TAER1079239
Techset Composition India (P) Ltd., Bangalore and Chennai, India
8/14/2015
Advances in Building Energy Research, 2015 http://dx.doi.org/10.1080/17512549.2015.1079239
REVIEW 5
Determination of optimum insulation thickness in different wall orientations and locations in Iran Hadi Ramin, Pedram Hanafizadeh* and Mohammad Ali Akhavan-Behabadi
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Center of Excellence in Design and Optimization of Energy Systems, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran (Received 15 September 2014; accepted 12 July 2015) The present study numerically investigated the optimum insulation thickness determination for conventional walls in Tehran, the capital of Iran. In this study, aerated brick and concrete were considered as the main wall materials, and XPS and EPS as the insulation materials. The onedimensional transient heat transfer problem for multi-layer walls has been solved to obtain temperature distribution within the wall. Different combinations of wall materials and insulations were examined. Furthermore, the effect of the position of the insulation (inside and outside of the wall) was studied as well. Finally, in order to determine the optimum thickness, which minimizes the total cost of insulation and energy dissipation, economic analysis was carried out for a lifetime of 25 years. It is worth mentioning that in the present study, both cooling and heating seasons were taken into account in the optimization process. The findings revealed that after using insulation, among different wall configurations, yearly transmission load can be decreased in the range of 70–82% compared with an uninsulated wall made from concrete and 31–58% for the aerated brick wall. Moreover, the findings indicated that two different locations of insulations resulted in an approximately equal transmission load and optimum insulation thickness, while their time lag and decrement factor were not the same.
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Keywords: optimal insulation thickness; multi-layer wall; wall orientations; time lag; decrement factor
Nomenclature 30
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Alphabetic symbols amplitude of the temperature wave at the Ao outer surface of a wall amplitude of the temperature wave at the Ai inner surface of a wall As annual energy saving per unit area ($/m2 ) B dummy variable (n − 1) 360/365 b payback period (year) cost of energy ($/m2 ) Cenr cost of electricity ($/kWh) Ce
Tb Ti To Te Tsurr tTmax x=0
Cg
cost of natural gas ($/m3 )
tTmax x=L
Ct
total cost (energy + insulation)
TXmax =L
*Corresponding author. Email: hanafi
[email protected] 45
Rb Se
© 2015 Taylor & Francis
geometric factor net energy saving per unit area ($/m2 ) base temperature indoor air temperature outdoor air temperature sol-air temperature surrounding temperature time when outdoor temperature is at its maximum (h) time when indoor temperature is at its minimum (h) maximum temperature at the inner surface of a wall (K)
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Cins
cost of insulation material per volume ($/m3 )TXmin =L
c
heat capacity (J/kg · K)
TXmax =0
d
inflation rate (%)
TXmin =0
E f Hu hi
IT k Lins Lloc Lst t n N
equation of time x decrement factor lower heating value of the fuel (J/m3 ) Greek symbols indoor surface combined convection heat a transfer coefficient (J/m2 · K) outdoor surface combined convection heat as transfer coefficient (J/m2 · K) interest rate (%) b total solar radiation on a horizontal surface g (W/m2 ) beam solar radiation on a horizontal surface d (W/m2 ) diffuse solar radiation on a horizontal surfaceDT (W/m2 ) total solar radiation (W/m2 ) u uz thermal conductivity (W/m · K) thickness of the insulation material (m) r longitude of the location rg standard meridian F f time (s or h) v the day of the year eDT /ho number of daylight hours
P
period of the temperature wave (24 h)
hs
Qc (Qc )un
cooling transmission load (J/m2 ) cooling transmission load through an uninsulated wall (J/m2 ) heating transmission load (J/m2 ) heating transmission load through an uninsulated wall (J/m2 ) heat transfer (W/m2 )
Acronyms COP
coefficient of performance
EPS PWF
expanded polyurethane present worth factor
XPS
extruded polystyrene
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ho i I Ib
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Id
Qh (Qh )un 75
q
1.
