Procedia Engineering 121 ( 2015 ) 1008 1015 [616846]

Procedia Engineering 121 ( 2015 ) 1008 – 1015
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of ISHV AC-COBEE 2015
doi: 10.1016/j.proeng.2015.09.072 ScienceDirectAvailable online at www.sciencedirect.com
9th International Symposium on Heating, Ventilat ion and Air Conditioning (ISHVAC) and the 3rd
International Conference on Building Energy and Environment (COBEE)
Determination of Optimum Insulation Thickness of Exterior Wall
with Moisture Transfer in Hot Summer and Cold Winter Zone of
China
Xiangwei Liua, Youm ing Chena,*, Hua Geb, Paul Faziob, Guojie Chena,c
aCollege of Civil Engineering, Hunan Univ ersity, Changsha, Hunan, 410082, China
bCentre for Zero -Energy Building Studies, Department of Bu ilding, Civil and Environ ment Engineering, Concord ia University, Montreal,
Quebec, H3G 1M8, Canada
cCollege of City Construction , University of South China, Hengyang, Hunan, 421001, China
Abstract
Thermal insulation plays an impor tant role in achieving building efficiency. Many engineering investigations were carried out to
determine the op
timum insulation thickness. In this paper, a coupled heat and moisture transfer model is presented to calculate the
annual energy consumption. Then, the li fecycle total cost is analyzed by the P1 -P2 economic model. Based on lifecycle total cost
ana
lysis, the optimum insulation thickness is determined. Three repre sentative cities, viz. Changsha, Chengdu and Sha oguan, are
chose n as the sample cit ies. The optimum insulation thickness, lifecycle saving and payback period are estimated. The results show
that the optimum thickness of extruded polystyrene (XPS) is between 0.053 and 0.069m and the optimum thickness of expanded
polystyrene (EPS) is between 0.081 and 0.105m. The maximum lifecy cle saving v aries from 16.60 to 28.50$/m2 and the payback
period varies from 1.89 to 2.56 years. EPS is more economical than XPS as insulation because of its lower lifecycle total cost.
© 2015 The Authors. Published by Elsevier Ltd .
Peer-review under responsibility of the organizing committee of ISHVACCOBEE 2015 .
Keywords: C oupled heat and moisture transfer; Optimum insulation thickness; Lifecycle total cost; Lifecycle saving; Payback period

* Corresponding author.
E-mail address: [anonimizat] © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer
-review under responsibility of the organizing committee of ISHV AC-COBEE 2015

