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Energy Conversion and Management 76 (2013) 674–684
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Energy Conversion and Management
journal homepage: www.elsevier .com/locate /enconman
Thermal, economical and environmental analysis of insulated buildingwalls in a cold climate
0196-8904/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.08.013
⇑ Tel.: +90 0424 2370000/5338.E-mail address: [email protected]
Meral Ozel ⇑Department of Mechanical Engineering, Firat University, 23279 Elazıg, Turkey
a r t i c l e i n f o
Article history:Received 21 May 2013Accepted 10 August 2013
Keywords:Dynamic thermal conditionsHeating transmission loadOptimum insulation thicknessEnergy savingsFuel consumption and emissions
a b s t r a c t
In this study, thermal, economical and environmental effects in insulated building walls are numericallyinvestigated under dynamic thermal conditions for two different wall structures and two different insu-lation materials. The investigation is carried out for different wall orientations during the winter period inKars city which is one of the coldest cities of Turkey.
For this purpose, a computer model based on an implicit finite difference procedure, which has beenpreviously validated, is used under steady periodic conditions. Firstly, thermal characteristics such asyearly heating transmission load, yearly averaged time lag and decrement factor are calculated for heat-ing season. The results show that maximum time lag, minimum decrement factor and lowest heatingload are obtained in the brick wall with XPS (Extruded polystyrene) while minimum time lag, maximumdecrement factor and highest heating load are obtained in the concrete wall with EPS (Expanded polysty-rene).
Secondly, yearly heating loads obtained under dynamic conditions are used as inputs to an economicmodel for the determination of the optimum insulation thickness. The optimum insulation thicknesses,energy savings and payback periods are calculated by using life-cycle cost analysis over lifetime of20 years of the building. For heating season, it is seen that the lowest value of heating load, optimuminsulation thickness and energy saving is obtained for the south-facing wall while highest value of themis obtained for the north-facing wall. The results show that for heating season, the most economical ori-entation is south-facing wall with an optimum insulation thickness of 9.2 cm at brick wall with XPS.
Lastly, fuel consumption and emissions of CO2 and SO2 are calculated by taking into consideration wallorientations for different structure and insulation materials. It is seen that as the insulation thicknessincreases, the yearly heating transmission load and consequently, fuel consumption and emissionsdecrease. The results show that for 9 cm insulation thickness, this decrement is 85% for all oriented walls.
� 2013 Elsevier Ltd. All rights reserved.
1. Introduction
The most important part of energy strategy of a country is en-ergy saving. Because of the limited energy sources and environ-mental pollution coming from using the fuels, energy saving hasbecome compulsory [1]. Energy consumption is rapidly increasingdue to the population increase and urbanization. The energy con-sumption is distributed among four main sectors: industrial, build-ing (residential/commercial), transportation and agriculture. Thebuilding sector is the largest energy consumer following the indus-trial sector [2]. Buildings are large consumers of energy in all coun-tries. In regions with harsh climatic conditions, a substantial shareof energy consumption and the consequent environmental pollu-tion are attributed to space heating of residential buildings. Theproper design and selection of building envelope and its compo-
nents is an efficient means to reduce the space heating load. Nota-ble among them is selecting well-insulated exterior walls to reduceenergy consumption and greenhouse gas emission [3]. Insulatedbuilding walls are integrated parts of a building envelope. Theyprotect the inner space from extreme weather conditions anddamp down large fluctuations in temperature. As such, the build-ing envelope should provide the necessary thermal comfort forthe occupants as well as reduce energy consumption requirementsfor cooling and heating. This is usually done through increasingthermal resistance of this envelope and, hence, reducing transmis-sion loads. Therefore, addition of thermal insulation is important,particularly in regions with extreme climates [4].
