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Part B

Introduction

The need of comfort in Tasmania home was determined by the building materials that

reduce the heat flow through roof in Hobarts climate zone. According to the ICANZ

insulation company (derived fromhttp://www.icanz.org.au/handbook/handbookpart1section1/), the Hobarts climate

zone belongs to the climate zone seven, which has a minimum required total R-value

for a roof of 3.8 12 KWm as required by the BCA 1996. To calculate the speed heat

is conducted through roof, the following formula was used:R

TTA

t

Q coldhot

=

)(, A

pitched metal roof with flat ceiling was chosen. If theres no insulation applied on the

roof, according to the BCA 1996, the building materials presents are: metal cladding,

roof batten, rafter, ceiling joist, ceiling batten and plasterboard. The structure and R-

values are shown in figure 1.

Figure 1: R-values of common roof construction materials. (Derived from

http://www.icanz.org.au/handbook/R0200/, and TABLE 1. R-VALUE OF COMMON

BUILDING MATERIALS, class note).

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According to figure one, R= 0.979 12 KWm . Using a roof of 100 2m , inside

temperature of 25 and outside temperature of 5, Wt

Q9.2042

979.0

)525(100

= .

This is a large amount of heat loss for a house which would be expensive and waste

resources. If the minimum R-value for zone seven was used,

Wt

Q3.526

8.3

)525(100

= ,which is three fourth of the speed of heat loss from the

house. From

http://www.sustainablelivingtasmania.org.au/content/documents/WebInsulation.pdf ,

up to 35% of heat loss is through the ceiling if it is not insulated in the roof space. A

suitable choice of roof insulation is economical and essential.

The insulation chosen is, unfaced fiber glass batt, foil-faced fiber glass batt (which

has a foil attaches on one side of the batt) and Single Bubble Foil, whose

technique data is shown in table one

Table one: technique data of the insulation.(derived from http://www.chang-

wang.com/foil-single-bubble-foil.htm,

http://www.specjm.com/files/pdf/bid0015.pdf&

http://www.specjm.com/files/pdf/bid0008.pdf)

and from http://www.chang-wang.com/foil-single-bubble-foil.htm, 04.0=foile .

Since they are insulations to reduce heat loss, the foil is placed above the ceiling joist

without contact to the plasterboard, the unfaced batt is also placed on the same

position, while the foil-faced batt is also placed on the plasterboard with the foiled

face at the bottom. The arrangement is shown in figure 2.

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Fig.2 Home insulation arrangement

A B

C

Reduction of up-flowing heat from calculations

For the roofs of three different types of insulation presents, R can be calculated to

indicates the heat flow out by conduction, and through the e value presents the total

heat flow can be calculated. The properties of the roofs with these three type of

insulation is shown in table two.

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Table two: properties of the roof with different insulation. (partly derived from

THERMAL RESISTANCE OF AIR SPACE class note)

Property R-foil(shown intable one)

e Increased R-valueof air space dueto the existence oflow-E surface

R-withoutfoil and batt

(shown in

fig.1)

Total R

(12

KWm

)

foil 0.04 0.32 0.979 1.299

batt 3.3 0.979 4.279

Foil-facedbatt

3.3 0.04 0.979 4.279

Therefore, according toR

TTA

t

Q coldhot

=

)(, the speed of heat loss through the

ceiling by conduction are:

Foil:R

TTA

t

Q coldhot

=

)(= 1539.6W

Batt and foil-faced batt:R

TTA

t

Q coldhot

=

)(= 467.4W

Also, according to the Stefan-Boltzmann Law: Q/ t = e A(Th^4 Tc^4) , where =

5.6703 *10-8 istheStefan-Boltzmann Constant, thus for the speed of heat flow by

radiation are:

Foil and foil-faced batt: Q/ t = e (Th^4 Tc^4) A=8.8*10 2 W

Batt: cannot stop heat loss by radiation.

According to Newton's Law of Cooling, the rate of change of the temperature of an

object is proportional to the difference between its own temperature and the ambient

temperature,(derived from

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html). Which

can be calculated using Q/ t= k A (Th Tc ), where k is the convective heat transfer

coefficient, but as the k-value is not constant(it change by the state of the fluid

medium), the exact value of heat loss cannot be calculated in this situation.

http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.htmlhttp://www.engineeringtoolbox.com/convective-heat-transfer-d_430.htmlhttp://www.engineeringtoolbox.com/convective-heat-transfer-d_430.htmlhttp://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html

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Throughout all the calculations above, there are several assumptions. Firstly, the

outside temperature is assumed as 5 . Secondly, as the insulation absorb and transfer

heat, the heat would flow to the air space above the insulation, which makes the air

temperature hotter. Thus, the difference in temperature should not equal to the

difference between the room and outside, but for calculation, the difference oftemperature is assumed constantly as 20 . Thirdly, the foil chosen is a single bubble

foil which has a layer of air cells inside. Therefore, there ought to be a thin air layer

inside the foil which helps reduce conduction loss, but as the data has not applied the

component of the material inside as well as the thickness of the air cells, thus the R-

value of the thin air cells and the materials consist the wall of the air cells cannot be

calculated. Therefore the air cells are assumed as not existed. The fourth is the e value

of the foil attaches to the batt, as the surface area and colour of the single foil and the

foil surface on the batt assembles and e is the ratio of the speed of heat emitted by an

object to the speed of heat emitted by that object painted in black at the same

temperature, thus, the e-value of the foil surface on the batt is assumed to be 0.04. The

fifth is the R-value of the foil has been neglected. The sixth is that in the real

situation, dust on the insulation would affects the performance of the insulation, while

in this report , the existence of dust is neglected.

