Upload
cindy-cao
View
218
Download
0
Embed Size (px)
Citation preview
8/8/2019 phy Part B
1/13
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).
8/8/2019 phy Part B
2/13
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.
8/8/2019 phy Part B
3/13
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.
8/8/2019 phy Part B
4/13
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.html8/8/2019 phy Part B
5/13
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-
8/8/2019 phy Part B
6/13
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
=
)(
8/8/2019 phy Part B
7/13
(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
8/8/2019 phy Part B
8/13
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.
8/8/2019 phy Part B
9/13
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
8/8/2019 phy Part B
10/13
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
8/8/2019 phy Part B
11/13
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.
8/8/2019 phy Part B
12/13
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
8/8/2019 phy Part B
13/13
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