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Energy and Buildings 39 (2007) 182–187
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Correlation between thermal conductivity and the thickness of
selected insulation materials for building wall
T.M.I. Mahlia a,*, B.N. Taufiq a, Ismail b, H.H. Masjuki a
a
b
Department of Mechanical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
Department of Physics, University of Syiah Kuala, 23111 Darussalam, Banda Aceh, Indonesia
Received 27 December 2004; received in revised form 5 June 2006; accepted 20 June 2006
Abstract
Correlation between thermal conductivity and the thickness of selected insulation materials for building wall has been analyzed. The study has
found that a relationship between the thermal conductivity (k) and optimum thickness (xopt) of insulation material is non-linear which obeys a
polynomial function of xopt = a + bk + ck2, where a = 0.0818, b = 2.973, and c = 64.6. This relationship will be very useful for practical use to
estimate the optimum thickness of insulation material in reducing the rate of heat flow through building wall by knowing its thermal conductivity
only.
# 2006 Elsevier B.V. All rights reserved.
Keywords: Thermal conductivity; Insulation; Building wall; Optimum thickness
1. Introduction
Air conditioners are used in almost all commercial building in
tropical country like Malaysia. This equipment is used to cool the
space or room in a building due to hot air outside building and to
absorb heat produced by people and appliances from inside
building in order to provide comfortable working environment.
Since this equipment is operated continuously all the time in the
tropical country, the energy consumption and cost for this
equipment is quite high. Consequently, the commercial sectors in
Malaysia need to spend a lot of money for electricity for each air
conditioner every year. It driven by the heat transferred through
building wall which is the largest component of cooling load for
spaces in the building. Any reduction in this cooling load results
in reducing the electricity consumption by air conditioner.
Therefore, a proper insulation material with the objective of
achieving acceptable comfort for building occupants and
reduced cooling load is imperative. A proper insulation material
also indirectly reduces emission from power plant [1]. A proper
insulation what we mean here is an optimal insulation thickness
where the total investment cost for the insulation and cooling can
be minimized over the lifetime of the building. The cost of
insulation installation will increase with thickness, while the cost
of cooling decrease thus the total cost of insulation and cooling is
minimal as the thickness of insulation is optimum. There will be
no energy savings to increase additional insulation beyond the
economic thickness. Optimizing insulation thickness for buildings using life cycle cost has been discussed by Refs. [2–4].
Moreover, optimum insulation thickness of external walls for
energy saving and using various energy sources is given by Refs.
[5–7]. Later, the effect of electricity tariff on the computed
optimum insulation thickness using a dynamic heat transfer
model is conducted by Ref. [8].
There are several kinds of insulation materials commercially
available in Malaysia right now such as fibreglass–urethane,
fiberglass (rigid), urethane (rigid), Perlite, extruded polystyrene
and urethane. Nonetheless, there is very difficult to chose which
one is the best, where it is cheap and thin but it would save
electricity power of air conditioner significantly. Based on this
reason, in this paper we would like to present the analysis of the
cost-benefit of optimum thickness of the insulation materials
mentioned above that are often used for building wall in the air
conditioned room.
2. Collected data input
* Corresponding author. Tel.: +60 3 7967 6842; fax: +60 3 7967 5317.
E-mail addresses: [email protected], [email protected]
(T.M.I. Mahlia).