1009 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015
1. Introduction
Heating and cooling loads of buildings are mostly due to heat transmission across the building envelope. From
energy conse
rvation viewpoint, thermal insulation is an ef fective way to achieve energy conservation in buildings. On
one hand, the energy consumption for space conditioning can be reduce d by increasing the thickness of insulation. On
the other hand, increasing the thickness of insulation will increase t he investment cost. Thus, it is inevitable to
determ
ine an optimum insulation thickness by considering economic analysis.
Many studies have been carried out to stu dy the optimum insulation thickness [1-10]. They can be classified into
two categories
according to the transmission load calculation method. Most of stu dies estimated the transmission load
through the exterior wall in to room by using the degree -time concept (degree -day/degree hour) which is one of the
sim
plest methods that applied in static conditions [1-7]. A few studies estimated the transmission load through the
exterio
r wall into room by using numerical method [8-10], which neglects the effect of moisture transfer on heat
transm
ission.
However, the building envelope s are exposed to the hot -hum id climate with intense temperature change and high
hum
idity in the hot summer and cold winter zone of China. The moisture transfer and storage in the building exterior
walls is c
ommon. Moisture transfer and accumulation in exterior wall ca n increase the heat capacity and buffering
effect and reduce the thermal insulation resistance which play s an important role in the transmission load through the
exterior wall into room . To accurately calculate the transmission load through th e exteri or wall into room, the effect
of moisture transfer on heat transfer should be considered.
In this paper, a coupled heat and moisture transfer model is proposed to estimate the annual energy consumption.
Then, the
lifecycle total cost is analyzed by the P1 -P2 economic model. Based on lifecycle total cost analysis, the
optim
um insulation thickness is determined. Three repre sentative cities, Chengdu, Changsha, and Shaoguan are
selected as
the sample cities. Two co mmonly used insulation materials, expanded polystyrene (EPS) and extruded
poly
styrene (XPS) , are selected to determine their optimum thickness for a commonly used wall construction in
residential
buildings of this region. The annual energy consumptions, lifecycle sa vi ngs and payback periods are
analyzed and presented as well.
2. Methodology for insulation thickness optimization
2.1. Coupled heat and moisture transfer model for an exterior wall
In this paper, the effect of moisture transfer on heat transm ission is ta ken into consideration. The simultaneous heat
and moisture transport model proposed by Liu et al [11] is selected. The governing equations are as follow:
ln( )s
p s llD p llDdP TPK R K R TtdTM[G UM G MU MM§·§·w §·˜ ’ ˜  ˜ ˜˜˜ ’ ˜ ˜ ˜ ˜˜ ˜ ’¨¸¨¸ ¨¸w ©¹ ©¹©¹ (1)
 ,,s
mp m p l l v p sdP Tcc T h T PtdTUZ O G M Măș w §·˜ ˜ ˜ ’ ˜’  ˜’ ˜ ˜ ˜’  ˜’ ¨¸«»w ©¹¬¼ (2)
where ξ (J/m3) is sorption capacity, φ is relative humidity, t (s) is the time coordinate , δp (s) is the water vapor
permeability, Ps (Pa) is the saturated water vapo ur pressure, Kl (s) is the liquid water permeability, Ul (kg/m3) is the
density of liquid water, RD (J/kg K) is the gas constant of water vapor, T (K ) is temperature, ρm (kg/m3) is the density
of the dry material , cp,m (J/kg K) is the specific capacity of the dry material, ω (kg/m3) is the moisture content , cp,l
(kg/m3) is specific heat of liquid water, λ (W/m K) is the thermal conductivity of the moisture building materials, hlv
(J/kg) is the latent heat of evaporation .

1010 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015
2.2. Cooling and heating energy consumption of exterior wall
The instantaneous transmission load is obtained as follows:
i, i cs u r f iqh T T ˜ 
(3)
ii , hs u r f iqh T T ˜  (4)
where qc (W/m2) is the instantaneous transmission load for cooling, qh (W/m2) is the instantaneous transmission
load for heating.
The annual energy consumption per unit area of the exterior wall (Eh, kW h/m2) for heating can be calculated by:
h
hQEK (5)
where Qh (kW h/m2) is the total transmission load per unit area of the exterior wall for heating, η is the efficiency
of the heating system .
The annual energy consumption per unit area of the exterior wall for cooling ( Ec, kW h/m2) is expressed as:
c
cQEEER
(6)
where Qc (kW h/m2) is the total transmission load per unit area of the exterior wall for cooling, EER is the energy
efficiency ratio of the
cooling system.
2.3. Economic analysis model
The present worth of capital is considere d in the economic analysis. The P1-P2 economic model proposed by Duffie
and Bechm
an [12] is applied. P1 is the lifecycle energy related to market discount rate ( d), electricity cost inflation
rate (i), and economic analysis period (Ne); P2 is the ratio of lifecycle expenditure s cau sed by the additional capital
investment to the initial investment.
11111,,
1eN
e
ei
id di dPP W F N i d
N
idi­ăș§·˜°«»¨¸z °©¹«»¬¼ ®
°°  ¯ (7)

min
2,0 ,1, ,,0 , 1ev
se N
LPWF N d RPD D M P W F N i dPWF N m d ˜  ˜ 
 (8)
where D is the ratio of down payment to the initial investment, Nmin is the number of years over which mortgage
paym
ents contribute to the analysis period, NL is the term of loan, Ms is the ratio of first year miscellaneous costs to
the initial investment, Rv is the ratio of resale value at the end of the a nalysis period to the initial investment.
The lifecycle total cost ( LCT, W /m2) can be estimated by using Eq. (9):