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minimum temperature at the inner surface of a wall (K) maximum temperature at the outer surface of a wall minimum temperature at the outer surface of a wall distance (m) thermal diffusivity (m2 /s) solar absorptivity (W ) slope of the surface (W ) surface azimuth angle (W ) declination angle (W ) temperature difference angle of incidence (W ) zenith angle (W ) density (kg/m3 ) ground reflectance time lag (h) latitude angle (°) hour angle (°) correction factor in the sol-air temperature equation efficiency of the heating system (%)
Introduction
Increasing demand for energy in the recent years is a result of population growth, urbanization, migration to larger cities and improvement of living standards. Nowadays, the building sector (residential, commercial and public) is one of the most important parts of energy consumption in each country. Finding ways for energy conservation in the building sector is an increasingly important issue (Balaras, Droutsa, Argiriou, & Asimakopoulos, 2000, 2005; Khudhair & Mohammed, 2004). Energy loss from the building envelope is one of the main sources of energy dissipation in buildings since it serves as an interface between indoor and outdoor environments (Yu, Tian, Yang, Xu, & Wang, 2011). Implementing insulations in walls is an important option to reduce the energy consumption in buildings. Finding proper materials, designing the building envelope and considering the location and orientation of its component are efficient means to reduce the annual heating and cooling load and consequently the need for energy (Kaynakli, 2012). It is obvious that larger insulation thickness will cause higher energy saving. However, increasing the insulation thickness will increase the investment cost linearly (Ozel, 2013b). Therefore, it is necessary that thermal and economic analysis be considered simultaneously to obtain the
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optimum insulation thickness, which is referred to as thermal economic insulation thickness (Kaynakli, 2012). Optimum thickness of insulation is one that compensates the investment cost of insulation with energy-saving benefit in less time. Therefore, insulation (type and thickness) must be selected based on both energy consumption and cost of insulation (Ozel, 2013b). Reliable estimation of the heating and cooling load is an important problem concerning optimization of insulation thickness. A simple and crude model for estimation of heating and cooling load under a static condition is known as degree-day or degree-hour method which is based on either ambient air temperature or sol-air temperature. Many studies in the literature used this model based on ambient temperature to obtain the optimum insulation (Al-Sanea, Zedan, & Al-Hussain, 2012; Bolattürk, 2008; Kaynakli, 2008; Ucar & Balo, 2009; Wang, Huang, & Heng, 2007). Also, several authors used sol-air temperature instead of ambient air temperature in this method (Al-Khawaja, 2004; Ozel & Pihtili, 2007; Yu, Yang, Tian, & Liao, 2009). The dynamic time-dependent model is an accurate model to determine heat loss or gain from the composite walls, which has been used in models proposed by several authors (Al-Sanea, Zedan, & AlAjlan, 2005; Daouas, 2011; Daouas, Hassen, & Ben Aissia, 2010; Ozel, 2012, 2013a; Ozel; Mav- AQ1 ¶ romatidis, EL Mankibi, Michel, & Santamouris, 2012). The dynamic transient model has been solved numerically and analytically for multi-layer walls in the literature. It should be noted that optimal insulation thickness can be obtained based on only cooling loads or only heating loads and also both heating and cooling loads simultaneously. In Iran the building sector’s share of final energy consumption is close to 37% of total consumed energy each year (Ministry of Energy, 2013). Emission of carbon dioxide (CO2), sulfur dioxide (SO2) and the other pollutant gases is the most important factor regarding energy con- AQ2 ¶ sumption in buildings especially in large cities. During recent years, levels of pollution gases in Tehran have increased hazardously and become the cause of many diseases and fatalities; especially in winter during which inversion worsens the situation. Based on the report of the Ministry of Energy (Ministry of Energy, 2013), the building sector’s (residential, commercial and public) share of emission of greenhouse gases is 25.6%. Eight million people at night and over 12 million people during the day living in Tehran make it the most populated city in Iran, which nearly accounts for 10% of the total population in Iran (Statistical Centre of Iran, 2012). A subsidy reform law, which was passed in Iranian Parliament on 5 January 2010, is planning for free market energy prices in the next few years. Considering this plan, much attention must be given to the conservation of energy, and applying thermal insulation material is one of those. The main objective of this study is investigation of optimal insulation thickness in the climate of Tehran based on the present price of insulation materials and energy. The conventional wall structure and materials (aerated brick and concrete block) in Tehran are examined here. Expanded polystyrene (EPS) and extruded polystyrene (XPS) are used as insulation. The dynamic transient model is used here and optimal insulation thickness is achieved when insulation is located on both the inside and outside surfaces of the main wall materials. All orientations of a wall, including south, west, east and north and also horizontal wall (roof), are under consideration. The next section of the study is devoted to the governing equation, calculation of solar radiation on the wall, outdoor temperature, the structure of the wall, economic analysis and finally numerical method to solve the problem. Afterwards, results and discussions are presented.
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2.
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Mathematical formulation
2.1. Governing equations and boundary conditions A schematic of an ordinary multi-layer wall is shown in Figure 1. Thermo-physical properties and length of each layer are shown in this figure. The outside layer of the wall is exposed to periodic
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ambient temperature and solar radiation and the inside layer of the wall is exposed to convection resulting from constant air temperature inside the building. Assuming no heat generation, constant thermal properties, one-dimensional conduction heat transfer and negligible interface resistance, the unsteady heat conduction equation for each layer of a multi-layer wall is as follows (Al-Sanea et al., 2005; Ozel, 2013b): ∂2 T 1 ∂T , = ∂x2 a ∂t
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(1)
where a = k/rc is the thermal diffusivity of each layer and k, c and r are the thermal conductivity, the heat capacity and the density of each layer, respectively. To solve the problem, two boundary conditions on both sides of the multi-layer wall and one initial condition are needed. As the initial condition, the constant inside temperature at t = 0 is considered (Asan, 2000). On both sides of the wall, convection heat transfer exists. On the inside of the wall, the convection boundary condition is as follows: ∂T = hi (Tx=L − Ti ). −k ∂x x=L
(2)
In the above equation, hi is the inside combined (convection and radiation) heat transfer coefficient and Ti is the indoor temperature, which is taken to be constant (Ozel, 2013b).
