EPF 3105 Food Process Engineering Laboratory 2

EXPERIMENT 3

RADIATION HEAT TRANSFERSESSION TIME: THURSDAY (2.00PM - 5.00PM)

GROUP: 1

GROUP MEMBERS:

YONG KAI SIANG 169428SURIANI BT JUMALI 169414

SITI MARIAM BT MOHD ZAHIRUDDIN

168721

SYAHRUL ANIS HAZWANI BT MOHD BAROYI

169433

SITI NUR FAZLIANA BT ABDULLAH

168797

LECTURER NAME :

DR. ROSELIZA BINTI KADIR BASHA

Faculty of Engineering

UN I V E R S I T I PU T R A MA L A Y S I A

EXPERIMENT 3: RADIATION HEAT TRANSFER

Introduction:

Radiation heat transfer is concerned with the exchange of thermal radiation

energy between two or more bodies. Thermal radiation is defined as electromagnetic

radiation in the wavelength range of 0.1 to 100 microns (which encompasses the

visible light regime), and arises as a result of a temperature difference between two

bodies. No medium need exist between two bodies for heat transfer to take place.

Rather, the intermediates are photons which travel at the speed of light. All bodies

radiate energy in the form of photons moving in a random direction, with random

phase and frequency. When radiated photons reach another surface, they may be

absorbed, reflected or transmitted. The heat transferred into or out of an object by

thermal radiation is a function of several components. These include its surface

reflectivity, emissivity, surface area, temperature and geometric orientation with

respect to other thermally participating objects. In turn, an object’s surface reflectivity

and emissivity is a function of its surface conditions (roughness, finish, etc.) and

composition. In this experiment, we conducted three experiments related to radiation

heat transfer which are inverse square law of heat, Stefan-Boltzmann law and

emissivity.

Inverse Square Law for Heat

Inverse square law is a relationship that states that electromagnetic radiation is

inversely proportional to the square of the distance from a point source. A point

source of gamma rays emits in all directions about the source. It follows that the

intensity of the gamma rays decreases with distance from the source because the rays

are spread over greater area as the distance increases. As light radiates from a point

source, the intensity of light (I) is inversely proportional to the square of the

distance(x) from the source.

I = (1/x2)

As intensity is the power per unit area (W/m2), it naturally decreases with the

square of the distance as the size of the radiative spherical wave front increases with

distance. Inverse square law is applied in radiation protection and patient dose

calculations. This is because, if the radiation strength (intensity) is known at a specific

point, then intensity at any distance from that source may be calculated. According to

Nave (2012), any point source which spreads its influence equally in all directions

without a limit to its range will obey the inverse square law. This comes from strictly

geometrical considerations. The intensity of the influence at any given radius r is the

source strength divided by the area of the sphere. Being strictly geometric in its

origin, the inverse square law applies to diverse phenomena. Point sources of

gravitational force, electric field, light, sound or radiation obey the inverse square law.

Figure: Illustration of intensity and the distance.

Stefan-Boltzmann Law

The thermal energy radiated by a blackbody radiator per second per unit area is

proportional to the forth power of the absolute temperature and is given by

PA

= 𝛔T4 j/m2s Stefan-Boltzmann Law

𝛔 = 5.6703x 10-8 watt/m2 K4

For hot objects other than ideal radiators, the law is expressed in the form:

PA

= ε𝛔T4

Where ε is the emissivity of the object (ε = 1 for ideal radiator/black body). If the hot

object is radiating energy to its cooler surroundings at temperature Tc, the net

radiation loss rate takes the form

PA

= ε (T4 – Tc4)

A black body is defined as a body that absorbs all radiation that falls on its surface. A

black body is a hypothetic body that completely absorbs all wavelengths of thermal

radiation incident on it. Such bodies do not reflect light, and therefore appear black if

their temperatures are low enough so as not to be self-luminous. All blackbodies

heated to a given temperature emit thermal radiation.

Emissive of different surface polished silver anodized matt black

Emissivity is a measure of the efficiency in which a surface emits thermal

energy.it is defined as the ratio of energy being emitted related to that emitted by a

thermally black surface (a black body). A black body is a perfect emitter of heat

energy and has an emissivity value of 1. A material with an emissivity value of 0

would be considered a perfect thermal mirror.

The emissivity coefficient, ԑ indicate the radiation of the heat from a ‘grey

body’ according the Stefan-Boltzmann Law, compared with the radiation of heat from

a ideal ‘black body’ with the emissivity coefficient = 1. For a grey body reactor, The

Stefan-Boltzmann Law can be expanded to give qg = ԑ σ (Ts4 – Ta

4). Where the

radiating surface for a black body ԑ=1, and for a grey body, ԑ <1.

