Scientific Research and Essays Vol. 5(23), pp. 3646-3659, 4 December, 2010 [616841]

Scientific Research and Essays Vol. 5(23), pp. 3646-3659, 4 December, 2010
Available online at http://www.academicjournals.org/SRE
ISSN 1992-2248 ©2010 Academic Journals

Full Length Research Paper

The effects of insulation location and thermo-physical
properties of various external wall materials on
decrement factor and time lag

Türkan Goksal Ozbalta1* and Necdet Ozbalta2

1Department of Civil Engineering, Faculty of Engineering, Ege University, 35100 Bornova-
zmir, Turkey.
2Department of Mechanical Engineering, Faculty of Engineering, Ege University, 35100 Bornova-
zmir, Turkey.

Accepted 5 October, 2010

Technological improvements and population growth make energy saving more important especially for
developing countries. As known, a considerable amount of consumed energy is used for space heating
in buildings; therefore, using insulation for external wall has gained more importance. In this sense,
this study, which consists of two parts, examines the efficiency of insulation location and thermo-
physical properties of various external wall materials (brick, reinforced and lightweight concrete). In the
first part, the optimum insulation thickness of external walls for various wall materials and different fuel
types in cold region (Eski
ehir) has been investigated. The optimization is based on the P1-P2 method.
Besides, the effect of the thermal properties of different wall constructions and the location of
insulation on time lag and decrement factor are studied; and then, the daily thermal behaviours of
various wall constructions are simulated. In consequence of the study, time lags were determined
between 4.34 and 6.74 on the outer insulated walls and 3.64 and 5.86 on the inner insulated walls. The
decrement factor was computed between 0.008 – 0.023 and 0.019 – 0.029 respectively.

Key words: External wall, time lag, decrement factor, P1-P2 method, optimum insulation thickness.

INTRODUCTION

Energy consumption of buildings has a very large
proportion in total social energy consumption of Turkey,
approximately 37% (Anon, 2008). It is known that the rate
of energy consumption is rising rapidly due to population
growth, urbanization, consumer tastes, industrial activity,
transportation and etc. Population growth means
constructing more buildings, which gives rise to energy
expenditure. Annual growing ratio of population in Turkey
was 1.45% at the end of 2009 (TUIK, 2010). In addition,
due to the very limited indigenous energy resources,
Turkey has to import approximately 75% of the energy
requirement from other countries, and this makes energy
saving evident in the country (Anon, 2008; Erdal et al.,
2008). As known, building sector plays a significant role
in global energy consumption. It is generally admitted that

*Corresponding author. E-mail: [anonimizat]. Tel:
+90 232 388 6026/5185. Fax: +90 232 342 56 29. most of the energy loss in building elements arises due to
building envelope, which contains walls and roofs. The
external walls of a building are the interface between its
interior and the outdoor environment. Therefore, using
insulation is an option for minimizing the energy loss and
for protecting indoor comfort. Application of thermal
insulation material on external walls is one of the most
effective energy conservation measures in buildings.
Energy conservation reduces fuel consumption and its
environmental effects such as polluting products.
Increasing energy demand and environmental conscious-
ness all over the world entail using energy efficiently.
Therefore energy conservation is an important part of any
national energy strategy. On the other side, global
warming is setting in and is going to change the climate
(Sayigh, 1999). In this context, the implementation of the
European Directive on the Energy Performance of
Buildings (EPBD) is a milestone towards the
improvement of energy efficiency in the building sector
(Theodosiou and Papadopoulos, 2008). The regulations