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Figure 1. Multi-layer wall and boundary condition on it; the insulation can be placed either on the inside surface of the main wall material (current structure) or on the outside of the wall between the cement plaster and the main wall material.
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And at the outer surface of the wall, the boundary condition can be written as follows: k
∂T = ho (Tx=0 − Te (t)), ∂x x=0
(3)
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where ho is the outside convection heat transfer coefficient and Te is the sol-air temperature including the effect of solar radiation on the outside of the wall. Sol-air temperature is defined as (Threlkeld, 1998): Te (t) = To +
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aIT eDT − . ho ho
(4)
In the above equation, To , IT and a are the outdoor air temperature, total solar radiation and solar absorptivity of the outdoor wall surface, respectively. The last term of Equation (4), eDT /ho , is the correction factor; ranging from 0°C for vertical walls to 4°C for horizontal walls (Mavromatidis et al., 2012; Ozel, 2013b). The solar absorptivity of daring colour wall is taken as equal to AQ3 ¶ 0.8 (Ozel, 2013b).
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2.2.
Calculation of solar radiation on the outer wall
Total solar radiation on the wall with different orientations is assessed by the method presented by Duffie and Beckman (1991), which is modified with given values every minute (Mavromatidis et al., 2012). Based on this method, the relation between solar time and standard time is given as 205
Solar time = Standard time − 4(Lst − Lloc ) + E,
(5)
where Lst is the standard meridian for the local time zone, Lloc is the longitude of the location and E is the equation of time, which is expressed as follows: 210
E = 229.2(0.000075 + 0.001868 CosB − 0.032077 sinB − 0.014615 cos2B − 0.04089 sin 2B).
(6)
In the above equation, B (in degrees) is defined as follows: 215
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B = (n − 1)(360/365) 1 ≤ n ≤ 365 ,
where n is the day of the year. The geometric relationship between a plan of any particular orientation relative to the earth at AQ4 ¶ any time and any incoming beam solar radiation can be described in terms of several angles (Duffie & Beckman, 1991). The angular position of the sun at solar noon with respect to the AQ5 ¶ plan of the equator is declination angle, d, and varies (−23.45W ≤ d ≤ 23.45W ) throughout the year and can be calculated by the following relation:
d = 23.45 sin(360(284 + n/365)) n = the day of the year 225
(7)
1 ≤ n ≤ 365 .
(8)
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There is a set of useful relationships between the angles. The angle of incidence (u) between the sun’s rays and a tilted surface is given by cos(u) = sin(d) sin(f) cos(b) − sin(d) cos(f) sin(b) cos(g) 230
+ cos(d) cos(f) cos(b) cos(v) + cos(d) sin(f) sin(b) cos(g) cos(v)
(9)
+cos(d) sin(b) sin(g)sin(v),
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where d, f, v and g are declination angle, latitude angle, hour angle and surface azimuth angle, respectively. b is the slope of the surface ranging from 0 for the horizontal surface to 180 for the horizontally upside down surface. It is notable that b = 0 represents the vertical wall. The surface azimuth angle varies between −180 ≤ g ≤ 180 (g = −180, −90, 0, 90 and 180 for the surface facing north, east, south, west and again north, respectively). The hour angle, which is the angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis at 15W per hour, being negative in the morning and positive in the afternoon, is calculated in minutes by the following equation: v=
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360 (Solar Time − 720) . 24 60
The angle between the vertical and the line to the sun is the zenith angle (uz ), which has the following relationship: cos(uz ) = sin(d) sin(f) + cos(d) cos(f) cos(v).
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2 cos−1 (− tan(f) tan(d)). 15
60 −1 cos (− tan(f) tan(d)). 15
(14)
And sunrise time can be calculated using equations (13) and (14): sunrise time = sunset time − N .
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(13)
It takes 60 minutes to transverse 15W of longitude; the exact time of sunset (in minutes) can be found by sunset time =
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(12)
The sunrise hour angle is the negative of the sunset hour angle. It follows that the number of daylight hours is given by N=
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(11)
Setting the cosine of the angle to zero in Equation (11) results in the following relation for the hour angle (vs ) at sunset: cos(vs ) = − tan(f) tan(d).
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(10)
(15)
The isotropic clear sky method of Hottle (1976) is used to determine total solar radiation. Details of the method of calculation can be found in Duffie and Beckman (1991) and
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Mavromatidis et al. (2012). Here, we just introduce the equation for calculation of total solar radiation, which is used in the sol-air temperature in Equation (4), as follows: IT = R b Ib + Id 275
1 + cos(b) 1 − cos(b) + I rg . 2 2
(16)
where Ib , Id and I are beam, diffuse and total solar radiation on the horizontal surface (three main components of radiation on a tilted surface). In Equation (16) rg is the ground reflectance and usually taken as 0.2 and Rb is a geometric factor which can be calculated by 280
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Rb =
2.3.
cos(u) . cos(uz )
(17)
The structures of external walls and the roof
Conventional walls and roofs in Tehran have been considered in this study. The walls and roofs consist of 2 cm cement plaster at the outer layer, 2 cm gypsum in the inner surface and 20 cm main wall materials, usually aerated brick or concrete. The insulation layer which can be placed either on the inside or on the outside surface of the main wall materials is used to save energy. The two most conventional insulation materials, XPS and EPS, are used as insulation (Figure 1). The thermo-physical properties of materials used in this paper have been tabulated in Table 1.
