculations
Source
Ambient
Radiometer
Temperature,
Temperature,
Reading, R
Ts (°𝑘)
Ta (°𝑘)
(W𝑚−2 )
𝑞̇ 𝑏 = 𝑎(𝑇𝑠 4 − 𝑇𝑎4 )
(W𝑚−2 )
𝑎=
𝑞̇ 𝑏
𝑅
333
139
239.19
1.72
343
166
327.25
1.97
219
423.36
1.93
363
278
528.00
1.90
373
343
641.64
1.87
353
300
Calculation of thermal energy radiated by a blackbody radiator per second per unit area :
𝑞̇ 𝑏 = 𝑎(𝑇𝑠 4 − 𝑇𝑎4 )
= 56.7x10^9 (333^4 – 200^4)
= 239.19 W𝑚−2
Calculation for 𝑎 ∶
𝑎=
𝑞̇ 𝑏
𝑅
= 239. 19 / 139
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= 1.72
Average  :
 avg = (1.72 + 1.97 + 1.93 + 1.90 + 1.87 ) / 5
= 1.88
Part C: Lambert’s Direct Law (Cosine Law)
Table 4: Table of Background Illuminance, Luxmeter Reading, Normal
Angle ( φ)
Luxmeter Reading,
Background
Normal Irradiance,
Correct Illuminance
Eφ (Lux)
Illuminance (Lux)
En (Lux)
(Lux)
0
181
181.0
-63
10
148
150.28
-30
20
84
89.39
34
30
45
51.96
73
40
33
43.08
85
50
20
31.11
98
60
13
26.0
105
70
10
29.24
108
80
7
40.31
111
90
6
-
112
118
Irradiance and Correct Illuminance
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1. Normal Irradiance at 0° :
Eφ = En . cos φ
En = Eφ/ (cos φ)
En = 181 /(cos 0°) = 180 Lux
2. Correct Illuminance at 0° :
𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑐𝑒
= 𝐵𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛ⅆ 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑐𝑒 – 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑐𝑒
= 118 – 181
= -63
5.3 DISCUSSION
From the presented Figure 3 and 4, it can be observed that the radiometer
reading decreases as the distance increases. It can be concluded that the greater the
distance travelled, the lower irradiance that the radiometer can measure.
In this experiment, the graph is decreasing proportionally, and it is having
a negative gradient, m hence verifying the inverse square relationship between the
distance and radiation intensity. The inverse square law stating that the intensity of
the radiation is inversely proportional to the square of its distance from the heat
source. Therefore, the intensity of heat waves radiating from a point source is
inversely proportional to the square of its distance from the source. It is then
calculated that the gradient of the Log10x against Log10 R is m= -0.465.
For Part B of this experiment, it is shown in Table 5 that when the power
is set to minimum, the temperature was first recorded at 60°c and the radiometer
reading is at 139 w𝑚−2 . The temperature is then increased by 10°c increments until
it reaches 100°c. The radiometer reading still increases with the increasing
temperature. Throughout this experiment, the ambient temperature remains
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constant as it is recorded as the room temperature, 27°c. By studying the pattern of
the results, we may deduce that as the power increases, the temperature also
increases, so does the intensity of the radiometer. With the aid of the StefanBoltzmann Law, we can determine a for each temperature respectively and the
average a calculated was 1.88. The distinct values of a are due to mistakes that
occurred during the experiment. However, we can still demonstrate the credibility
of the Stefan-Boltzmann Law through this experiment.
For the last part of the experiment, Lambert’s direct law, the Luminous
Intensity, Eφ is directly proportional to Normal Irradiance, En. The angle of
incidence between the normal to the surface and the incident ray determines the
angle of illumination of a surface by a light ray. The radiance is directly proportional
to the cosine of the angle concerning the maximum radiance from the source. An
area element on the surface has the same brightness when viewed from any angle.
This happens due to the area on the surface viewed from any angle is decreased by
the cosine of the emission angle, and the perceived solid angle of the area element
is likewise decreased by the same amount, so the area element seems smaller, but its
brightness remains constant.
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6.0 EROR ANALYSIS
Because of some errors that occurred throughout the experiment, the experimental
results are not reliable as we can see that the values are a bit different from the theoretical
value. As a result, the graph plot lacks the best-fit linear line. The first inaccuracy that
we have justified is that it is difficult to keep the ambient temperature in the laboratory
constant during the experiment due to heat change. This may be caused by the presence
of the air conditioner, making the room is somewhat cooler than the average room
temperature. Next, the equipment may be insensitive during the experiment as they were
systematic error, resulting in data inaccuracies. Lastly, random errors may occur when
reading the apparatus as the eyes were not parallel to the reading of the measurement.
This carelessness will lead to inaccuracy of the result obtained.
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7.0 CONCLUSION
To sum up, based on this experiment, we can investigate the
relationship between the distance between radiometer and heat source and
radiometer reading for the Inverse-square law of heat. The value of a is almost the
same regardless of the temperature change on average. Thus, Stefan-Boltzmann
Law is experimentally proven. In addition, we are also able to determine the
relationship about the angle between the light source and luxmeter and luxmeter
reading for Lambert’s direct law. Next, we may learn how the distance between
the radiometer and the heat source affects the radiometer reading, as well as the
relationship between luminous intensity and normal irradiance, throughout the
experiment. However, several errors need to be avoided to get more precise data.
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8.0 REFERENCES
1. Unknown. (2014). Stefan-Boltzmann Law. Available:
http://hyperphysics.phyastr.gsu.edu/hbase/thermo/stefan.html. Last accessed
23rd May 2021
2. unknown. (2014). Introduction to the principle of heat transfer. Available:
http://www.efunda.com/formulae/heat_transfer/home/overview.cfm. Last
accessed 23rd May 2021
3. Bosdurmaz, E. B. (2019). Thermal Radiation: Introduction to Thermal
Radiation & Inverse Square Law. Bilkent university: ResearchGate.
4. Introduction to Thermodynamics and Heat Transfer,” Yunus A. Cengel, Chapter
12: Radiation and Heat Transfer, McGraw Hill, 1997, pp. 625 – 700.
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