of EPBD have been in force since 5th December, 2009 in
Turkey, and the obligation of Kyoto Protocol requires
the energy efficiency and reduction of emissions.
As a main part for energy loss, the thermal
performance of exterior wall has an important influence
on the energy-saving effects of buildings. For providing
indoor thermal comfort, the ratio of consumed energy
(heating and cooling) may vary in different climate zones.
Therefore, wall materials and thermal insulation systems
should be chosen according to the characteristics of
climate and energy consumption. Thus, by utilizing
adequate wall materials, it is possible to optimize the
performance of thermal insulation systems which have
positive effects on energy efficiency. There are many
studies about the estimation of optimum insulation
thickness for buildings because of the large potential for
energy savings.
Bolattürk investigated the determination of optimum
insulation thickness for building walls with respect to
various fuels and climate zones in Turkey and found out
that optimum insulation thicknesses vary between 0.02
and 0.017 m, and energy savings vary between 22 and
79% (Bolattürk, 2006). In another study, life-cycle cost
analysis is used to determine optimum insulation thick-
nesses for two types of insulation materials under the
climatic conditions of the Mediterranean region and found
savings up to 21 $/m2 of wall area (Hasan, 1999).
Çomaklı and Yüksel computed optimum insulation thick-
nesses between 0.085 and 0.107 m and energy saving
as 12.14 $/m2 of wall area over a 10 year lifetime for the
cities with cold climate (Çomaklı and Yüksel, 2003). In
the study, it is stated that the insulation in external walls
of buildings has been gaining much more interest in
recent years not only for the environmental effect of the
consumed energy but also for the high cost of the energy.
Generally in foregoing studies and literature, it is
emphasized that the optimum insulation thickness
depends on the cost of insulation material and cost of
energy, as well as cooling and heating loads, efficiency of
the heating system, lifetime of building, and current
inflation and discount rates.
External wall materials in terms of thermo-physical
properties have an effect on energy saving and control
the indoor climatic conditions which affect human health
and their efficiency. In this context, the effects of thermo-
physical properties of wall materials on time lag and
decrement factor are investigated by Vijayalaksmi et al.
(2006), Asan and Sancaktar (1998) and Yumruta et al.
(2007). Vijayalaksmi et al. studied the thermal behaviour
of building wall elements by using finite difference model,
and they compared the result with the experimental
findings (Vijayalaksmi et al., 2006). Asan and Sancaktar,
in their study, investigated the effects of thermo-physical
properties and thickness of a wall of a building on time
lag and decrement factor (Asan and Sancaktar, 1998).
They emphasized that thermo-physical properties have a
very profound effect and they computed this process for Ozbalta and Ozbalta 3647

different building materials. Yumruta et al. calculated
time lag and decrement factor using periodic solution of
one-dimensional transient heat transfer equation and
stated that the thermo-physical properties of a wall have
very important effects on decrement factor and time lag
(Yumruta et al., 2007).
Annual cooling and heating loads change according to
different climate zones but the thermo-physical properties
of wall construction ought to be taken into consideration
in terms of indoor thermal comfort and energy efficiency.
Energy conscious building design consists of controlling
the thermo-physical characteristics of the building enve-
lope such as thermal transmittance (U-value) (Aste et al.,
2009). It is stated that Aste et al. (2009) besides the U-
value, the envelope thermal inertia should also be
considered. It is also stated that Al-Homoud (2005) “the
thermal performance of building envelope is determined
by the thermal properties of the materials used in its
construction characterized by its capability to absorb or
emit solar energy in addition to the U-value of the con-
cerning component including insulation”. In the literature
a wide range of estimates existed regarding the energy
saving potential associated with the use of an adequate
inertia, ranging from a few percentages to more than 80%
(Aste et al., 2009).
Therefore, this study aims at investigating the role of
thermal inertia of external walls made of brick, lightweight
and reinforced concrete in addition to the effect of the
position of insulation which is placed in the inner and
outer surface of the external wall. For this purpose, six
different types of external wall constructions (Figure 1)
currently used are selected to determine the optimum
insulation thickness for various fuel types in Eskiehir,
where the ratio of energy consumption is high. Climatic
conditions are the major factors governing the heat load
requirements of the buildings. Turkish Standard (TS 825)
“Heat insulation rules in the buildings” was established
(1998) for calculating the heat load. According to TS 825,
four different degree-day (DD) regions have been defined
for Turkey (TS 825 Thermal Insulation in Buildings,1998).
Eskiehir (Altitude 800 m, Longitude 30°31' E, Latitude
39°46' N) is in the third zone with the value of 3649
heating DD (Table 1) (Buyukalaca et al., 2001). Heating
procedure is implemented between October-April periods
in this city. In general the fuel types used for heating are
mainly coal, natural gas, fuel oil and electricity. The
prices and lower heating values of the mentioned fuel
types and efficiency of heating systems are displayed in
Table 2 (Dosider, 2009; Çoban, 2006; Anon, 1997).
In this study, the optimum insulation thickness for the
chosen materials for building external wall is determined
by considering the heat conductivity and the cost of the
insulation material, average temperature in the region,
fuel price, and economical parameter using the P1-P2
method. On the other side, the effect of insulation
position of the wall on decrement factor and time lag are
investigated in view of energy saving and thermal comfort