The employ of thermal insulation is one of the most effectiveways of building energy conservation for cooling and heating.Therefore, the selection of a proper insulation material and deter-mination of optimum insulation thickness are particularly vital [5].It is well known that the heat-transmission load decreases withouta limit with increasing insulation thickness, however, the rate of
Nomenclature
a solar absorptivity of outdoor surface of wallAs annual energy savings ($/m2 yr)c specific heat (J/kg K)CA yearly total cost of energy ($/m2 year)Ci cost of insulation material per unit volume ($/m3)CF fuel cost ($/kg)Ct total cost ($/m2)g inflation ratehi heat-transfer coefficient at the indoor surface of wall
(W/m2 K)ho heat-transfer coefficient at the outdoor surface of wall
(W/m2 K)Hu lower heating value of the fuel (kJ/kg)IT incident total solar radiation for vertical surfaces (W/
m2)Ib beam solar radiations on the horizontal surface (W/m2)Id diffuse solar radiations on the horizontal surface (W/
m2)I total solar radiations on the horizontal surface (W/m2)i interest ratek thermal conductivity (W/m K)Li insulation thickness (m)MF yearly fuel consumption (kg/m2 year)N lifetime (years)pb payback period (years)PWF present worth factorqi heat flux at indoor surface of the wall (W/m2)Ql total heat loss per year of insulated wall (kW h/m2)
Se The energy savings ($/m2)t time (s)Ti indoor air temperature (�C)To outdoor air temperature (�C)Tx=L(max) maximum of indoor surface temperature (�C)Tx=L (min)
minimum of indoor surface temperature (�C)Tx=0 (max) maximum of outdoor surface temperature (�C)Tx=0 (min)
minimum of outdoor surface temperature (�C)U overall heat transfer coefficient of the wall (W/m2 K)
Greek lettersa thermal diffusivity (m2/s)b slope of the tilted surfacegs efficiency of the heating systemd declination angle (�)/ latitude (�)U time lag (h)f decrement factorc surface azimuth angle (�)x hour angle (�)q density (kg/m3)h incidence angle (�)hz zenith angle (�)
Layer j
kj, ρj
cj
LM
Layer M
qi(t)
Indoor
Ti, hi kM, ρM
cM
Lj
x
qo(t)
L1
To(t), ho
Outdoor Layer 1
k1, ρ1
c1
ITSun
Fig. 1. M-layered composite wall.
M. Ozel / Energy Conversion and Management 76 (2013) 674–684 675
decrease drops quite fast as the thickness increases. From a purelyconservation point of view, the designer should select an insulationmaterial with the lowest possible thermal conductivity and thehighest thickness that the owner can afford. However, the cost ofinsulation increases linearly with its thickness, and there is a point,for each type of insulation material, beyond which the saving inenergy consumption will not compensate for the extra cost of insu-lation material. Thus, there must be an optimum insulation thick-ness at which the total cost of the insulation material plus thepresent worth of energy consumption over the lifetime of thebuilding is a minimum [6].
In literature, studies dealing with the optimum insulation thick-ness are based on only heating loads [1,7–14], only cooling loads[15–18] and, both heating and cooling loads [2,5,6,19–29]. Whilemost of those studies use degree-days (or degree-hours) conceptwhich is a simple and crude model to estimate the transmissionloads under static conditions [1,2,5,7–12,17–19], the others useddynamic transient models based on numerical and analyticalmethods to obtain highly accurate results [6,13–15,20–29].
In literature, although there are many studies on the determina-tion of the optimum insulation thickness, these studies obtained byusing dynamic models considering the transient thermal behaviorof building envelope and solar radiation are in a limited number asmentioned above. The main objective of this study is to analyse asthermal, economical and environmental of the insulated buildingwalls. The calculations are carried out under dynamic thermal con-ditions by considering different wall orientations for the climaticconditions of Kars located in a cold climate. Firstly, the thermalcharacteristics are calculated under steady periodic conditions.Secondly, the insulation thickness is optimized by using a costanalysis over lifetime of 20 years of the building. Lastly, fuel con-sumption and emissions of CO2 and SO2 are determined for differ-ent structure and insulation materials. Results are compared withcorresponding results in under different climatic conditions.
2. Mathematical formulation and calculation procedure
A composite structure with M layers is shown schematically inFig. 1. The outside surface is exposed to periodic solar radiation andoutdoor environmental temperature while the inside surface is ex-posed to room air maintained at constant indoor designtemperature.
Assuming no heat generation, constant thermal properties, one-dimensional heat transfer and negligible interface resistance, time-dependent heat conduction equation in a multi layer wall may bewritten as [20]:
@2Tj
@x2 ¼1aj
@Tj
@tð1Þ
where að¼ k=ðqcÞÞ is the thermal diffusivity and the subscript j islayer number (j = 1,2,. . ., M), q, c and k are the density, the specificheat and the thermal conductivity, respectively.
Table 1Thermophysical properties of building materials.