Figure for the experiment on emissivity

A mirrored surface may reflect 98% of the energy, while absorbing 2% of the

energy. A good black body surface will reverse the ratio, absorbing 98% of the energy

and reflecting only 2%. Effective emissivity is the ratio of the total amount of energy

exiting a black body to that which is predicted by Planck’s law. This is the most

frequently to as ‘emissivity’. Effective emissivity of a cavity type black body will

normally be much higher than the surface emissivity due to the multiple energy

bounces inside the body cavity.

Equipment Setup:

P. A. Hilton Limited thermal radiation unit, polished plate, silver anodized plate and

matt black plate with black plate.

Figure 1: P. A. Hilton Limited thermal radiation unit.

Experiment A: Inverse Square Law for Heat

Objectives:

The objective for this experiment is to show the intensity of radiation on a

surface is inversely proportional to the square of the distance of the surface from the

radiation source.

Materials and Apparatus:

P. A. Hilton Limited thermal radiation unit

Procedures:

Initial Position: Distance from heat source(X) = 800mm

1. The power control was set to widen the position and the heater was allowed

approximately 5 minutes to reach a stable temperature prior to starting the

experiment.

2. The radiometer reading(R) and the distance from the heat source (X) were

recorded for a number of positions of the radiometer along the horizontal

track.

3. The radiometer was allowed approximately 2 minutes to stabilize after being

moved to each new position.

4. The logarithm values (log10) of the data taken were calculated.

5. A log-log plot of radiometer reading against distance was generated.

*Note that radiometer sensor surface is 65mm from center line of detector carriage

and therefore center line position will be 865 mm.

Results:

Table A-1: Radiometer reading and distance from the heat source.

Distance, X

(mm)800 700 600 500 400 300 200

Radiometer

, R (Wm-2)52 68 92 131 192 292 564

Table A-2: Log X and Log R

Log10 X 2.903 2.845 2.813 2.778 2.602 2.474 2.301

Log10 R 1.716 1.833 1.964 2.117 2.283 2.465 2.751

100 200 300 400 500 600 700 800 9000

100

200

300

400

500

600

Graph of Radiometer Reading against Distance from the Heat Source

Distance from Heat Source, X (mm)

Radi

omet

er R

eadi

ng, R

(Wm

-2)

Figure A-1: Graph of Radiometer Reading against Distance from the Heat Source

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 31.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9

f(x) = − 1.61956949616965 x + 6.49155181290161

Graph of log10R against log10X

log10X

log1

0R

Figure A-2: Graph of log10R against log10X

Discussion:

In this experiment, the radioactive source will allowed the radiation to emit

about 2 minutes to stabilize before the reading taken. The graph of radiometer reading

against distances from the heat source and graph of Log10 R against Log10 X were

plotted based on the collected date. For the graph of radiometer reading against

distances from the heat source, the radiometer reading is inversely proportional to the

distance. On the other words, as the distances decrease, the radiometer readings will

increase. The graph is decreasing proportionally from log10 X = 2.301 to log10 X =

2.903.

From the reading obtained, a graph of log10 R against log10 X is in a straight

line that having a negative slope of 1.6196 which is approximately -2, therefore,

verifying the inverse square relationship between distance and radiation intensity that

satisfy the equation

The inverse square law stating that the intensity of the radiation at a location is

inversely proportional to the square of its distance from the source of radiation.

Hence, in terms of light and radiation, the intensity of light or other linear waves

radiating from a point source is inversely proportional to the square of the distance

from the source. The inverse-square law generally applies when some force, energy,

or other conserved quantity is evenly radiated outward from a point source in three-

dimensional space. Since the surface area of a sphere which is 4πr2 is proportional to

the square of the radius, as the emitted gets farther from the source, it is spread out

over an area that is increasing in proportion to the square of the distance from the

source.

The experimental results are not accurate due to some errors occur during the

experiment. Thus, the plot obtain is not give the best fit of a linear line. Firstly,

varying of ambient temperature causes some deviation in the results obtained. This is

because ambient temperature is difficult to be kept constant all the time during the

experiment and might be effluent due to the air conditional in the room. In fact, thr

ambient room temperature is lower than usual during the experiment is carried our.

Secondly, the insensitivity of equipment used during the experiment which is the

thermal radiation unit also will led to some inaccuracy of data collected during the

experiment. The equipment must be ensured is in a perfect and good condition to get

accurate readings. Besides that, it may due to parallax error during fixing the distance

of surface from source of radiation.

Conclusion:

It is proven that the intensity of radiation on a surface is inversely proportional

to the square of the distance of the surface from the radiation source according to the

experimental results and graph.

Experiment B: Stefan-Boltzmann Law

Objectives:

The objective for this experiment is to show that the intensity of radiation

varies as the fourth power source temperature.