3648 Sci. Res. Essays

Figure 1. Wall types, constructions and materials with various thermo-physical properties.

Table 1. The climatic data of Eskisehir.

Month 1 2 3 4 5 6 7 8 9 10 11 12 Annual
average
Mean daily temperature
(°C) -0.8 1.2 4.6 10.2 15.2 18.7 21.5 21.4 16.9 12.0 7.0 2.4 10.9

Monthly average daily
global radiation
(MJ m-2 day-1) 4.48
6.73
9.12
12.53
15.61
17.83
18.38
16.91
13.12
8.99
5.58
3.52
11.07

Maximum temperature
(°C) 3.8 5.8 10.7 171 22.0 25.8 28.9 29.2 25.1 20.1 13.1 6.4 17.3
Minimum temperature
(°C) -3.8 -3.4 -1.0 3.3 7.9 10.9 13.3 13.3 9.2 5.0 1.6 -1.3 4.6

Table 2. The parameters used in the calculations.

Parameter Value
Degree-days DD = 3649 °C days
Indoor temperature 20 °C

Fuel Coal Natural gas Fuel oil Electricity
Lower heating value (H) 29.307 MJ/kg 34.541 MJ/m3 40.612 M J/kg 3.600 MJ/kWh
Efficiency of the heating system () 0.60 0.93 0.80 0.99
Price 0.266 $/kg 0.445 $/m3 1.170 $/kg 0.163 $/kWh

Insulation material: Extruded polystyrene (XPS)
Conductivity k =0.028 W/mK
Density  = 32 kg/m3
Price 118.11 $/m3

Discount rate i 8.63%
Inflation rate g 5.30%
P1 8.036
Lifetime (N) 10 years

Ozbalta and Ozbalta 3649

Table 3. Wall structure and thermal characteristics of materials.

for inhabitants.

BUILDING MATERIALS AND EXTERNAL WALL
STRUCTURE

Brick and varieties of concrete (lightweight and
reinforced) are the common materials used for the con-
struction of external walls. But in some cases, depending
on the load-bearing characteristics of building and its
climate zone, materials and wall construction may vary.
External walls are generally constructed as single layered
and multilayered. Insulation installation of the walls
depends on the type of structure, the type of insulating
material used, and its location in the structure (Al-
Homoud, 2005). The insulation can be placed to the
inside, to the outside or in between (sandwich wall).
In this study, the selected wall constructions and the
characteristics of the wall materials (brick, lightweight and reinforced concrete) are demonstrated in Figure 1 and
Table 3 (Tsilingiris, 2004; Sambou et al., 2009; Vivancos
et al., 2009). The wall is multilayered and consists of
plaster on both sides. For calculations, the chosen
insulation material is extruded polystyrene (XPS).

HEATING LOAD CALCULATION FOR EXTERNAL
WALLS

Energy loss in buildings generally arises through external
walls, named building envelope, windows, floors and
ceilings, and air infiltration. In this study, as mentioned
before, energy loss due to building envelope is taken into
account, but not the loss due to infiltration. The annual
heat loss from walls in unit area is calculated by the
following equation (Hasan, 1999; Yu et al., 2009):

UDD qA × × =86400 [1] Wall types and
constructions Thickness
(m) Thermal conductivity
k (W/mK) Density
 (kg/m3) Specific heat
c (J/kg K) Thermal resistance
R (m2K/W)
Wall 1
External plaster 0.02 0.872 1442 837
Heavyweight concrete 0.20 2.000 2400 1060
Internal plaster 0.02 0.698 1442 837 0.3174