0378-7788/$ – see front matter # 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2006.06.002
Since an air conditioner is a climate dependent appliance,
the climatic condition for a particular country or region is an
T.M.I. Mahlia et al. / Energy and Buildings 39 (2007) 182–187
Nomenclature
A
CA
CE
Cf
Ci
d
Ew
hi
ho
i
kn
kins
N
Oh
P1
P2
Qw
Rins
Rwall
S
To,av
To,des
Ts
Dt
DT
U
Uins
Uun
DU
x
xn
xopt
area of wall (m2)
cost of insulation material per unit volume ($/m3)
cost of electricity ($/kWh)
energy cost ($)
total insulation cost ($)
electricity price increase rate (%)
total annual energy consumption of air conditioner (kWh)
convection heat transfer coefficient for inside
surface refrigerated space (W/m2 8C)
convection heat transfer coefficient for outside
surface refrigerated space (W/m2 8C)
discount rate (%)
thermal conductivity of nth layer of wall
(W/m 8C)
thermal conductivity of insulating material
(W/m 8C)
life cycle period (year)
annual operating hour of air conditioner
life cycle energy
life cycle expenditures for additional investment
instantaneous wall heat gain load (W)
internal resistance of insulating material
(m2 8C/W)
internal resistance of wall (m2 8C/W)
present value of net savings ($)
annual average temperature of outside air (8C)
design temperature of outside air (8C)
design temperature of refrigerated space (8C)
equivalent full load hours operation of air conditioner (h)
difference between inside and outside design
temperature (8C)
heat transfer coefficient (W/m 8C)
heat transfer coefficient of insulated wall
(W/m2 8C)
heat transfer coefficient of uninsulated wall
(W/m2 8C)
difference between overall heat transfer coefficient of uninsulated and insulated walls
insulation thickness (m)
thickness of nth layer of wall (m)
optimum insulation thickness (m)
important determinant. Malaysia is a hot and humid country
and a large variation of ambient temperature is rare throughout
the country. The sensible cooling load is normally dominant in
commercial building air conditioning applications but in
Malaysia’s hot and humid climate the latent cooling load is
often a significant factor in air conditioner energy consumption.
Table 1 shows the data collected from the Meteorological
Department of Malaysia in six towns around the country [9]. It
is note that the highest maximum temperature recorded was
183
Table 1
Records of local cities temperatures and relative humiditya
City
24 hrM
(8C)
Mdx
(8C)
Mdn
(8C)
Hm
(8C)
Lm
(8C)
RH
(%)
Kota Kinabalu
Senai
Subang
Ipoh
Bayan Lepas
Kota Bharu
Kuantan
Kuching
27.0
25.9
26.7
26.9
27.2
26.8
26.1
26.2
31.2
31.7
32.3
33.0
31.3
31.2
31.6
31.6
23.5
22.4
23.0
23.1
23.8
32.5
22.7
23.0
36.0
36.0
36.8
37.0
36.3
36.5
36.9
36.5
18.6
18.2
18.1
17.8
18.7
18.3
16.8
18.9
81.5
86.9
82.7
81.4
82.2
82.2
85.4
85.4
Average
26.6
31.74
23.12
36.5
18.2
83.5
a
24 hrM: 24 h mean temperature; Mdx: mean daily maximum temperature;
Mdn: mean daily minimum temperature; Hm: highest maximum temperature;
Lm: lowest minimum temperature; RH: relative humidity.
37 8C in Ipoh, and the lowest minimum temperature was
recorded as 16.8 8C in Kuantan. Since commercial building are
only occupied from 8 a.m. to 5 p.m., only the temperatures and
relative humidity during the building is occupied are considered
for this study, as presented in Fig. 1, with the average
temperature 29 8C and average relative humidity 75%.
Besides ambient temperature, the information of comfort
range and effective temperature are needed in our calculation.
This temperature is selected based on comfort range and the
effective temperature for the population in the country. In fact, it
is rather difficult to define a range of effective temperatures at
which the majority of individual will be able to work at maximum
efficiency. However, the comfort range and effective temperature
for tropical climate has been discussed in the user manual for
ASEAN as tabulated in Table 2 [10]. Based on the data presented
in Table 2, we have selected the indoor temperature for our study
in the range of optimum temperature which is 21 8C to proven the
optimum comfort for building occupants.
As room air conditioners are not used for heating in
Malaysia, these appliances have not been considered in this
study. Other data that is necessary for the study are life cycle
period, unit cost of electricity, discount rate, operation hour, etc.
All of these essential input data are presented in Table 3.
In order to be able to conduct the analysis, thermal
conductivity and the price of material for insulation are required.
Fig. 1. The average temperature and relative humidity from 8:00 a.m. to
5:00 p.m.