Material k (W/m K) q (kg/m3) c (J/kg K) Ci ($/m3)
Brick block 0.620 1800 840
676 M. Ozel / Energy Conversion and Management 76 (2013) 674–684
As initial condition, an arbitrary uniform temperature field isassumed. The boundary conditions are given as follows:
I. For boundary condition at the inside surface (x = L):
Concrete block 1.370 2076 880Extruded polystyrene 0.029 35 1213 304.23Expanded polystyrene 0.038 18 1500 188.42�kM@T@x
� �x¼L¼ hiðTx¼L � TiÞ ð2Þ
Cement plaster 0.700 2778 840
where hi is the inside-surface combined (convective and radiative)heat-transfer coefficient and Ti is the indoor air temperature.II. For boundary condition at the outside surface (x = 0):
�k1@T@x
� �x¼0¼ h0ðTeðtÞ � Tx¼0Þ ð3Þ
where ho is outside-surface combined heat-transfer coefficients. Te
is the sol–air temperature including the effect of solar radiationon the outdoor temperatures and is expressed as follows [30]:
Te ¼ To þaIT
ho� eDR
hoð4Þ
where To is the outdoor air temperature. IT and a denote the totalsolar radiation and solar absorbtivity of the outdoor wall surface,respectively. eDR/ho is the correction factor and is assumed to be4 �C for horizontal surfaces and 0 for vertical surfaces from ASHRAE.
The total solar radiation (IT) is calculated as:
IT ¼ RbIb þ Id1þ cos b
2
� �þ Iqg
1� cos b2
� �ð5Þ
where Ib, Id and I are beam, diffuse and total solar radiations on thehorizontal surface. Ground reflectance qg is usually taken as 0.2, b isthe slope of the tilted surface. The geometric factor Rb is the ratio ofbeam radiation on the tilted surface to that on a horizontal surfaceat any time and is calculated as:
Rb ¼cos hcos hz
ð6Þ
where h and hz are incidence and zenith angles, respectively. Theseangles are defined as:
h ¼ sin d sin / cos b� sin d cos / sin b cos c
þ cos d cos / cos b cos xþ cos d sin / sin b cos c cos x
þ cos d sin b sin c sin x ð7Þ
hz ¼ cos / cos d cos xþ sin u sin d ð8Þ
where d, /, x and c are declination angle, latitude angle, hour angleand surface azimuth angle, respectively. c is zero for an inclinedplane facing south. It is taken as negative from the south to the east,and the north, and positive from south to west, and the north, i.e.�180� < c < þ180�. Detailed calculation procedures for Eqs. (5)–(8) are given by Ref. [31].
The transient heat conduction problem was solved by using animplicit finite difference method. Detailed calculation proceduresare given in reference [32]. The numerical solution gives the tem-perature distribution across the composite wall thickness at anytime instant. It is assumed that the boundary condition on the out-side surface is periodic, i.e. the daily cycle of the outdoor air tem-perature and the solar radiation is repeated on consecutive days,and a steady periodic solution is obtained.
3. The structure of the external walls and flat roof
The wall and flat roof structures with an insulation layer placedon the outside as consists of 2 cm external plaster, an insulationlayer of variable thickness, 20 cm brick (or concrete) block and2 cm internal plaster. Extruded polystyrene (XPS) and Expanded
polystyrene (EPS) are selected as insulation material. Thermalproperties of materials used in the wall structure are given inTable 1.
The investigation is carried out for the climatic conditions ofKars (latitude: 30.36�N, longitude: 43.05�E) which is one of thecoldest cities of Turkey. The hourly solar radiation flux on the wallis calculated by using isotropic sky model given in Duffie and Back-man [31], and by using solar radiation measured on the horizontalsurface. The outdoor air temperatures are obtained by averaginghourly measurements recorded in meteorological data over theyears 2005–2012 [35]. The indoor design temperature is taken con-stant to be 20 �C during winter period (September–May). The solarabsorptivity of opaque wall is selected to be equal to 0.8 for dark-colored surfaces, and the combined heat-transfer coefficients at theindoor and the outdoor wall surfaces are taken to be 9 and 22 W/m2 K, respectively [36].
4. Calculation of thermal characteristics
4.1. Heating transmission load
In the present study, the 21st day of each month of winter per-iod (September–May) in a cold climate is considered as a represen-tative day. The instantaneous heating transmission load isobtained as following:
qi ¼ hiðTx¼L � TiÞ ð9Þ
To calculate daily total load, this instantaneous load is inte-grated over 24 h periods. Yearly heating load is separately calcu-lated from daily transmission loads which are added over winterperiod.
