TABLE OF CONTENT

Abstract 2

Introduction and Objectives 3

Theory 4

Description of the Experimental Apparatus 6

Procedure 8

Data and Observations 10

Analysis and Results 12

Discussions 16

Conclusions 19

References 20

Appendix 20

ABSTRACT

1

An experiment was conducted to perform and demonstrate how the intensity of radiation

varies. This following experiment outlines the proper procedure for verifying the Inverse Square

Law for Heat and the Stefan-Boltzmann Law as well as to study Area Factors. Consequently the

student will then demonstrate them graphically by doing the analysis based on the all the data

and readings obtained.

As commonly known heat is transferred due to a temperature difference. Heat can be

transferred in three different ways, which are known as conduction, convection and radiation.

Any object that is hot gives off light known as Thermal Radiation. The hotter an object is

the more light it emits. And, as the temperature of the object increase, it emits most of its light at

higher and higher energies. (Higher energy light means shorter wavelength light.) 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 with respect to each other,

the extent to which the intervening medium scatters, emits and absorbs thermal radiation and

other factors. In these experiments, we will prove some fundamental law relating to radiation

INTRODUCTION AND OBJECTIVES

2

In this particular laboratory session, the experiment has been divided to three parts. In

experiment 1, students are required to show that the intensity of radiation varies as the fourth

power of the source temperature.

Besides that, experiment 2 is conducted to show the tile intensity of radiation on a surface

is inversely proportional to the square of distance of the surface from the radiation source. On the

other hand, experiment 3 required the students to demonstrate that the exchange of radiant

energy from one surface to another is dependent upon their interconnecting geometry, i.e. a

function of the amount that each surface can ‘see’ of the other.

In addition to that, this experiment is also useful in such a way that it helps to provide

some exposure to the students so that they are able to interpret the obtained test data and at the

same time are able to apply the theory they have learned in class.

THEORY

3

The Stefan-Boltzmann Law

The Stefan-Boltzmann Law states that:

qb= (Ts4 –Ta

4)

Where qb = energy emitted by unit area of a black body surface (Wm-2)

(Note: Energy emitted by surface = 3.040 × reading from radiometer R – refer to

Radiometer Data sheet for explanation)

= Stefan-Boltzmann constant equal to 5.67 x 10-8 (Wm-2K-4)

Ts = Source temperature and surrounding = black plate temp. (K)

Ta = Temperature of radiometer and surrounding = room temp. (K)

The Inverse Square Law

The total energy dQ from an element dA can be imagined to flow through a hemisphere of radius

r. A surface element on this hemisphere dA1 lies on a line making an angle with the normal and

the solid angle subtended by dA1 at dA is dw = dA1/r2

If the rate of flow of energy through dA1 is dQthen dQ= idwdA where iis the intensity of radiation in the direction.

Figure 3.1 Radiation Heat Transfer: Solid Angle

Radiation Heat Transfer: Area Factor

4

Figure 3.2 Radiation Heat Transfer: Area Factor

The heat transfer rate from one radiating black surface to another is dependent on the amount

that each surface can see of the other surface. In order to solve radiant heat transfer problems an

area factor F is introduced where F is defined by the fraction of energy emitted per unit time by

one surface that is intercepted by the other surface.

Thus the time rate of radiant heat transfer (Q12) between two black surfaces of area A1and A2 at

temperature T1 and T 2 respectively is given by:

Q12= A1 F12 (T14 –T2

4)

Area factors are found by analysis, numerical approximation and analogy and results for

common configurations have been published in graphical form.

DESCRIPTION OF THE EXPERIMENTAL

APPARATUS

5

Description of the experimental rig

The Radiation Heat Transfer Rig consists of a pair of electrically heated radiant heat and

light sources, together with a comprehensive range of targets and measuring instrumentation.

The unit consists of a horizontal bench mounted track fitted with a heat radiation source

end and a light source at the other. Between the two sources may be placed either a heat radiation

detector or a light meter. In addition, a number of accessories can be fitted for experimental

purposes. These include metal plates with thermocouples attached, two vertically oriented metal

plates to form an aperture, and a number of acrylic filters. The radiation detectors and

accessories are all clamped to stands which enable them to be positioned at different distances

from the appropriate source. Distances are measured with a scale mounted on the front track.

Electrical power for the two radiation sources is supplied from control panel and a

variable transformer. Temperatures of the two metal plates used in conjunction with the heat

radiation source are displayed on a digital read-out, either reading being selected by switching

the connectors. Output from heat radiation detector and light meter are displayed on digital read

out.

Figure 3.3: View of the Radiation Heat Transfer Unit

6

Figure 3.4: Experiment I Set-up the Stefan-Boltzmann Law

Figure 3.5: Experiment II Set-up the Inverse Square Law

Figure 3.6: Experiment III Set-up Radiation Heat Transfer: Area Factor

7

PROCEDURE

Experiment I

1. Turn on the power source is switched on.

2. Connect black plate cable terminal is connected to the panel and measure the room

temperature is measured using the black plate

3. Install the black plate is installed on the horizontal rig with a distance of 50mm from the

heat source.