184
T.M.I. Mahlia et al. / Energy and Buildings 39 (2007) 182–187
Table 2
Comfort range and effective temperature for hot climate
Comfort range
Effective temperature, F (8C)
Above acceptable
Upper acceptable
Optimum
Lower acceptable
Below acceptable
Above 76 (above 24.5)
73–76 (22.8–24.5)
69–73 (20.6–22.8)
66–69 (18.9–20.6)
Below 66 (below 18.9)
Table 3
Essential input data
Rwall ¼
Description
Values
Life cycle period (N)
Resistance of the uninsulated wall (Rwall)
Unit cost of electricity (CE)
Discount rate (i)
Electricity price increase rate (d)
Coefficient of performancea (COP) (cooling)
Total heat transfer area (A)
Design temperature of outside air (To,des)
Inside temperature (Ti)
Average annual outside temperature (To,av)
20 years
0.307 m2 8C/W
0.0649 ($/kWh)
7%
1%
2.93
944.9 m 2
37 8C
21 8C
29 8C
a
where A is the surface area of wall, To,des the design temperature
of outside air, Ts the design temperature of refrigerated (cooled)
space and U is the overall heat transfer coefficient.
The total resistance of un-insulated wall (Rwall) is equal to
the summation of the surface resistances of convective heat
transfer inside and outside surfaces of the wall and the total
internal resistances of all layers of the wall which is can be
expressed by the following equation:
COP for split-room air conditioner.
1 x1 x2
xn 1
þ þ þ þ þ
hi k 1 k 2
k n ho
(2)
where hi and ho are convection heat transfer coefficient for
inside and outside surface of refrigerated space, respectively.
k1, k2, etc. are thermal conductivity of layer of wall, and x1, x2,
etc. are their thicknesses.
The difference between the overall heat transfer coefficients
of un-insulated and insulated walls can be written as
DU ¼ U un þ U ins ¼
1
Rwall
1
Rwall þ ½x=kins
(3)
3.2. Insulation thickness
Table 4
Data for insulation materials
For our case, the data of thermal conductivity and price for each
selected material per meter cubic are listed in Table 4.
In order to lower the heat flow from outside into inside
building having air conditioner system, insulation material is
usually used. This material has a very low thermal conductivity.
In this case, a suitable insulation material with its optimal
thickness is necessary in order to have an economic air
conditioning system. The insulation thickness will increase the
investment cost, but the cost of energy will decrease, until at
one point the thickness of material is optimum and will
contribute the highest overall cost savings. This can be done by
conducting life cycle cost or cost benefit analysis due to the
installation of insulation material.
To calculate cost benefit it is necessary know the total cost of
insulation (Ci), which is can be calculated by the following
equation:
3. Methodology
C i ¼ AxC A
Type of
insulation
Thermal
conductivity,
kins (W/m 8C)
Cost of
insulation,
CA ($/m3)
CA/kins
($ m 8C/W m3)
Fibreglass–urethane
Fiberglass (rigid)
Urethane (rigid)
Perlite
Extruded polystyrene
Urethane (roof deck)
0.021
0.033
0.024
0.054
0.029
0.021
214
304
262
98
182
221
10,190
9,212
10,917
1,815
6,276
10,524
3.1. Basic concept
The building wall is affected by all three heat transfer
mechanisms; conduction, convection, and radiation. The
incoming of solar radiation into the outer wall surface will
converted to heat by absorption and transmitted into the
building by conduction. At the same time, convective thermal
transmission occurs from air outside of the building to the outer
surface of the wall and the inner surface of the wall to the air
inside of the building. It makes most portion of heat gains from
the outside of the building wall occurs by conduction through
the building wall and by air leakage since the inner building
area has lower temperature.
This thermal transmission process through the wall can be
calculated by the following equation:
Qw ¼ UAðT o;des T s Þ ¼ UA DT
(1)
(4)
where A is the surface area of insulation material, x the thickness,
and CA is the cost of insulation material per unit volume.