Wall 2
External plaster 0.02 0.872 1442 837
Heavyweight concrete 0.20 1.700 2300 920
Internal plaster 0.02 0.698 1442 837 0.3351

Wall 3
External plaster 0.02 0.872 1442 837
Heavyweight concrete 0.20 1.731 2143 840
Internal plaster 0.02 0.698 1442 837 0.3329

Wall 4
External plaster 0.02 0.872 1442 837
Horizontally hollow brick 0.20 0.341 768 781
Internal plaster 0.02 0.698 1442 837 0.8039

Wall 5
External plaster 0.02 0.872 1442 837
Lightweight concrete 0.20 0.381 609 840
Internal plaster 0.02 0.698 1442 837 0.7423

Wall 6
External plaster 0.02 0.872 1442 837
Lightweight concrete 0.20 0.571 609 840
Internal plaster 0.02 0.698 1442 837 0.5677

3650 Sci. Res. Essays

where DD is the degree days, U is the overall heat
transfer coefficient. The overall heat transfer coefficient is
determined by the following equations:

1) (-+ + + =o ins w i R R R R U [2]

where Ri and Ro are the inside and outside air film
resistances respectively, Rw is total thermal resistance of
the wall layers without insulation, Rins is the thermal
resistance of the insulation layer. The thermal resistance
of the insulation material is given below:

kx Rins /= [3]

where x and k are the thickness and thermal conductivity
of the insulation material, respectively. Therefore, U, the
overall heat transfer coefficient can be substituted with
the following equation:

1)/ (-+ = kx R Utw [4]

where Rtw is the total wall thermal resistance excluding
insulation layer resistance.
When the efficiency of heating system is , the annual
heating energy load is:

h×


+×=
kxRDDE
twA86400 [5]

The parameters used in the calculations are displayed in
Table 2.

OPTIMIZATION OF INSULATION THICKNESS AND
THE ENERGY SAVINGS

In the present study, the P1-P2 method was employed for
calculating the optimum insulation thickness (Yu et al.,
2009; Duffie and Beckman, 2006; Bacos and Tsagas,
2000). This is a practical, well-known method and can be
used for optimizing the thickness of insulation of external
walls. P1 is the ratio of the life cycle fuel cost savings to
the first-year fuel cost savings. The equation for P1 is
defined as

),,( ) 1(1 diN PWF iC P -= [6]

where i is inflation rate, d is the discount rate, C is a flag
indicating income producing or non-income producing (1
or 0, respectively). The installation is not income-
producing one, so C=0. N is the lifetime and assumed to
be 10 years. P2 is the ratio of the life cycle expenditures
incurred because of the additional capital investment to
be initial investment. The equation for P2 is defined as:

N V SdiCRdiN PWF iC MDP
)1() 1(),,( ) 1(2+– – += [7]

where MS is the ratio of first year miscellaneous costs
(insurance, maintenance) to the initial investment, D is
the ratio of down payment to initial investment, RV is the
ratio of resale value at end period of analysis to initial
investment. Maintenance, insurance, tax savings, resale
value are zero in this application. (D = 1, as investment
cost paid earlier) P2 can be taken as 1 in this application.
If an obligation recurs each year and inflates at a rate
of i per period, present worth factor (PWF) of the series of
N such payments can be found through the following
equation:







=+¹










++–=++=
=-
diifiNdiifdi
id
didiN PWFN
N
jjj
)1(111) (1
) 1()1(),,(
11
[8]

The building insulation cost is calculated by

xC Ci ins ×= , [9]

The annual heating cost per unit area may be determined
by the equation:

h××+× ×=
HkxRC DDC
twf
h
) (86400 [10]

where H is lower heating value of fuel.