4. Position the radiometer is positioned at x=110 mm from the heat source, the radiometer

must be aligned such that the sensing surface is parallel to the heater surface.

5. Switch on the radiometer knob is adjusted to no. 2. The front surface of the radiometer is

closed with a black surface object and the knob is adjusted to get 0 reading.

6. Set the heater power input is set to maximum level.

7. When the black plate temperature (Ts) reaches 600C, all the corresponding radiometer

reading (R)* for black plate temperature from 600C to 1000C with the temperature

increment of 50C is recorded.

8. The black plate is dissembled with care.

Experiment II

1. Set the power input is set to maximum.

2. Position the radiometer is positioned at x=100 mm from the heat source. The radiometer

must be aligned such that the sensing surface is parallel to the heater surface.

3. After the heater is heated to a considerable constant rate, the radiometer reading can now

be observed to be almost constant.

4. The radiometer reading (R )* and its distance (x) from the heat source is recorded.

5. The above procedure is repeated for different radiometer to heat source distance (x), from

100 mm to 1000 mm with the increment of 100 mm.

8

Experiment III

1. The black plate is installed on the horizontal rig with a distance of 50 mm from the heat

source.

2. The aperture, which is formed by two aluminium-coated plates, is installed on the rig

with a distance of 200 mm from the heat source. The aluminium-coated surface is

positioned facing the heat source.

3. The radiometer is positioned at 300 mm from the heat source. The radiometer must be

aligned such that the sensing surface is parallel to the heater surface.

4. The heater power input is set to maximum level.

5. The aperture opening is set to 60 mm.

6. When the temperature of the black plate (Ts)has reached a steady value, the radiometer

reading (R)*for the aperture-opening from 60 mm down to zero in step of 5 mm is

recorded.

7. The black plate and aperture is disassembled, the heat source power is set to minimum

and the power source is turned off.

9

DATA AND OBSERVATIONS

Experiment I: Stefan-Boltzmann Law

= 5.67 X 10-8 (Wm-2K-4)

Room temperature (T∞) = 28°C

Black plate,

Ts (C)

Radiometer

Reading, R

(W/m2)

Ts

(K)

T∞

(K)

qb = 3.040 R

(W/m2) exp.

qb = (Ts4 - T∞

4)

(W/m2) theo.

Percentage

Error (%)

60 69 333 297 209.76 256.03 18.07

65 81 338 297 246.24 298.86 17.60

70 93 343 297 282.72 343.63 17.73

75 107 348 297 325.28 390.40 16.70

80 122 353 297 370.88 439.23 15.60

85 134 358 297 407.36 490.18 16.90

90 151 363 297 459.04 543.31 15.50

95 170 368 297 516.8 598.69 13.70

Table 3.1: Result for Experiment III

10

Experiment II: Inverse Square Law

Heat Sources

Distance, X (mm)

Radiometer

Reading, R

(mW/cm2)

log 10 X log 10 R

100 174.5 2 2.24171

200 93.0 2.30103 1.96848

300 50.2 2.47712 1.70070

400 31.0 2.60206 1.49136

500 21.2 2.69897 1.32634

600 15.8 2.77815 1.19866

700 11.7 2.84510 1.06819

800 9.4 2.90309 0.97313

900 7.5 2.95424 0.87506

1000 5.6 3 0.74819

Table 3.2: Result for Experiment II

Experiment III: Area Factors

Aperture (mm) 60 55 50 45 40 35 30 25 20 15 10 5 0

Radiometer Reading

(mW/cm2)2.2 3.0 4.4 4.0 3.5 3.0 2.7 2.4 2.1 1.6 1.1 0.5 0.1

Table 3.3: Result for Experiment III

11

ANALYSIS AND RESULTS

All the required graphs are shown on the following pages:

For Experiment II

Graph 1: Graph of Radiometer Reading (Intensity of Radiation) vs. Distance

Graph 2: Graph of log10 R versus log10 x

For Experiment III

Graph 3: Graph of Radiometer Reading against Aperture Opening

12

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

120

140

160

180

200

Radiometer Reading vs. Distance

DISTANCE, X (mm)

RADI

OM

ETER

REA

DIN

G, R

(mW

/cm

2)

Graph 1: Graph of Radiometer Reading (Intensity of Radiation) vs. Distance

13

1.8 2 2.2 2.4 2.6 2.8 3 3.20

0.5

1

1.5

2

2.5

f(x) = − 1.52339323075501 x + 5.40528629591971

log 10 R vs. log 10 X

log 10 X

log

10 R

Graph 2: Graph of log 10 R vs. log 10 X

14

0 10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Radiometer Reading vs. Aperture Opening

APERTURE OPENING (mm)

RADI

OM

ETER

MET

ER (m

W/c

m2)

Graph 3: Graph of Radiometer Reading vs. Aperture Opening

15

DISCUSSIONS

Experiment I

The comparison of the emissivity of the black plate and Stefan Boltzmann Law, as well as the trend and the discrepancy between both results.