2.4.
Estimation of heating and cooling transmission load
The twenty-first of each month is considered as the representative day for calculation of both cooling and heating demands (Ozel, 2013b). As mentioned earlier, indoor temperature is assumed to be constant throughout the day, and hence instantaneous heat transfer through a wall, after determining the inside wall temperature Tx=L from numerical solution, can be calculated as follows: qi = hi (Tx=L − Ti ).
(18)
Integrating this value over the day, daily heating or cooling transmission load can be obtained. Yearly heating and cooling transmission loads are also obtained by daily heating or cooling load 305
Table 1. Thermo-physical properties of material used in the paper (most of these data have been extracted from Najafian and Bahrami (2012), Ozel (2013b) and 19th ntional regulaion for building (2012). 310
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Materials Aerated brick Concrete block Cement plaster Gypsum plaster XPS EPS
Thermal Conductivity k (W/m · K)
Density r (kg/m3 )
Specific Heat c (1/kg · K)
0.3 1.37 0.7 0.18 0.029 0.038
1000 2076 2778 800 40 17
840 880 840 1090 1213 1500
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over its season (Ozel, 2013b). Constant inside temperature is selected based on thermal comfort and energy saving for each month (Al-Sanea et al. 2005; Ozel, 2012). These values, which vary for each month, are summarized in Table 2. 320
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2.5.
Time lag and decrement factor
There is a different temperature profile on the outer surface of the wall. The temperature profile in the outer surface changes while penetrating the wall. Time lag and decrement factor are two important characteristics that are defined in problems of propagating heat through a wall (Asan, 2000). The time taken for maximum or minimum temperature waves’ propagation from AQ6 ¶ the outer surface of the wall to the inner surface is known as time lag. Also, decrement factor is defined as the ratio of temperature wave amplitude that enters the wall. Time lag and decrement factor depend on the thermo-physical properties, thickness and materials of the walls (Asan & Sancaktar, 1998). The time lag is defined as (Asan, 2000):
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f=
tTmax . tTmax tTmax − tTmax , x=0 x=L x=0 x=L max max max tTx=0 , tTx=L tTx=0 − tTmax + P, x=L
and tTmax are the time when outside and inside temperatures are at their maximum, where tTmax o i respectively, and P is the period of the wave (24 hours here). Also the decrement factor is defined as (Asan, 2000): f =
TXmin =L
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2.6.
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(20)
Economic analyses
As mentioned earlier, optimal insulation thickness is obtained after economic analysis as well as thermal analysis are carried out. Utilization of insulation in the wall is accompanied by additional costs of insulation material and installation charge, although it reduces yearly heating and cooling loads and hence saves money. Economic analysis is performed to obtain the thickness that has the highest economic efficiency. Economic analysis depends on the cost of energy, yearly heating transmission load of insulated and un-insulated walls, efficiency of heating and cooling systems, lifetime of the building and inflation and interest rates (Ozel, 2013b). In order to accomplish economic analysis, net energy saving (which has actually reduced fuel consumption) from using insulation over the building’s lifetime is evaluated in the present value by using present worth factor (PWF; Daouas, 2011; Kaynakli, 2012). PWF is defined as (Daouas, 2011):
PWF = 360
min Ai TXmax =L − TX =L = max , Ao TX =0 − TXmin =0
Ao and Ai are the amplitudes of the temperature wave at the outer and inner of the wall. TXmax =L , AQ7 min ¶ and TXmax =0 , TX =0 are maximum and minimum temperatures at the inner and outer surfaces of the wall, respectively. Time lag and decrement factor are calculated for the representative days of each month of the cooling and heating seasons, and finally yearly time lag and decrement factor are obtained by arithmetic average of these monthly values (Ozel, 2013b).
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(19)
n u=1
1+i 1+d
u
⎧ 1+i 1+i n ⎪ ⎪ ⎨ 1− , i = d, 1+d = d−i n ⎪ ⎪ ⎩ , i = d, 1+i
(21)
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Table 2.
Constant Indoor temperature for each month (Al-Sanea et al., 2005; Ozel, 2012).
Month
February
March
April
May
June
July
August
September
October
November
December
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Temperature(°C)
January
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where i, d and n are interest rate, infiltration rate and lifetime period, respectively. Lifetime period is assumed to be 25 years. The total present cost of heating and cooling per unit area during the lifetime, Cenr (J/m2), is determined from the following equation (Ozel, 2013b):
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Cenr
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Qc Cel Qh = PWF + Cg , COP 3.6∗106 Hu hs
(22)
where Qc , Qh , Cel and Cg are the yearly cooling transmission load (J/m2), the yearly heating transmission load (J/m2), the cost of electricity ($/kWh) and the cost of natural gas ($/m3), respectively. Also, Hu is the lower heating value of the fuel (J/ m3), hs is the efficiency of the heating system and COP is the coefficient of performance of the air-conditioning system. The total cost is obtained by adding the present value of the cost of energy consumption over the lifetime of the building and the cost of insulation as below:
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Ct = Cenr + Ci = Cenr + Cins Lins .