4.2. Time lag and decrement factor
The time lag is defined as the time that sinusoidal temperaturewave reaches from outdoor surface of wall to indoor. On the otherhand, the decrement factor is defined as reduction ratio in ampli-tude of the temperature wave at the indoor surface compared tothe outside surface. The time lag and decrement factor are com-puted using the following relations [32]:
U ¼ tTx¼LðmaxÞ � tTx¼0ðmaxÞ ð10Þ
f ¼ Tx¼LðmaxÞ � Tx¼LðminÞTx¼0ðmaxÞ � Tx¼0ðminÞ ð11Þ
where tTx¼LðmaxÞ and tTx¼0ðmaxÞ represent the time that indoor surfacetemperatures and outdoor surface temperatures are being maxi-mum, respectively. Tx¼LðmaxÞ; Tx¼LðminÞ and Tx¼0ðmaxÞ; Tx¼0ðminÞare maximum and minimum temperatures on the indoor and out-door surfaces of wall, respectively. The time lag and decrement fac-tor are calculated for the representative day of each month ofwinter. Than, average time lag and decrement factor for winter per-iod (September–May) are determined as the arithmetic average ofthese monthly values.
Table 2The parameters used in calculations.
Parameter Value
CoalCF 0.3777 $/kgHu 29.307 � 106 J/kggs %65Chemical formula of Coal [27] C7.078H5.149O0.517S0.01N0.086
Interest rate, i %8.75Inflation rate, g %7.50Lifetime, N 20
M. Ozel / Energy Conversion and Management 76 (2013) 674–684 677
5. Cost analysis and optimization of insulation thickness
Thermal insulation used in the external walls of buildings re-duces heating load, and consequently reduces energy consump-tion. However, purchase and installation of insulation layerincrease the initial cost of the construction. Therefore, an economicanalysis should be performed to determine the optimum insulationthickness which minimizes the total cost including the insulationand the energy consumption costs [15]. In the present analysis,optimum insulation thickness is calculated by considering onlyheat transmission from external walls because insulation of exter-nal walls is analysed. The other loads do not affect this optimumvalue.
The optimum insulation thickness depends mainly on the costand the thermal conductivity of insulation material, cost of energy,yearly heating transmission load in uninsulated and insulated wall,efficiency of the heating system, building lifetime, and interest andinflation rates. The yearly energy cost for heating per unit area, (CA)is determined from:
CA ¼Q l:CF
Hu:gsð12Þ
where Ql is the total heat loss per year of insulated wall (kW h/m2),CF is fuel cost ($/kg), Hu is lower heating value of the fuel (kJ/kg) andgs is the efficiency of the heating system.
The total cost is the sum of the cost of insulation material plusthe present worth of the cost of energy consumption over the lifetime of the building. It is written as:
Ct ¼ PWF:CA þ Ci:Li ð13Þ
where Ci is the cost of insulation material per unit volume ($/m3), Li
is the insulation thickness (m) and, PWF are the Present WorthFactor.
Based on a life-cycle analysis, a present value of fuel con-sumption cost over the life time of the building is computedby accounting for the effects of the inflation rate g (for the en-ergy cost) and interest rate i (for the value of money) over thisperiod. An actual value of energy cost during a building life cycleof N years is obtained by multiplying the annual cost of energyby PWF [28]. In this case, PWF for the lifetime of N years is de-fined as below:
PWF ¼ ð1þ rÞN � 1
rð1þ rÞN;
i > g r ¼ i�g1þg
i < g r ¼ g�i1þi
( )ð14Þ
PWF ¼ N1þ i
; i ¼ g ð15Þ
The energy savings (life-cycle savings over n years) per unit areaof the wall surface are calculated from the difference between thetotal cost when the wall is uninsulated and the total cost when it isinsulated with optimum thickness [15]. It can be written as:
Se ¼ððQ lÞun � Q lÞ � CF
Hu � gs
� �PWF � Ci:ðLiÞopt ð16Þ
where ðQlÞun is the total heat loss per year in uninsulated wall(kW h/m2). Annual energy savings (As) are calculated as the differ-ence between energy cost without insulation and energy cost withoptimum insulation, divided by the PWF. It can be written as:
As ¼ððQlÞun � QlÞ � CF
Hu:gsð17Þ
In order to take into account the effects of inflation and interestrates, the payback period (pb), defined as the insulation cost di-vided by the annual energy savings, should be deduced from thefollowing expression [28]:
PWFðpbÞ ¼Ci � ðLiÞopt
Asð18Þ
pb ¼lnð1� r
Ci �ðLiÞopt
ASÞ
lnð 11þrÞ
ð19Þ
This means that the cost of insulation will be paid back in pb
years by savings in energy.