1011 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015
12 Ech i n s i n s LCT P C E E P C x ˜˜  ˜ ˜ (9)
where CE is the price of electricity ($/ kW h), Cins is the price of insulation material ($/m3), xins is the thickness of
the ins
ulation material ( m). The optimum insulation thick ness is the value that gives the minimum lifecycle total cost.
The lifecycle saving ( LCS, $/m2) is the difference between the saved ene rgy cost over the lifetime and the insulation
payout:
12 Ech i n s i n s LCS P C E E P C x ˜˜ ' ' ˜ ˜ (10)
where ᇞEc and ᇞEh are the difference between the annual energy co nsumption per unit area of the wall without
and with insulation under cooling and heating conditions , respectively.
The payback period Np (year) can be obtained by setting LC S to zero.

2
2ln 1
1ln1
1ins
Ech
p
ins
Ec
hPC x d iid
CEE
iNd
PC x iidCE
E­ăș˜˜ ˜ z °«»˜' '°¬¼
°  ° §· ® ¨¸©¹ °
°˜˜ ˜  °˜'  '°¯ (11)
The parameters used to analyze the lifecycle total costs are given in Table 1.
Table 1. The parameters used in calculation
Parameters Value
а 0.6 [6]
Electricity 0.087 ($/kW h) [13]
EER 2.3 [14]
η 1.9 [14]
i 1%
d 5%
D 1
Ms 0
Rv 0

3. Results and discussions
3.1. Exterior wall configuration
A typical exterior wall representing the construction practice in residential buildings is selected in hot summer and
cold wi
nter zone of China. From exterior to interior, the wall consists of 20mm cement plaster, thermal insulation,
240mm red brick, and 20mm lime plaster.

The hydrot hermal properties of the wall compon ents obtai ned from Kumaran [15] a re shown in Table 2. The price
of expanded polystyrene is 41.0$/m3 and the price of extruded polystyrene is 64.1$/m3 [13].
Table 2. Prop erties of the exterior wall components .

1012 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015
Component Um
(kg/m3) cp,m
(J/kg K) δp
(10-12s) ω
(kg/m3) λ
(W/m K) Dw
(m2/s)
Cement
plaster 1807 840 54.67 20.022 0.025 0.0001M
MM 30.854 4.5 10 Zu 9exp(0 1.4 10 .027 ) Zu
Red brick 1918 840 26.00 20.02451 0.2362 0.273M
MM 31.035 4.2 10 Zu 9exp(0. 7.4 10 0316 ) Zu
Lime plaster 1500 840 13.57 20.052 0.052 0.005M
MM 30.526 3.1 10 Zu 9exp(0. 2.7 10 0204 ) Zu
Expanded
polystyrene 30 1470 11.00 20.5277 0.9647 0.07086M
MM 30.0331 1.23 10 Zu N/A
Extruded
polystyrene 35 1470 1.200 24.462 18.96M
M 4
520.0241 1.3 10
5.9 10Z
Z
u
u N/A
where the moisture diffusive 1lD
wl p sRTDK PUGM[§˜ ˜ · ˜  ˜˜¨¸©¹ m2/s
3.2. Climate conditions
Three repre sentative cities, Chengdu, Changsha, and Shaoguan are selected as the sample cities. The outdoor
conditi
ons are taken from typical meteorological year data [16], which is generated based on the measured weather
data of years 1971- 2003. The cooling season is from June 15th to August 31st, and the heating season is from December
1st to February 28th [14]. The indoor conditions are set as 26oC and 60% relative humidity for cooling and 18oC and
50% relative humidity for heating according to the design co de for heating ventilation a nd air conditioning of civil
buildings [17].
3.3. Optimum wall insulation thickness
The optimum insulation thickness of a typical south -facing brick wall used in representative cities, Chengdu,
Changsha, and Shaoguan, is determined for two types of insulati on m aterials (XPS & EPS) over a life time of 20 years .
The variation of the annual energy consumption ( AEC ) of e xterior wall facing south orientation with respect to the
thickness of insulation is shown in Fig.1. As can been seen in Fig.1, the annu al energy consumption decreases with
the increase of insulation thickness, while the rate decrease s with the continued increase of the insulation thickness.
The annual energy consumption of exterior wall using XPS as insulation material is much lower than that using EPS
as insulation material. The annual energy consumption of exterior wall in Changsha is t he highest, and followed by
Chengdu and Shaoguan.
The variation of the lifecycle total cost of exterior wall facing sout h orientation with respect to the thickness of
insulation is shown in Fig.2 (XPS as insulation ma terial) and Fig.3 (EPS as insulation material). The lifecycle total
cost
of the exterior wall using EPS as insulation material is lower than that using XPS as insulation material. It
indicates that EPS is more economical than XPS. The insulation thickness at whic h the lifecycle total cost is the
minimum (as shown in Fig.2 and Fig.3) is defined as th e optimum thickness. The optimum thickness of XPS in
Changsha, Chengdu and Shaoguan are 0.069, 0.064 and 0.053 m, respectively. And the optimum thickness of EPS in
Changsha, Chengdu and Shaoguan are 0.105, 0.097 and 0.081 m, respectively . It is obvious that the optimum wall
insulation t
hickness in Changsha is the highest, and followed by Che ngdu and Shaoguan since the annual energy
consumption of exterior wall in Changsha is the highes t, a nd followed by Chengdu and Shaoguan.