Materials and Apparatus:

P. A. Hilton Limited thermal radiation unit

Procedures:

1. The equipment was set up as the Figure 1 above. The reflective disc was also

placed in the radiometer to prevent heating reflect and zero drift.

2. The initial values of variables to be used was set :

- Distance from radiometer to black plate (X) = 200 mm

- Distance from black plate to heat source (Y) = 50 mm

3. The power knob was set to 3 W.

4. After the reading of heat source temperature was stabilized, the reflective disc

was taken out from radiometer, the black plate was placed in the holder, and

timer was set for 2 minutes.

5. After 2 minutes, the reading of heat source temperature, TS, radiometer

reading, R, and temperature of surrounding, TA were recorded. The reflective

disc was placed again in the radiometer.

6. Steps 3 to 5 were repeated for power of 3W, 5 W, and 7 W.

Results:

Distance from radiometer to black plate (X) = 200mm

Distance from black plate to heat source (Y) = 50mm

Q emitted = radiometer reading x (0.0632 + L2) / (0.063)2

L = 200mm (0.2m)

Q emitted = radiometer reading x (0.06322 + 0.22) / (0.063)2

= radiometer reading x 11.07

Table B-1: The reading of temperature and radiometer with calculated value of qb

Reading Calculation

Powe

r (W)

Temperature

Reading,

Ts(oC)

Radiomete

r

Reading,R

(W/m2)

Ts(K) TA(K) qb=

11.07xR

(W/m2)

qb=

σ(Ts4 -

TA4)

(W/m2)

3 183 102.5 456 298 1134.675 2005.829

5 224 163.1 497 298 1805.517 3014.443

7 350 296.2 623 298 3278.934 8100.087

Where

The Stefan Boltzmann Law states that q emitted = σ (Ts4 - TA

4)

Q emitted = energy emitted by unit per area of a black body surface

σ = Stefan Boltzmann constant (σ = 5.674x 10-8 Wm-2K-1)

Ts = Source temperature of radiometer and surrounding

TA = temperature of radiometer and surrounding

C alculation:

Ambient temperature = 200C

σ = 5.674x 10-8 Wm-2K-1

For power = 3W

Qb = 11.07xR

= 11.07x102.5

= 1134.675W/m2

For Stefan-Boltzmann Law

Qb =σ (Ts4 - TA

4)

= 5.674x 10-8 (4564 – 2984)

= 2005.829W/m2

For power = 5W

Qb = 11.07x 163.1

= 1805.517W/m2

For Stefan-Boltzmann Law

Qb =σ (Ts4 - TA

4)

= 5.674x 10-8(4974 –2984)

= 3014.443W/m2

For power = 7W

Qb = 11.07x296.2

= 3278.934W/m2

For Stefan-Boltzmann Law

Qb =σ (Ts4 - TA

4)

= 5.674x 10-8(6234 –2984)

= 8100.087W/m2

Discussion:

The intensity of radiation and temperature varies at four different power inputs

which are 3W, 5W and 7W. The value of qb can be calculated by two formula which

are qb= 11.07 x R and qb = σ (TS4 - TA4) which is the Stefan-Boltzmann formula.

From the result calculated, the radiometer readings were increasing as the

temperature of black plate increase. This result shows that the black body was

absorbing the heat emitted from the heat source and some of the heats are transmitted

through radiation. The result also shows that, as the power input increase, the higher

the temperature and radiometer and this indirectly the value of q emitted increase also.

All the result calculated were recorded in the table B-1. The calculated values of qb

from these two formulae are different. By theoretically, the qb value of these two

formulas should be same or closed to each other. However, the trends of the result

calculated from these two formulae are the same, which is increasing as the power

input increasing.

These deviations of the result may be due to some errors that occurred during

the experiment. First, the sensitivity of the equipment used in this experiment. The

equipment might be too old and has low sensitivity that lead to inaccuracy of the data

collected. Parallax error might be occurred during measuring the distances between

the black plate and heat source. To get an accurate result, some precaution steps must

be taken for example, eyes must be at the correct position when measuring the

distance between the black metal and heat sources. Others than that, the radiometer

readings should be taken sharply every two minutes.

Experiment C: Emissivity

Objective:

The objective for this experiment is to determine the emissive of different

surface which include polished plate, silver anodized plate and matt black.

Procedure:

1. The matt black plate was installed in the carrier.

2. The power to the heat source was varied and the temperature of the metal plate

(Ts) and radiometer reading (R) were recorded at various settings.

3. It was recommended that while waiting for the black plate temperature to

stabilize between each increase of the heater power control the reflective disc

was placed in the radiometer to prevent heating effects and zero drift.