The first calculation is made according to the Stefan – Boltzmann Law and the other one is according to emissivity of the black plate, which is the experimental value. By comparison both results, generally we can say that the percentage error is quite small. Thus the experimental results agree closely with the Stefan-Boltzmann law, which is the theoretical value.

The uncertainty, in percent, of qb, if the measurement of the temperature is uncertain by 2%? Calculation is shown.

Consider the data at Ts = 60 C and the corresponding radiometer reading R = 69 W/m2. Thus the

emissivity of the black plate is qb = 3.040 x 69 = 209.76 W/m2.

Ts = 60 + 273 = 333 K

T∞ = 24 + 273 = 297 K

qb = (Ts4 - T∞

4) = 5.67 x 10-8 (3334 – 2974) = 256.03 W/m2 .

% Error = (256.03 – 209.76) x 100 / 256.03 = 18.07 %

16

Experiment II

The Radiation Heat transfer Rig set-up

The gradient of the slope for the graph of log10 R versus log10 x and what does it indicates?

From the best fit line equation, Y = -1.523X + 5.405 the gradient of the slope for the graph of log10 R vs. log10 X is equal to -1.523.

In theory, the intensity of radiation on a surface should be proportional to the square of distance of the surface from the radiation source. That is,

R= k

X 2where k is aconstant

log10 R=log10k−log10 X2

log10 R=−2 log10X+ log10k

From the derivation above, the theoretical gradient value is found to be -2. Thus, the

experimental gradient value calculated seems to lie within good tolerance from the theoretical

one.

What can your verified from the graphs?

17

From both Graph 1 and Graph 2, the negative slope shows the inversely proportional relationship

between the intensity of radiation on a surface and the square of distance of the surface from the

radiation source. The gradient actually the rate of heat generated, qgen.

Experiment III

The Radiation Heat transfer Rig set-up

Analysis of Graph 3

From the data recorded and also from Graph of Radiometer Reading against Aperture Opening,

we can say that generally the radiometer reading increases linearly with increasing aperture

opening. However, the radiometer readings for distance 55 mm and 60 mm show another story,

probably due to some errors. Errors may rise from numerous sources such as equipment faulty

and parallax error. Therefore, despite the errors, we can conclude that the exchange of radiant

energy from one surface to another is dependent upon their interconnecting geometry.

Why the radiometer is not showing zero reading when the aperture opening is 0mm?

In this experiment, we could not obtain radiometer reading equals to zero when the aperture

opening is zero because of fraction of the incident radiation from the heat source. Thus, the

radiometer will still give a small reading although the aperture opening is zero.

18

CONCLUSIONS

Experiment I

In Experiment I, it proven that the intensity of radiation varies as the fourth power of the source

temperature. Comparing the emissivity of the black plate and Stefan Boltzmann Law, generally

we can say that the percentage error is small. Thus the experimental results agree closely with

the Stefan-Boltzmann law, which is the theoretical value.

Experiment II

From best fit line of Graph 2, the experimental gradient obtained is equal to -1.523. The inverse

square law says that the theoretical slope of graph log10R vs. log10X has a value of -2. Thus, the

experimental gradient value calculated seems to lie within good tolerance from the theoretical

one. Besides, the negative slope shows the inversely proportional relationship between the

intensity of radiation on a surface and the square of distance of the surface from the radiation

source.

Experiment III

From the data recorded and also from Graph of Radiometer Reading against Aperture Opening,

we can say that generally the radiometer reading increases linearly with increasing aperture

opening. Despite the errors, we can conclude that the exchange of radiant energy from one

surface to another is dependent upon their interconnecting geometry. It is also found out that we

could not obtain radiometer reading equals to zero when the aperture opening is zero because of

fraction of the incident radiation from the heat source.

19

REFERENCES

Instruction manual from the Heat Transfer & Applied Thermodynamics Lab

2012, Radiation Heat Transfer, http://www.engineeringtoolbox.com/radiation-heat-transfer-d_431.html

2012, Wikipedia, Inverse Square Lawhttp://en.wikipedia.org/wiki/Inverse-square_law

2012, Wikipedia, Heat Transferhttp://en.wikipedia.org/wiki/Heat_transfer

2012, The overview behind heat radiationhttp://www.efunda.com/formulae/heat_transfer/radiation/overview_rad.cfm

Incropera, DeWitt, Bergmann, Lavine, Fundamentals of Heat and Mass Transfer, 7 th Edition, Wiley Asia Student Edition

Yunus A. Cengel, Michael A. Boles, Thermodynamics An Engineering Approach, 7 th Edition, Mc Graw Hill

APPENDIX

20

Figure 3.7: Heat Transfer Mode

21