1013 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015

Fig.1. The annual energy consumption of exterior wall facing south orientation .

Fig. 2. Lifecycle total cost of exterior wall facing sout h o rientation using XPS as insulation material .

Fig. 3. Lifecycle total cost of exterior wall facing south o rientation using EPS as insulation material .

1014 Xiangwei Liu et al. / Procedia Engineering 121 ( 2015 ) 1008 – 1015
The maximum lifecycle saving (the lifecycle saving corresponding to the optimum insulation thickness, LCS op) is
shown in Table 3. The maximum lifecycle saving varies from 16.60 to 28.50$/m2. The lifecycle saving of exterior
wall usi
ng EPS as insulation is higher than that using XPS as insulation. It indicates that using EPS as insulation has
higher saving potential than XPS.
Table 3. The maximum lifecycle saving (LCS op) ($/m2).
Material Changsha Chengdu Shaoguan
EPS 28.50 24.21 16.69
XPS 28.39 24.11 16.60

The payback period is shown in Table 4. The payback period is between 1.89 and 2.56 years. T he payback period
of exterior wall using EPS as insulati on is l ower than that using XPS as insulation.
Table 4. The payback period (years) .
Material Changsha Chengdu Shaoguan
EPS 1.89 2.00 2.52
XPS 1.97 2.14 2.56
4. Conclusions
In this paper, a coupled h eat and m oisture transfer model that considers the effect of moisture transfer on heat
transfer is used to estimate the annual energy cons umption. The lifecycle total cost is analyzed by P1-P2 economic
m
odel. The optimum insulation thickness, lifecycle saving, and payback period are estim ated in three representative
cities, Changsha, Chengdu and Shaoguan, in hot summer and cold winter zone of China. The result shows that the
lifecycle total cost of exterior wall using EPS as insula tion material is lower than that using XPS as insulation. It
indicates that EPS is more economical than XPS. The optimum thickness of XPS is between 0.053 and 0.069 m and
the optim
um thickness of EPS is between 0.081 and 0.105 m. The maximum lifecycle saving varies from 16.60 to
28.50 $/m2 and the payback period varies from 1.89 to 2.56 years.
Acknowledgements
This work was supported by Natural Science Foundation of China (Grant No.51078127 , 51408294) and China
Scholarship Council. Support was also receive d from Concordia University.
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