Difficulties also existed in the research. The first one is the calculation on the heat

transfer by convection, since there is a temperature difference existed, convection

would occur, but as the k-value varies according to the state of the fluid, accurate

number cannot be calculated. The second problem is that the information given by the

insulation company is not accurate and covers all the bases, such as the thickness of

the air cells in the foil and the material consists the wall of the air cell have not be

given, thus some calculation might not be accurate. Thirdly, the temperature of the air

in the air space varies but the rate and the amount of change cannot be found.

When talking about the effect on reducing heat loss, foil helps to reduce the heat

transferred by radiation, as the shinny surface can reflect 96% the heat through

radiation back to the room, thus, according to the calculation above, 8.8*10 2 W

which is a relatively low number of heat transfer. But foil is a good conductor of heat

which has a very small R-value that can be neglected, thus foil cannot reduce heat

transferred by conduction. When talking about convection, as foil has a low e-value,

the speed of heat emitted is relatively low, thus the temperature of the foil would rise.

Since Q/ t by convection is proportional to the difference on temperature, foil would

reduce heat loss by convection. As for the unfaced batt, batt is a poor conductor of

heat as the fiber glasss k=0.035 11 KWm in 20 (derived from

http://www.engineeringtoolbox.com/fiberglas-insulation-k-values-d_1172.html) and

there is also air inside it which has a low k=0.024 11 KWm , thus the R-value of the

batt is relatively high at 3.3 12 KWm which decreases the heat loss by conduction

that q former - q withbatt = 1575.5W. When talking about radiation, the batt has a non-

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reflective surface, which has a high E. therefore, batt cannot stop heat loss by

radiation. For convection, as the temperature of batt eventually rise, the temperature

difference decreases, so the rate of convection transfer decreases. For the foil-faced

batt, the foil can reflect some of the heat by radiation, but as it is a good conductor,

the heat would rapidly conduct to the batt, batt would then reduce the heat transferredby conduction. For convection, as the heat in the foil would conduct to the batt

rapidly, the insulation would not help on reducing heat transfer by convection.

In order to evaluate the effectiveness of these three insulation, compare the time that

5000J heats flow out through the ceiling. The longer the time taken, the better the

performance is.

Foil: Q/ t = e (Th^4 Tc^4) ARTTA

tQ coldhot

= )(

(radiation loss) (conduction loss)

5000/ t= 5.6703 *10-8 *0.04*(25^4- 5^4)* 100 5000/ t= 100(25- 5)/ 1.299

t1 = 56524.8s t 2 = 3.2s

t= t1 + t 2 = 3.2 +56524.8 =56528.0s

Unfaced batt:R

TTA

t

Q coldhot

=

)((conduction loss)

5000/ t= 100(25- 5)/ 4.279

t= 10.6975s

Foil-faced batt:

Q/ t = e (Th^4 Tc^4) A R

TTA

t

Q coldhot

=

)(

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(radiation loss) (conduction loss)

5000/ t= 5.6703 *10-8 *0.04*(25^4- 5^4)* 100 5000/ t= 100(25- 5)/ 4.279

t1 = 56524.8s t 2 = 10.7s

t= t1 + t 2 = 56524.8+ 10.7= 56535.5s

Tabulate the data into table three.

Table three: the time need for 5000J heat to flow out

Insulation

Time (s)

Foil Batt Foil-faced batt

Conduction 3.2 10.6975 10.7

Radiation 56524.8 56524.8

t 56528.0 10.6975 56535.5

b af o i lf o i l b a t t

ttt

As the result shows, the foiled-faced batt has the best effect on reducing heat loss,

then the foil and the unfaced batt performed the worst.

The total R-value is calculated by the addition of all the mediums through the way the

heat flows, including the air. And as the insulation was added into the roof, the

properties of some of the medium changes such as the R-value of the air space when

one of the contact surface is reflective. Also the air film have been taken into thecalculation, thus the R should be valid. The speed of heat loss (Q/ t) is also

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calculated. But the data is not very exact as the Q/ t through convection has not been

taken into calculation as the convection constant k varies as the state and properties of

the fluid change.

Design of Investigation of thermal performance

Experiment A:

Aim: To investigate the performance of foil, batt and foil-faced batt on reducing heat

flow.