6. Calculation of the yearly fuel consumption and emissions
In buildings, increasing the insulation thickness reduces heatloss. Moreover, the fuel consumption and air pollution are broughtdown. The general chemical formula of combustion for fuel is givenby [33,34]
CaHbOdSeNf þ e � XðO2 þ 3:76N2Þ
! aCO2 þb2
� �H2Oþ ðe� 1ÞXO2 þ eSO2 þ YN2 ð20Þ
The constants X and Y are calculated from the oxygen balanceformulas given in the following expressions:
X ¼ aþ b4þ e� d
2
� �ð21Þ
Y ¼ 3:76:e � X þ ðf=2Þ ð22Þ
In Eq. (20), NOx and CO emissions are neglected. The emissionrate of combustion products resulting from the burning 1 kg of fuelcan be calculated by [34]
MCO2 ¼aCO2
M� kg CO2=kg fuel ð23Þ
MSO2 ¼eSO2
M� kg SO2=kg fuel ð24Þ
M is fuel mol weight and can be calculated as follows:
M ¼ 12aþ bþ 16dþ 32eþ 14f kg=kmol ð25Þ
The total emissions of CO2 and SO2 can be calculated using thefuel consumption (MF) as follows:
MCO2 ¼44aM
MF ð26Þ
MSO2 ¼64eM
MF ð27Þ
Yearly fuel consumption can be calculated using yearly heatingtransmission load obtained by dynamic method as follows:
MF ¼Q l
Hu:gsð28Þ
The parameters used in calculations are given in Table 2.
678 M. Ozel / Energy Conversion and Management 76 (2013) 674–684
7. Results and discussion
7.1. Environmental conditions
Hourly variations of incident solar radiation and sol–air temper-ature for all wall orientations and horizontal surface in December21 are shown in Fig. 2a and b, respectively. The incident solar radi-ation is highest at 10:00 for east orientation and at 14:00 for westorientation while it is maximum at noon (12:00) for south andnorth orientations, and horizontal surface. It is seen that maximumpeak value of sol–air temperatures of east oriented wall is highercompared to the west wall since maximum outdoor temperatureappears at 11:00 for December 21.
Fig. 3. Hourly variation of inside surface heat flux of uninsulated brick structure forthe all wall orientations and flat roof in December 21.
7.2. Heating transmission loads
Fig. 3 shows daily fluctuations of inside surface heat flux ofuninsulated brick structure for the all wall orientations and flatroof in December 21. It is seen that wall orientation has a signifi-cant effect on inside surface heat flux. Peak loads for south, north,east, west oriented walls and flat roof are obtained as 55.66, 57.38,57.08, 56.83 and 64.03 (W/m2), respectively. It is seen that for brickstructure material, the peak is highest for flat roof while it is lowestfor south oriented wall. The other hand, lowest fluctuation occursin the north-facing wall while highest fluctuation occurs in thesouth-facing wall. It is assumed that the use of brick materials
Fig. 4. Daily total heating transmission loads of uninsulated walls for therepresentative days of each month of winter for the all wall orientations and flatroof.
Fig. 5. Variation of yearly heating transmission loads according to increasinginsulation thickness for all wall orientations and flat roof.
Fig. 2. (a and b) Hourly variation of incident solar radiation and sol–air temperaturefor all wall orientations and horizontal surface in December 21.
M. Ozel / Energy Conversion and Management 76 (2013) 674–684 679
regarding the construction of roofs refers to a theoretical situationfor the purposes of the present investigation. Daily total heatingtransmission loads of uninsulated walls (for the all orientations)
Fig. 7. (a and b) Variations of time lag and decrement factor with insulationthickness for all wall orientations and flat roof.
Fig. 6. Variation of yearly heating transmission loads in the south-facing wall isshown for two different wall structures and two different insulation materials.
and flat roof are shown in Fig. 4 for brick structure material. Sep-tember gives the lowest heating loads while December gives thehighest heating loads. It is seen that the east and west orientationsprovide equal heating loads. The maximum heating load is ob-tained for flat roof from October to March while it is obtained fornorth wall in September, April and May.