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In the above equation Ci is the total cost of the insulated wall, Cins is the cost of the insulation material per volume ($/m3) and Lins is the thickness of the insulation material (m). The value of Lins that minimizes Ct is the optimum insulation thickness (Daouas, 2011). At the optimum insulation thickness, the energy saving is calculated by subtracting the cost of consumed energy of an un-insulated wall from that of an insulated one. Net energy saving per unit area (over life time of the building, n years) is deduced from the difference between the present value of energy saving and cost of insulation as (Ozel, 2013a):
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((Qc )un − Qc ) Cel ((Qh )un − Qh ) + Cg − Cins Lins , Se = PWF COP Hu h s 3.6∗106
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(24)
where (Qc )un and (Qh )un are the total heat gain and loss (J/m2·year) through an un-insulated wall, respectively. The term (((Qc )un − Qc )/COP)(Cel /3.6∗106 ) + (((Qh )un − Qh )/Hu hs )Cg in the above equation is annual energy saving (As ). The payback period, b, defined as the number of years that energy saving from optimum insulation thickness compensates the cost of initial investment of the insulation materials, is defined as (Daouas, 2011): PWF(b)∗As = Ci, opt ,
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(23)
⎧ d − i Ci ⎪ ⎪ ⎨ Ln 1 − 1 + i As b= ⎪ Ci ⎪ ⎩ (1 + i) As
(25) i=d
(26)
i=d
Figure 2 shows the diagram of the financial flow during the life time of the building. Money from energy saving is obtained at the end of each year during the lifetime, while the investment cost of insulation must be paid at the beginning of the life time. Taking the inflation and interest rates into account, the value of energy saving becomes less than what is obtained by multiplying AQ8 ¶ the life time and annul energy saving. In this study, infiltration and interest rates are taken as equal to 20% and 22%, respectively.
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Figure 2. Diagram of financial flow during the life time of the building.
2.7. Numerical procedure The one-dimensional transient heat conduction problem within a multi-layer wall, under the dynamic boundary condition on the outside surface, is considered here. The transient heat conduction problem has been numerically solved using an implicit finite difference procedure for a multi-layer wall. General finite difference equations derived by zeal and Pihtili (Optimum location and distribution, 2007) are used to obtain the set of equations. The Gauss–Seidel iterative method was used for solving the linear system of equations with the inner wall temperature as the initial approximation (Burden & Faires, 2011). A FORTRAN code was developed to accelerate the numerical computation. Inputs of the code include thermo-physical and geometrical properties of each layer of the wall and time-dependent outdoor temperature, while the output is the propagated temperature wave on the inside surface of the wall. The boundary condition was assumed to be periodic on the outside; therefore until reaching the steady solution, the daily cycle of solutions of equations with sol-air temperature on the outside was repeated (Ozel, 2012). Time lag, decrement factor, heating and cooling transmission loads were obtained from the output of the Code. The combined heat transfer coefficient on the inside of the envelope, hi , and combined heat transfer coefficient on the outside were taken equal to 8 and 22 w/m2·K, respectively (Ozel, 2013b). 3.
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Results and discussions
This study focuses on the behaviour of the different wall structures located in Tehran, the capital of Iran (which has the geographical coordinate of 35W 41′ 39′ ′ N and 51W 25′ 17′ ′ E). All vertical wall orientations (south, west, east and north) and the horizontal wall were investigated. The actual outdoor air temperature was obtained by averaging recorded meteorological date, over the period of 2006–2012 (I. R. Iran’s Meterological Organization, 2013). The data pertain to a representative day of each month during a year. Two-hourly outdoor air temperatures resulting from averaging over the aforementioned period, one for July 21 and another for January 21, are shown in Figure 3. The clear sky model has been used to take the solar radiation on the wall surface into account. For the representative day of each month during the year, solar radiation has been calculated in the different wall orientations and the roof. Figure 4 shows hourly incident solar radiation in all wall orientations and the roof in two representative days of the summer and winter seasons, July 21 and
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Figure 3. Average outdoor air temperature on representative days of summer and winter (July 21 for summer and January 21 for winter). 510
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Figure 4. Hourly incident solar radiation on the horizontal and all vertical wall orientations on representative days of (a) July 21(summer season) and (b) January 21(winter season).