The effect of insulation thickness on the thermal transmission efficiency can be obtained by differentiating Eq. (3) and
the result is as follow:
@ðDUÞ
Rwall kins
¼
2
2
@x
ðRwall kin þ Rwall xÞ
(5)
Based on the assumption of minimizing of internal loads, the
annual equivalent full load cooling hours operation can be
formulated in terms of full load hours time period which can be
calculated by the following equation:
Dt ¼ Oh
T o;av T s
T o;des T s
(6)
where To,des, To,av and Ts indicate the outside design, annual
average outside and inside design temperatures, respectively. If
T.M.I. Mahlia et al. / Energy and Buildings 39 (2007) 182–187
any of the outside surfaces of the air conditioned space are
exposed to an interior part of a neighboring wall with an area of
Aint, the annual average temperature of this interior space, To,int,
must be taken into account for calculating a corrected average
outside temperature which can calculated by the following
equation [3]:
T o;av ¼
T o;out Aout þ T o;int Aint
Aout þ Aint
(7)
An air conditioning system is generally designed to meet the
setting temperature inside the room, when the temperature in
the room is reaching setting temperature, the system will stops
automatically. Thus the total operating hour of air conditioner
needs to be used in calculating energy consumption. In this
case, the total amount of energy consumption for air
conditioner can be calculated by using the following equation:
Ew ¼
Qw Dt
COP
(9)
where CE and P1 are the cost of electricity and the life cycle
energy, respectively. The savings from the use of insulation
system then becomes:
S¼
P1 C E A DU DT Dt
P2 C A Ax
COP
(10)
where P2 is the ratio of the life cycle expenditures incurred due
to the additional capital investment.
The optimal thickness of insulation can be obtained by
differentiating Eq. (10) with respect to x and it is equal to 0 as
follows:
dS P1 C E A DT Dt dðDUÞ
¼
P2 C A A
dx
COP
dx
equation:
1
1þi N
1
P1 ¼
di
1þd
(13)
If the electricity normal price rate is equal to electricity
discount price rate for the whole year (or d = i), P1 becomes:
P1 ¼
N
1þi
if i ¼ d
(14)
Similarly for P2, if we assume that there is no additional
capital investment to the initial investment of air conditioner
system (the maintenance cost is 0), then P2 = 1. Now, by setting
Eq. (10) to zero, yields the payback period of investment which
can be written as
Np ¼
P2 C A ðRwall x þ R2wall kins Þ 103 COPð1 þ iÞ
C E DT Dt
if i ¼ d
(15)
(8)
where Qw is given from Eq. (1), Dt is from Eq. (6), and COP is
the coefficient of performance of air conditioner. While, the
total cost of energy consumption for insulation material can be
calculated as follow:
C f ¼ E w C E P1
185
(11)
Finally, the optimal of insulation thickness, in meters, can be
performed in term of:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½ ðR2wall kins P1 C E DTDt=P2 C A COP 103 Þ R2wall kins xopt ¼
Rwall
(12)
ln½1 ðP2 C A ðRwall x þ R2wall kins Þ
103 COPð1 dÞ=CE DT DtÞ
Np ¼
lnfð1 þ dÞ=ð1 þ iÞg
if i 6¼ d
(16)
4. Results and discussions
The results of our calculations for insulation materials are
tabulated in Table 5 and displayed in Fig. 2. The thermal
transmission through the wall (Qw), energy consumption (Ew),
cost of insulation (Ci), cost of energy consumption (Cf), and
savings are calculated as a function of the thickness of
insulation material. Our results show that as the insulation
thickness is increased, the insulation cost increases but the
energy cost decreases significantly until at certain point where
the insulation cost is about equal to the energy cost. The annual
operation hour (OA) of air conditioner in commercial building
in Malaysia obtained by assuming the air conditioner is on from
8:00 a.m. until 5:00 p.m. during working day, that is 1170 h.