The yearly heating loads of uninsulated brick wall are obtainedas 644.40, 766.12, 704.55, 704.55 and 795.71 (MJ/m2 year) forsouth, north, east, west oriented walls and flat roof, respectively.It is seen that the lowest heating load is provided for south wallwhile the highest heating load is obtained for flat roof. The otherhand, the east and west-facing walls provide equal heating loads.Fig. 5 indicates variation of yearly heating transmission loadsaccording to increasing insulation thickness for all wall orienta-tions and flat roof. As expected, transmission loads decrease asthe insulation thickness increases. But, this decrease is more rapidat smaller values of insulation thickness. As the insulationthickness increases, transmission loads for all wall orientations be-come closer. Identical trends of variations and similar conclusionswere obtained by Refs. [15,20,24,28] under different climaticconditions. It is seen that the yearly heating loads decrease whenthe wall is insulated. For example, the yearly heating loads for9 cm insulation thickness (XPS) are obtained as 94.9, 112.8,108.9, 108.9 and 117.2 (MJ/m2 year) for south, north, east, west ori-ented walls and flat roof, respectively. This decrement is approxi-mately 85% for all wall orientations and flat roof.
Fig. 8. (a and b) Variations of time lag and decrement factor in the south-facingwall for two different wall structures and two different insulation materials.
Fig. 9. (a–d) Variation of cost to insulation thickness for two different wall structures and two different insulation materials in a south oriented wall.
680 M. Ozel / Energy Conversion and Management 76 (2013) 674–684
The variation of yearly heating transmission loads in the south-facing wall is shown for two different wall structures and two dif-ferent insulation materials in Fig. 6. It is seen that at smaller valuesof insulation thickness, the highest heating load is obtained in con-crete wall with EPS which has the lowest thermal resistance, whilethe lowest heating load is obtained in brick wall with XPS whichhas the highest thermal resistance. As the insulation thickness in-creases, it is seen that brick and concrete walls with same insula-tion material become closer. However, it is seen that at 2 cminsulation thickness, yearly heating transmission loads of concretewall with XPS and brick wall with EPS are approximately same.
7.3. Time lag and decrement factors
Fig. 7 presents variations of time lag and decrement factor withinsulation thickness for all wall orientations and flat roof in thebrick wall with XPS. It is seen that wall orientation has a great ef-fect on time lag while it has a small effect on decrement factor. Thelongest time lag is obtained for east-facing wall while shortest timelag is obtained for west-facing wall. However, it is seen that thetime lag values of flat roof and south wall are almost the samefor all insulation thickness. On the other hand, although the graphof decrement factors follows similar trends for all directions,
minimum decrement factor is obtained in the east wall while max-imum decrement factor is obtained in the flat roof. Besides, it isseen that as the insulation thickness increases, decrement factordecreases while time lag increases, as expected. The variations oftime lag and decrement factor in the south-facing wall is shownfor two different wall structures and two different insulation mate-rials in Fig. 8. It is seen that maximum time lag and minimum dec-rement factor are obtained in the brick wall with XPS whileminimum time lag and maximum decrement factor are obtainedin the concrete wall with EPS. Results show that at smaller valuesof insulation thickness, time lag values of walls which have samestructure materials with different insulation approximate. How-ever, it is seen that as the insulation thickness increases, time lagsvalues of walls with XPS increase much more than walls with EPS.The reason is that XPS has the higher heat capacity and the lowerthermal conductivity than EPS.
7.4. Optimization of insulation thickness
To determine the optimum insulation thickness, the heatingtransmission load obtained under dynamic thermal conditions isnow used as inputs to an economic model including the cost ofinsulation material and the present value of energy consumption
Table 3The optimum insulation thickness, energy saving and payback period for twodifferent wall structures and two different insulation materials in all directions.
Description Orientations Brick Concrete
XPS EPS XPS EPS
Optimuminsulationthickness (m)
South 0.092 0.136 0.098 0.142
North 0.102 0.150 0.107 0.155East 0.098 0.144 0.102 0.150West 0.098 0.144 0.102 0.150Horizontal 0.104 0.155 0.110 0.160
Energy savings ($/m2)
South 166.1 171.7 275.9 281.8
North 203.0 209.2 307.8 314.3East 184.3 190.2 280.0 286.2West 184.3 190.2 280.0 286.2Horizontal 212.1 211.6 337.9 344.5
Payback period(years)
South 2.61 2.35 1.75 1.56
North 2.40 2.15 1.70 1.53East 2.52 2.26 1.80 1.62West 2.52 2.26 1.80 1.62Horizontal 2.35 2.19 1.62 1.45
Fig. 11. Variation of energy savings for two different wall structures and twodifferent insulation materials in a south oriented wall.