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January 21, respectively. As it is expected, the maximum values of the incident radiation take place at different times for each orientation. East- and west-facing walls received the same radiation (Mavromatidis et al., 2012; Ozel, 2013b). It is seen from this figure that unlike July, the highest value of solar radiation belongs to the south-oriented wall during January (Mavromatidis AQ9 ¶ et al., 2012). It is also notable that solar radiation on the north-facing wall in the July has two maximum values at two different times during the day. Sol-air temperature is obtained by using Equation (4). Sol-air temperature, which is a combination of radiation and ambient air temperature, is shown in Figure 5 for the representative days of January and July. As shown in Figure 5, Sol-air temperature is strongly affected by solar radiation. The inside surface temperatures (and hence the inside surface heat flux), for both concrete and aerated brick on un-insulated walls (in January 21 and July 21), are obtained in the form of a numerical solution. It was seen that the orientation of the wall has a profound effect on the inside temperature of the walls and resulting heat flux. Results show that concrete has a higher maximum inside temperature in summer and lower minimum inside temperature in winter in comparison with aerated brick, which implies that aerated brick has a lower decrement factor (Asan, 2006). It is also seen that concrete has a higher amplitude of inside temperature compared with aerated brick. In January, the south-facing wall has the highest inside temperature and therefore lowest heating is needed, while the horizontal wall in July has the maximum temperature and hence the maximum cooling load is required. All walls with different orientations and the horizontal wall made from aerated brick reach their maximum temperatures later than the concrete one, which implies that aerated brick has a higher time lag compared with concrete (Asan, 2006). The daily transmission load is obtained through the integration of the inside heat flux over the day and the yearly transmission load is the sum of the total daily transmission load over a year. Figure 6 shows the daily transmission load of an un-insulated wall, for all orientations of the wall and the roof. Both aerated brick and concrete block walls are shown in Figure 6. From the figure, aerated brick wall has lower heating and cooling requirements compared with a concrete wall. It is also seen that west- and east-facing walls have the same daily transmission load. The horizontal wall has the maximum heating and cooling transmission loads during the year for both aerated brick and concrete block walls. Finally, it is observed that daily heating and cooling loads (for the horizontal wall) reach their maximum values in January and July, respectively. Yearly transmission load per square metre of un-insulated walls are also presented in Table 3. The horizontal wall (roof) has the highest yearly heating and cooling loads in both aerated brick and concrete walls. When insulation is installed in the wall, transmission load decreases. In the present study, two places where insulation can be placed are chosen, one between the cement plaster and main wall structure, i.e. outside, and the other between the gypsum plaster and the main wall structure (concrete or aerated brick in Figure 1), i.e. inside. After utilization of insulation, the time lag increases and the decrement factor decreases.
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Table 3.
Yearly transmission load (concrete block)
Yearly transmission load (aerated brick)
Heating
Cooling
Heating
Cooling
13.18058 11.05748 11.41614 11.41614 8.003887
−19.2496 −11.682 −16.0959 −16.0959 −18.8242
28.29076 23.7334 24.50328 24.50324 17.17876
−41.3215 −25.0776 −34.552 −34.552 −40.4084
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Yearly transmission load (MJ/m2) of an un-insulated wall of aerated brick and concrete block.
Horizontal South West East North
Horizontal South West East North
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Figure 5. Hourly sol-air temperature on the horizontal and all vertical wall orientations on representative days of (a) July (summer season) and (b) January (winter season).
Figure 7 shows the variation of time lag and decrement factor for all wall orientations and the horizontal wall versus insulation thickness for aerated brick when EPS insulation was placed on AQ10 ¶ the inside; Figure 8 shows the details for the outside. From these two figures it is apparent that the AQ11 ¶ orientation of the wall has a strong effect on the time lag and decrement factor. Increasing the insulation thickness decreases the rate of change of time lag and decrement factor. It is also notable that the east-facing wall has the highest time lag and lowest decrement factor among all wall orientations and the horizontal wall. A comparison between Figures 7 and 8 reveals that the place of insulation (inside or outside) does not change the overall trend discussed above. However, when insulation is placed on the outside of the wall, the time lag will be higher and decrement factor will be lower. The same trend has also been reported in a recent study by Ozel. AQ12 ¶ Other combinations of wall material and insulation show the same trend as above when wall orientations are examined. In order to determine the effect of different materials and insulations on time lag and decrement factor, Figures 9 and 10 are presented. Because of many orientations of the wall, in these figures only the south-facing wall is displayed. AB is an abbreviation used for
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Figure 6. Daily transmission load on the representative day of each month in the horizontal and all other orientations of a wall made from aerated brick and concrete block without insulation (positive and negative values represent heating and cooling transmission load, respectively) 650
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aerated brick and C is used for concrete in the legend of the figures. As mentioned before, aerated brick has a higher time lag and a lower decrement factor in comparison with the concrete block in both positions of insulation. Using XPS instead of EPS in the wall increases the time lag and decreases the decrement factor. The higher the insulation thickness is, the higher is the perceived difference between the walls insulated with EPS and XPS. By increasing the thickness of insulation, the effect of different wall materials and insulations on the decrement factor will be lessened. As stated earlier, higher time lag and lower decrement factor are the results of placing the insulation on the outside of the wall instead of on the inside. Yearly heating and cooling transmission loads for different wall materials and insulations placed on the inside and the outside of the wall are presented in Figures 11 and 12, respectively. First of all, it is obvious that heating load is the dominant need for Tehran, which is consistent with
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Figure 7. Time lag (left axis) and decrement factor (right axis) for all wall orientations and the horizontal wall of aerated brick and EPS insulation placed on the inside of the wall.