The total cost (summation of insulation cost and energy cost)
is dependent of the insulation thickness, where at a certain
thickness its value is minimum. The life cycle saving is also
dependent upon the insulation thickness. Its value reaches
maximum which is $71,773 at a certain thickness for
fibreglass–urethane. The life cycle savings increment of
cooling costs, caused by the increment of insulation thickness
Table 5
Optimum insulation thickness and cost savings for each insulation material
3.3. Insulation economy
Insulation
material
Energy
consumption
(kWh/year)
Optimum
thickness
(m)
Life
cycle
savings ($)
To calculate insulation economy it is necessary to identify
the ratio of life cycle energy (P1) and the ratio of life cycle
expenditures incurred because of the additional capital
investment to the initial investment (P2). P1 has relation with
electricity normal price rate (d), electricity discount price rate
(i), and life cycle period (N) as expressed by the following
Fibreglass–urethane
Fiberglass (rigid)
Urethane (rigid)
Perlite
Extruded polystyrene
Urethane (roof deck)
4657.1
6974.5
5533.7
5151.2
5081.9
4744.3
0.048
0.047
0.045
0.11
0.060
0.047
71773
62528
68250
70115
70134
71450
186
T.M.I. Mahlia et al. / Energy and Buildings 39 (2007) 182–187
insulation material is the less thermal transmission will be.
Therefore, there should be a relationship between the thermal
conductivity and optimum thickness for every insulation
material. However, to our knowledge this relation has not
been found yet. In this study we find that the relationship
between the thermal conductivity (k) and optimum thickness
(xopt) is non-linear as shown in Fig. 3. It obeys a polynomial
function of xopt = a + bk + ck2, where a = 0.0818, b = 2.973,
and c = 64.6. This relationship will be very important in the
future since we will be able to estimate the optimum thickness
of insulation material easily (without doing a long analysis) by
knowing its thermal conductivity only.
Fig. 2. Comparison saving for all insulation materials studied.
which is exceeding the installation cost of insulation material.
Beyond a certain thickness, incremental cost will exceed the
savings, which means; additional thickness of insulation
material is not economical anymore. The optimum insulation
thickness is achieved when the savings start to drops as the
thickness of insulation material is increased. The optimum
thickness for fibreglass–urethane is found to be 0.048 m. The
optimum thicknesses for other insulation materials are
tabulated in Table 5.
The results suggest that fibreglass–urethane is the most
economic (saving up to $71,773 in 20 years) among other
insulation materials. If we see the thermal conductivity (see
Table 5), Perlite has the highest thermal conductivity among the
insulation materials. Higher the thermal conductivity of an
insulation material means lower thermal resistance; therefore
the thickest thickness is required to be used in order to get
optimum thermal insulation. The thickness of insulation
material is an important part in designing of building since
thick insulation material will reduce the space of building
significantly.
Thermal transmission in a certain material depends upon the
thermal property (in this case the thermal conductivity) and the
thickness of that material. The lower value thermal conductivity
is the less thermal transmission will be. Similarly, the thicker
5. Conclusions
Our results show that the insulation cost would increase
while cooling cost decreases, as the thermal resistance of
insulation material increases. The savings increment of cooling
costs, caused by the increment of insulation thickness which is
exceeding the installation cost of insulation material. Beyond a
certain level, incremental cost will exceed the savings, which
means additional thickness of insulation material is not cost
effective anymore. The optimum insulation thickness achieved
when the savings start to drops the thickness of insulation
material is increased. Our study found that using fibreglass–
urethane as an insulation material for air conditioner system
will save up to $71,773 which is the highest savings among the
others materials with almost similar to the thickness of
Fiberglass (rigid), Urethane (rigid) and Urethane. The relationship between the thermal conductivity (k) and optimum
thickness (xopt) is non-linear and obeys a polynomial function
of xopt = a + bk + ck2, where a = 0.0818, b = 2.973, and
c = 64.6. This relationship will be very important in the future
since we will be able to estimate the optimum thickness of
insulation material easily, without doing a long analysis just by
knowing its thermal conductivity only. Hopefully this work
would initiate the developers to introduce insulation material
and policymakers can implement insulation as one of building
code particularly for commercial building. This policy would
generate huge of energy and cost savings as well as reduces
environmental emissions from power plant.
References
Fig. 3. Optimum thickness as a function of thermal conductivity for materials
investigated (dotted line is a polynomial fitting).
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