Fig. 10. Effect of insulation thickness on energy savings according to all wallorientations and flat roof.
M. Ozel / Energy Conversion and Management 76 (2013) 674–684 681
cost over lifetime of 20 years of the building. Fig. 9a–d shows var-iation of cost to insulation thickness for two different wall struc-tures and two different insulation materials in a south orientedwall. While the energy cost decreases with increasing insulationthickness, the insulation cost increases linearly with insulationthickness. Total cost is sum of insulation and energy cost. The insu-lation thickness at which the total cost is the minimum is taken asthe optimum insulation thickness. Conclusions show that optimuminsulation thicknesses for brick and concrete walls with XPS andEPS are obtained as 9.2, 13.6, 9.8 and 14.2 cm, respectively.
The effect of insulation thickness on energy savings according toall wall orientations and flat roof is shown in Fig. 10 for brick wallwith XPS. As insulation thickness increases, energy saving in-creases and reaches its maximum value at optimum insulationthickness. For heating season, it is seen that lowest value of energysavings is obtained for south-facing wall while the highest energysaving is obtained for flat roof. As expected, the east and west wallsprovide equal energy savings because of same insulation thick-nesses of them. The values of energy savings at optimum insulationthicknesses for south, north, east, west orientations and flat roofare obtained as 166, 203, 184, 184 and 212 $/m2, respectively.Fig. 11 shows variation of energy savings for two different wallstructures and two different insulation materials in a south ori-ented wall. It is seen that energy savings of walls which have samestructure materials with different insulation follows close curve.The results show that Structure materials have big effect on energysavings because the energy saving also depends on yearly heatingtransmission loads of uninsulated wall.
The optimum insulation thickness, energy saving and paybackperiod for all directions and all materials (for two different wallstructures and two different insulation materials) are illustrated
Table 4The summary results of the other studies related to effect of wall orientation on optimum
Reference study Location Insulat
Present study (heating) Kars, Turkey ExtrudOzel [14] (cooling) Antalya, Turkey ExtrudOzel [24] (heating + cooling) Elazıg, Turkey ExtrudIbrahim et. al. [29] (heating) Zahle ExpandIbrahim et. al. [29] (cooling) Beirut ExpandAl-Sanea and Zedan [20] (heating + cooling) Riyadh MoldedDaouas [28] (heating + cooling) Tunisia Expand
in Table 3. For heating season, the lowest value of optimum insu-lation thickness and energy saving is obtained for the south-facingwall while highest value of them is obtained for flat roof (horizon-tal surface). On the other hand, flat roof gives the lowest value ofpayback period. It is seen that as thermal conductivity increases,optimum insulation thickness and energy savings increase whilepayback period decreases. The results show that optimum insula-
insulation thickness.
ion materials Optimum insulation thickness (cm)
South North East West
ed polystyrene 9.2 10.2 9.8 9.8ed polystyrene 3.6 3.1 4 4ed polystyrene 5.5 6.0 6 6ed polystyrene 3.4 4.7 3.9 4ed polystyrene 4.1 1.9 4.8 4.9polystyrene 8.75 8.88 9.2 9.25
ed polystyrene 10.1 10.1 11.7 11.6
Fig. 12. (a and b) Variation of daily total heating transmission loads of brick andconcrete walls at uninsulated and optimum insulation thicknesses.
Fig. 13. Variations of the yearly fuel consumption with insulation thickness for alldirections.
Fig. 14. (a–c) Variations of the yearly fuel consumption and, CO2 and SO2 emissionsin the south-facing wall for two different wall structures and two differentinsulation materials.
682 M. Ozel / Energy Conversion and Management 76 (2013) 674–684
tion thicknesses, energy savings and payback periods significantlydepend on the thermal conductivity of structure and insulationmaterials, not only on the costs.
The results of the other studies related to effect of wall orienta-tion on optimum insulation thickness are summarized in Table 4. Itis seen that for heating plus cooling and only heating; the mosteconomical case is south orientation while for only cooling; thenorth orientation gives the lowest insulation thickness. The resultsof present study are in harmony with those obtained by Ref. [29]for heating season in Beirut.
Table 5Values of fuel consumption and emissions obtained at 9 cm insulation thickness and at the optimum insulation thickness for different orientations.