Hypothesis: Foil-faced batt performs the best, then the foil, the batt is the worst.

Equipment: Three same sized and coloured foam box, six temperature sensors, three

lights, one computer, one data logger,same surface area of a of piece foil, batt and

foil-faced-batt.

Procedure

1. Set up three groups of experiment in the same environment (controls the outside

temperature.) as shown in figure 3. Make the bottom of the three insulations at the

same height as the ceiling height of the house is constant. The foam box

represents the house without insulated roof. As the size of the three boxes is the

same, this step controls the surface area and the rate of heat loss through walls and

the roof. Foam is used since its k value is relatively low at 6.5, thus the heatwouldnt flow instantly. Note that the surface of the insulation should be the same.

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Fig.3

2. Turn the lights on to generate heat, use data logger and temperature sensors to

record temperature in upper and lower spaces in 3 boxes. Use the software on the

computer to graph. (Control the inside temperature, the surface area of the

insulation and the rate of heat flow through walls and bases the same, let the type

of insulation be the variable).

3. Wait for 40 minutes.

4. Compare the temperature detected by the three upper temperature sensors.

Experiment B:

Problem: Some producers say that the best way to reduce heat flow is the foil-faced

batt. While according to the theory, having the foil and batt separated would perform

better since the second method has an extra layer of air. As air is a poor conductor of

heat whose k= 0.024 11 KWm , thus the statement of the producers is incorrect.

Aim: Prove that a separated foil and batt layer is better than a foil-faced batt on

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reducing heat loss.

Hypothesis: Seperated foil and batt layer is better than a foil-faced batt on reducing

heat loss.

Equipment: Two same sized and coloured foam box, four temperature sensors, two

lights, one computer, one data logger, same surface area of a of piece foil, batt and

foil-faced-batt.

Procedure:

1. Set up two groups of experiment in the same environment (controls the outside

temperature.) as shown in figure 4. Make the bottom of the two insulations at the

same height as the ceiling height of the house is constant. The foam box

represents the house without insulated roof. As the size of the two boxes is the

same, this step controls the surface area and the rate of heat loss through walls and

the roof. Note that the surface of the insulation should be the same.

Fig.4

2. Turn the lights on to heat lower space, use data logger and temperature sensors torecord temperature in upper and lower spaces in 2 boxes. Use the software on the

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computer to record temperature of the upper and lower layers. (control the inside

temperature, the surface area of the insulation and the rate of heat flow through

walls and bases the same, let the type of insulation be the variable).

3. Wait for 40 minutes.

4. Compare the temperature detected by the two upper temperature sensors.

Conclusion

Generally speaking, roofing insulation is essential, but as the variety choices present

but no standardized test has been conducted, the choice of insulation remains a

problem to most of the consumers as every insulation has its own advantages and

disadvantages. As for foil, the outstanding advantage is its good low e-value to reduce

radiation loss, but the disadvantages are the low R-value to conduction and the

existence of dust would largely affects its effectiveness. As for batt, its advantage is

the high R-value which reduces conduction loss effectively, while its disadvantage isthe high emissivity value which leads to heat loss by radiation. For the foil-faced batt,

it effectively reflects the radiation and also reduce the heat loss by conduction, but

when comparing to the separated layers of foil and batt, the foil-faced batts R-value

is smaller as the absence of an air layer which existed between the separated layers of

the foil and batt(the total R-value would reduce approximately 0.17 12 KWm ), and

the radiation would also be affected by the existence of dust.

Above all, the choice of insulation is variable, as they also have its own merits and

drawbacks, thus the choice meanly depends on the living environment and request ofcustomer.

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References

1. TABLE 1. R-VALUE OF COMMON BUILDING MATERIALS, class note

2. THERMAL RESISTANCE OF AIR SPACE class note

3. n.a., Building Code of Australia, viewed Aug. 09, 2010, derived from

http://www.icanz.org.au/handbook/handbookpart1section1/

4. n.a., Dec. 16, 2009SUSTAINABLE LIVING TASMANIAviewed Aug. 07,

2010, derived from

http://www.sustainablelivingtasmania.org.au/content/documents/WebInsulation.pdf

5. n.a.,Fibreglass Insulation, viewed Aug. 09, 2010, derived from

http://www.engineeringtoolbox.com/fiberglas-insulation-k-values-d_1172.html

6. n.a.,foil-faced batt, viewed Aug. 07, 2010, derived from

http://www.specjm.com/files/pdf/bid0015.pdf

7. n.a., Foil Single Bubble Foil, viewed Aug. 07, 2010, derived from

http://www.chang-wang.com/foil-single-bubble-foil.htm

8. n.a., Other differential equations, viewed Aug. 09, 2010, derived from

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

9. n.a., R0200 Pitched Metal Roof with Flat ceiling, viewed Aug. 07, 2010, derived

from

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http://www.icanz.org.au/handbook/R0200/

10. n.a., Unfaced batts, viewed Aug. 07, 2010, derived from

http://www.specjm.com/files/pdf/bid0008.pdf