4. The procedure ware repeated for the silver anodized plate.

Results:

E = Emissivity of surface

Initial values of variable to be used

i. Theoretical Formula :

Stefan-Boltzmann law

q Emitted = σ (Ts4 – TA

4)

σ = 5.674 x 10-8 (Wm-2K-1)

ii. Calculation Formula :

Distance from radiometer to black plate (X) = 100 mm

Distance from heat source to nearest metal plate (Y) = 50mm

qemitted = radiometer reading x (0.0632 + L2) / (0.063)2

Hence for L = 100mm (0.1m)

qemitted = Radiometer Reading x (0.0632 + 0.12) / (0.063)2

= Radiometer Reading x 3.519

For each plate in turn:

Where K = oC +273 = 293K

Ambient temperature, TA = 20oC

Powerheat

source

s(watt)

Temperatur

e Reading

(TS),oC

Radiometer

Reading (R)

Wm-2

TS

(K)

TA

(K)

qb =

3.519 x R

(Wm-2)

E =

qb / σ (TS4 –

TA4)Wm-2

3 125 401.8 427 298 1413.93 0.9827

5 172 507.8 445 298 1766.95 0.9940

7 193 587.3 466 298 2066.71 0.9275

Average

E :

∑ E3

=

2.90423

= 0.9681

≈0.97

Table C-1: The readings of the matt black plate

Table C-2: The readings of the silver anodized plate.

Powerheat

source

s(watt)

Temperatur

e Reading

(TS),oC

Radiomete

r Reading

(R)

Wm-2

TS

(K)

TA

(K)

qb =

3.519 x R

(Wm-2)

E =

qb / σ (TS4

– TA4)Wm-2

3 37 26.2 315 298 92.20 0.8293

5 54 49.0 326 298 172.43 0.8916

7 86 67.8 342 298 238.59 0.7257

Average E : ∑ E3

=

2.44663

= 0.8155

≈0.82

Calculation:

Average value of emissivity of matt black plate, E

¿ 0.9827+0.9940+0.92753

= 0.97

Average value of emissivity of silver anodized plate, E

¿ 0.8293+0.8916+0.72573

= 0.82

i) Matt Black plate

Heat power = 3 watt, TS = 427K, TA = 298K, R = 401.8 Wm-2

Thus, q emitted, qb = Radiometer Reading (R) x (0.0632 + 0.12) / (0.063)2

= R x 3.519

= 401.8 x 3.519

= 1413.93 Wm-2

Emissivity of surface, E = qb / σ (TS4 – TA

4)

= (1413.93) / (5.674 x 10-8 × (4274 – 2984))

= 0.9827 Wm-2

ii) Silver anodized plate

Heat power = 3 watt, TS = 315K, TA = 298K, R = 26.2Wm-2

Thus, q emitted, qb = Radiometer Reading (R) x (0.0632 + 0.12) / (0.063)2

= R x 3.519

= 26.2 x 3.519

= 92.20Wm-2

Emissivity of surface, E = qb / σ (TS4 – TA

4)

= (92.20) / (5.674 x 10-8 × (3154 – 2984))

= 0.8293Wm-2

Discussion:

This experiment is carried out to determine the emissive of different surface,

matt black, silver anodized and polished. Formulae like qb = 3.519 x R and E = qb/

σ(Ts4 – TA4) are applied and all the results are recorded in Table C-1, C-2, and C-3.

The results show that as the temperature increase, the radiometer reading will

increase too while the emissivity of the surface will decrease. This is due to the ability

of the surface to emit energy by radiation. The average value of the emissivity of the

matt black plate, silver anodized plate and polished plate are approximately 0.97 and

0.82 respectively. The ideal surface for a perfect emitter and absorber of radiation is

black body and this is why black plate has the highest average value of emissivity.

Stephan-Boltzmann equation prove that a small increase in the temperature of

a radiating body results in a large amount of additional radiation being emitted while

this statement holds true with our result. The result show that R increase in

exponentially with the Ts of the metal plate. Other than that, silver anodized plate

which has a thick coating surface compare to polished plate will has higher

emissivity.

Conclusion:

In conclusion, matt black has higher emissivity than silver anodized plate. The

emissivity of the plate is caused by its surface characteristic and colour. The matt

black plate which is in black colour has higher emissivity.

Reference:

1. “Radiation heat transfer”. Retrieved December 19, 2013 from

http://www.mhtlab.uwaterloo.ca/courses/ece309/lectures/pdffiles/summary_ch12. pdf

2. “Stefan-Boltzmann Law”. Retrieved December 19, 2013 from

http://www.wright.edu/~guy.vandegrift/climateblog/smallfiles01/Stefan.pdf

3. “An emissivity primer”. Retrieved May 5-9, 2014 from

http://www.electro-optical.com/eoi_page.asp?h=What+Is+Emissivity?