Insulation thickness (cm) Yearly fuel consumption and emissions (kg/m2 year) Orientations
South North East West
Fuel consumption 4.981 5.923 5.447 5.447At 9 cm CO2 emission 15.53 18.46 16.98 16.98
SO2 emission 0.032 0.038 0.035 0.035Fuel consumption 4.889 5.318 5.063 5.063
At the optimum CO2 emission 15.24 16.58 15.78 15.78SO2 emission 0.031 0.034 0.032 0.032
M. Ozel / Energy Conversion and Management 76 (2013) 674–684 683
Fig. 12a and b shows the variation of daily total heating trans-mission loads of brick and concrete walls at uninsulated and opti-mum insulation thicknesses. It is seen that when optimumthicknesses of insulation materials is applied, daily heating loadsfor all months at heating season decrease 85.5% for brick wall withXPS, 87% for brick wall with EPS, 90% for concrete wall with XPSand 91%, for concrete wall with EPS.
7.5. The environmental analysis
The environmental impacts of thermal insulation are also inves-tigated. Yearly fuel consumption and emissions of CO2 and SO2 arecalculated by using yearly heating load obtained by dynamic meth-ods. Fig. 13 shows the variations of the yearly fuel consumptionwith insulation thickness for all directions. Because the graph ofyearly fuel consumption the yearly heating transmission load fol-lows the similar trend of the yearly heating transmission load, asinsulation thickness increases, fuel consumption decrease. It isseen that the lowest fuel consumption is obtained for south wallwhich has lowest heating load, while the highest fuel consumptionis obtained for flat roof which has highest heating load. The otherhand, the east and west-facing walls provide equal fuel consump-tion because of equal heating loads. The variations of the yearlyfuel consumption and, CO2 and SO2 emissions in the south-facingwall is also shown for two different wall structures and two differ-ent insulation materials in Fig. 14a–c. The results show that thehighest value of fuel consumption and emissions are obtained inconcrete wall with EPS which has the lowest thermal resistance,whereas the lowest value of they is obtained in brick wall withXPS which has the highest thermal resistance.
Table 5 illustrates values of fuel consumption and emissions ob-tained at 9 cm insulation thickness and at the optimum insulationthickness for different orientations. At 9 cm and optimum insula-tion thicknesses, lowest fuel consumption and emissions are ob-tained by south-facing wall, whereas highest fuel consumptionand emissions are provided by north-facing wall. These resultsare influenced by yearly heating transmission load. As the insula-tion thickness increases, the yearly heating transmission load andconsequently, fuel consumption and emissions decrease. It is seenthat for 9 cm insulation thickness, this decrement in the heatingload, fuel consumption and emissions is% 85 for all oriented walls.It is seen that when optimum thicknesses of insulation materials isapplied, yearly heating load, fuel consumption and emissions forsouth, north, east and west-facing walls decrease 85.5%, 86.7%,86.3% and 86.3%, respectively, because of different optimum insu-lation thicknesses of wall orientations. The similar conclusionswere obtained to be 68–89.5% depending on insulation materialsby reference [27] using same dynamic method.
8. Conclusion
In this study, thermal, economic and environmental parametersfor insulated building walls of in a cold climate are numerically
investigated by using a computer program developed in Matlab.The results show that at brick wall without insulation, the lowestheating load is obtained as 644.40 (MJ/m2 year) for south-facingwall while the highest heating load is obtained as 766.12 (MJ/m2 -year) for north-facing wall. It is seen that the yearly heating loadsdecrease when the wall is insulated. This decrement in all wall ori-entations is 80.5% for 9 cm XPS insulation.
It is seen that at 9 cm insulation thickness, values of time lag forsouth, north, east and west oriented walls are obtained as 10.43,10.60, 11.92 and 9.13 h, respectively while decrement factor valuesare obtained as 0.0041, 0.0039, 0.0037 and 0.0038. The resultsshow that the longest time lag is obtained as 11.92 h for east-fac-ing wall while shortest time lag is obtained as 9.13 h for west-fac-ing wall. On the other hand, east and west walls give lowerdecrement factor compared to south and north oriented walls
It is seen that optimum insulation thicknesses for south, north,east and west orientations are obtained as 9.2, 10.2, 9.8, 9.8 cm,respectively. The results show that for heating season, the mosteconomical orientation is south-facing wall (brick wall with XPS)by an optimum insulation thickness of 9.2 cm.
Besides, as the insulation thickness increases, the yearly heatingtransmission load and consequently, fuel consumption and emis-sions decrease. It is seen that for 9 cm insulation thickness, thisdecrement in the heating load, fuel consumption and emissionsis% 85 for all oriented walls.
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