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Figure 8. Time lag (left axis) and decrement factor (right axis) for all wall orientations and the horizontal wall of aerated brick and EPS insulation placed on the outside of the wall. 690
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the values in the national regulation of buildings in Iran. It is seen that, the thinner the insulation is, the higher the difference between transmission loads of different materials. As the insulation thickness increases, the yearly transmission load will be relatively independent of materials and come closer to the same value. The yearly transmission load is higher if the insulation is placed on the outside of the wall. However, this difference is in the order of 1 (MJ/m2); therefore it is negligible (compared with the value of heating and cooling transmission load of the order of 100 (MJ/ m2)). It is also noteworthy that increasing the insulation thickness will decrease this difference and yearly transmission load will come closer for two different locations of insulation. A financial analysis was carried out to find the optimum insulation thickness. The necessary parameters used in the financial analysis are presented in Table 4. Most of the data presented in this table are taken from available data in a market and official websites of the Ministry of Energy and Ministry of Economy in 2013. Insulation cost increases linearly with increasing insulation thickness, while energy cost decreases. There must be a point at which the total cost, i.e. insulation cost and energy cost,
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Figure 9. Effect of different wall materials and insulations on the time lag (left axis) and decrement factor (right axis) versus insulation thickness placed on the inside of the wall material (AB is an abbreviation for aerated brick and C for concrete).
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Figure 10. Effect of different wall materials and insulations on the time lag (left axis) and decrement factor (right axis) versus insulation thickness placed on the outside of the wall material. 735
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Figure 11. Variation of (a) yearly heating transmission load and (b) yearly cooling transmission load with insulation thickness for different wall materials and insulations placed on the inside of the wall (AB is an abbreviation for aerated brick and C for concrete).
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Figure 12. Variation of (a) yearly heating transmission load and (b) yearly cooling transmission load versus insulation thickness for different wall materials and insulations placed on the outside of the wall (AB is an abbreviation for aerated brick and C for concrete).
Table 4. Parameters used in the financial analysis (most of these data have been extracted from the market and official website of the ministry of energy and ministry of economic affairs). Parameter
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Inflation rate, g Interest rate, i Life time, n Cel Cg Heating value, Hu Coefficient of performance, COP Efficiency of combustion of natural gas, ηs Cins(EPS) Cins(XPS)
Value 20% 22% 25 0.027 USD/kWh 0.04 USD/m3 35.948 × 106 J/m3 3 0.65 66 USD/m3 150 USD/m3
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reaches its minimum. Figure 13 shows cost diagrams versus insulation thickness for the aerated brick wall and EPS of the horizontal wall when insulation has been placed on the outside of the wall. Other orientations of the wall have the same pattern; so to avoid duplication of content their diagrams are not presented here. However, different optimum insulation thicknesses were obtained for different wall orientations and the horizontal wall. It is seen that approximate optimum thicknesses of 5, 3.68, 4.31, 4.31 and 4.06 cm were obtained for the horizontal wall and the south-, west-, east- and north-facing walls, respectively. The south-facing wall has the lowest optimum insulation thickness and the horizontal wall has the highest one. The optimum insulation thickness, energy saving during the life time (per square metre), the payback period for different wall orientations and the roof (for different combinations of wall materials and insulations and also the positions of insulation) are tabulated in Table 5. It is seen from this table that the aerated brick wall has a lower optimum insulation thickness compared with the concrete one and therefore it has more energy saving and a lower payback period. Investment cost return for the concrete wall in the reasonable years while aerated brick AQ13 ¶ needs more time. The horizontal wall has the highest value of optimal insulation thickness, highest energy saving and lowest payback period while the south-facing wall is positioned opposite to the horizontal wall. It is also notable that the east- and west-facing walls have the same value of optimum thickness, energy saving and payback period. Because of the higher investment cost of XPS insulation compared with EPS (approximately three times) in the wall with the same position and material, it is seen that optimal insulation thickness and energy saving decrease when XPS is used while payback period increases. Concerning the position of the insulation, as shown in Table 5, it is realized that for EPS, optimal insulation thickness and payback period remain constant or increase when insulation is placed on the outside of the wall, while energy saving decreases. It is seen that for XPS insulation when it is placed on the outside of the wall, optimal insulation thickness and payback period decrease while energy saving increases. It should be noted that the aforementioned difference in the position of insulation is more noticeable for the payback period. Higher payback period and small energy saving are obtained for aerated brick walls, while reasonable payback period is reported for concrete walls and energy saving as well.
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Figure 13. Variation of total cost, energy cost and insulation cost versus the insulation thickness for aerated brick and EPS insulation (placed on the outside of the wall) for the horizontal wall (south-, west-, east- and north-oriented walls have the same pattern, so they are not presented).
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Description Optimal thickness (cm)
Energy saving (USD/m2)
Payback period (years)
Inside Wall orientation Horizontal South West East North Horizontal South West East North Horizontal South West East North
Outside
AB EPS 4.97 3.68 4.30 4.30 4.05 4.43 2.38 3.30 3.30 2.90 9.40 10.78 10.28 10.28 10.70
C XPS 2.43 1.68 2.08 2.08 1.83 2.04 0.70 1.34 2.08 1.16 14.65 18.33 16.30 16.30 16.23
EPS 6.89 5.62 6.24 6.24 6.0 18.4 12.1 14.99 14.99 13.72 4.2 5.0 4.57 4.57 4.77
AB XPS 3.78 3.06 3.38 3.38 3.25 15.40 9.81 12.31 12.31 11.15 5.76 6.90 6.27 6.27 6.56
EPS 5.0 3.68 4.31 4.31 4.06 4.34 2.34 3.23 3.23 2.84 9.56 11.4 10.42 10.42 10.86
C XPS 2.26 1.42 1.87 1.87 1.68 2.39 0.95 1.59 1.59 1.27 13.18 15.66 14.56 14.56 13.28
EPS 7.0 5.66 6.30 6.30 6.04 18.27 12.04 14.90 14.90 13.64 4.28 5.05 4.72 4.72 4.82
XPS 3.77 3.06 3.37 3.37 3.24 15.45 9.81 12.35 12.35 11.20 5.73 6.90 6.24 6.24 6.51
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Table 5. Optimum insulation thickness, payback period and energy saving per each square metre of insulation for all wall orientations and a combination of wall materials and insulations and also position of the insulation (AB is an abbreviation for aerated brick and C for concrete).
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The energy cost in Iran is much lower than the average global price. Followed by the Iran subsidy reform law mentioned in introduction section, it is predictable that the energy cost in Iran will be increased in the next few years; therefore, the optimum insulation thickness and energy saving will increase. For example, if electricity and natural gas cost double simultaneously while the other parameters remain constant, optimal insulation thickness, energy saving and payback years for the concrete wall with EPS insulation on the inside of the wall will become 10.39 cm, 42.28 USD/m2 and 2.9 years, respectively, which is remarkably better analogously in comparison with the present values of 6.89 cm, 18.4 USD/m2 and 4.2 years.
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Figure 14. Effect of (a) inflation rate (b) discount rate (c) electricity price (d) natural gas price and (e) efficiency of combustion of natural gas on optimum insulation thickness and payback period for a wall made of aerated brick and EPS as insulation material on the inside of the wall.
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A sensitive analysis has been conducted in order to investigate the effect of different economic and also thermal parameters on the optimum insulation thickness and payback period. The obtained results for a south-facing wall made of aerated brick and EPS as insulation material on the inside of the wall are illustrated in Figure 14 (other combinations show the same trend, so it is not presented). Figure 14(a)–(e) shows the variation of insulation thickness and payback period as a function of inflation rate, discount rate, electricity price, natural gas price and efficiency of combustion of natural gas, respectively (all other parameters are set to be constant and equal to the values presented in Table 4). Rising inflation rates increase the optimum insulation thickness while they decrease the payback period. Both payback period and optimum insulation thickness decrease as the discount rate increases. The effect of energy price on the payback period and optimum insulation thickness is also investigated. Investigations reveal that increasing electricity and natural gas price will lessen payback period and increase optimum insulation thickness. It is also seen from the figure that an increase in the efficiency of combustion of natural gas tends to decrease optimum insulation thickness while it increases the payback period; therefore improving the combustion efficiency has a profound effect on the optimum insulation thickness and payback period as well. According to the subsidy law in Iran, the energy price will increase inevitably; therefore application of insulation material will be far more reasonable in the future. Total heating and cooling transmission load are obtained for the optimum insulation thickness for different combinations of walls and insulations and also for all wall orientations and the horizontal wall. Figure 15 shows the percentage ratio of yearly transmission loads (heating and cooling) for the wall with an optimum insulation thickness and the un-insulated wall. Firstly, percentage ratios of cooling and heating transmission load for the same combination of wall and insulation have approximately the same value. It is also realized that the south-facing wall has the highest percentage ratio of yearly heating and cooling transmission load while the horizontal
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Figure 15. Yearly cooling and heating transmission load for all orientations of the wall and the horizontal wall in combination of insulation and material of wall and also position of insulation (AB is an abbreviation for aerated brick and C for concrete).
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wall has the lowest percentage ratio among all wall orientations. This implies that utilization of insulation on the south-facing wall has a smaller effect on the yearly transmission load compared with the other wall orientations. Moreover, concrete walls (when optimum insulation thickness is applied) reduce the transmission load from 70% to 82% in comparison with the un-insulated wall, while this value lies in the range of 42–58% for the aerated brick wall.
4. Conclusion In this paper optimal insulation thicknesses, based on heating and cooling seasons, for conventional walls in Tehran are obtained. It was found that the concrete wall has a higher optimum insulation thickness compared with aerated brick. Higher time lag and lower decrement factor have been achieved when insulation is placed on the outside of the wall. Also the location of insulation does not change the yearly transmission load considerably. Among all wall orientations, it was found that the horizontal wall has the highest optimum insulation thickness and the southfacing wall has the lowest optimum thickness. The results showed that using insulation in walls made of concrete and aerated brick reduces the yearly transmission load up to 82% and 58%, respectively. Due to the high investment cost of XPS, although obtaining higher payback period, smaller insulation thickness and energy saving have been achieved. Finally, the results showed that increase in the energy cost in Iran will make utilization of insulation more reasonable.
Disclosure statement No potential conflict of interest was reported by the authors.
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