The total heating cost of the insulated building is given by

xCP CP Ci h t 2 1+ = [11]

Substituting Ch from equation 10 into equation 11 gives
the following equation:

xCP
HkxRC DDP Ci
twf
t 2 1
) (86400+
××+× ×=
h [12]

The optimum insulation thickness is obtained by
minimizing the equation 12 by which total heating cost is
calculated. For this calculation, the derivation of Ct to x is
determined and equalized to zero. Thus, the optimum
insulation thickness (xopt) is obtained:

tw
if
opt RkCHPkDD CPx ×-




=2/1
21 86400
h [13]

The payback period of insulation cost, N can be
calculated through the following equations:

diif
diCDDid HxRkRPC
Nfw w i
¹






++


 – +-
=
11ln86400) ( ) (1ln2
2 h

[14]

diifCDDi xRkR HPCN
fw w i=+ +=86400)1() (2
2h
[15]

THE EFFECT OF THE INSULATION POSITION OF A
WALL ON DECREMENT FACTOR AND TIME LAG

External walls between interior and the outdoor
environment are under continuous changing climatic
conditions and can be attempted as thermal mass of
passive conditioning (heating/cooling) systems. They can
manage radiating stored energy to the internal room
related to indoor temperature. Energy saving is provided
with improved thermal performance through solar energy
gain and thermal mass characteristic of the walls. Heat
gain from opaque and transparent surfaces of buildings is
critically important to determine maximum heat gain and
time in external walls. Therefore to provide energy and
indoor climate conditions, insulating external walls is
inevitable. Moreover, the location and thermo-physical
properties of wall layers are important parameters in case
of thermal performance of buildings. In this context, time
lag and decrement factor are very important thermal
inertia parameters to evaluate and interpret the heat
storage capabilities of building envelopes. The deter-
mination of time lag and decrement factor is valuable
primarily in case where there are wide diurnal
temperature variations. Furthermore, their determination
promotes the design of energy efficient buildings for
reducing the heating energy demand. Time lag and
decrement factor depend on material properties, thick-
ness and their location in the wall construction (Asan,
2006; Kontoleon and Bikas, 2007; Kontoleon and
Eumorfopoulou, 2008; Asan, 1998). The decrement
factor is defined as the decreasing ratio of its temperature
amplitude during the transient process of a wave
penetrating through wall materials. The decrement factor
is defined as: Ozbalta and Ozbalta 3651

(min) (max)(min) (max)
wo wowi wi
T TT Tf–= [16]

where Twi(max), Twi(min), Two(max), Two(min) are maximum and
minimum temperatures on indoor and outdoor wall
surfaces, respectively. Time lag is defined as the time
required for a wave, with period P (24 h), propagate
through a wall from the outer surface to the inner surface.
The time lag is defined by the following equation:

(max) (max) Two Twi t t – =f [17]

where tTwi(max) and tTwo(max) represent the time in hours
when indoor and outdoor surface temperatures are at
their maximum levels respectively.
The location of insulation is determined by considering
maximum time lag and minimum decrement factor. For
this purpose, one dimensional transient heat conduction
equation is solved using an explicit finite-differences
procedure under convection boundary conditions. When
the model is established, it is assumed that there is one-
dimensional transient heat conduction in wall
construction, and governing equation may be written as
(Antonopoulos and Valsamakis, 1993; Antonopoulos and
Democritou 1993; Ozbalta and Ozbalta, 2010).

)/ (* )/(2 2xT tT ¶ ¶ =¶¶ a [18]

where T(x,t) is the temperature, t and x stand for the time
and space coordinates,  is the thermal diffusivity. The
calculation of the equivalent quantity for a layered wall is
given in Appendix (Tsilingiris, 2002).
When the absorption of the solar radiation is taken into
account from the energy balance, the heat-flux in the
outer surface(x = 0) of the wall is:

qout (t, 0) = g*I(t)+ hout *[Tout(t)-T(t,0)] [19]

where I(t) is the total solar radiation incident on the wall
surface, g is the absorption of the outer wall surface for
solar radiation, hout is heat transfer coefficient between
the outer surface of wall and outdoor, Tout(t) denotes
outdoor temperature, T(t,0) is the outer surface
temperature. The heat-flux in the inner surface of the wall
is;

qin = hin*[T(t,L)-Tin] [20]

where hin is the heat transfer coefficient between inner
space and inner surface of the wall, Tin denotes indoor
temperature, T(t,L) is the inner surface temperature of the
wall. As the initial condition, an arbitrary uniform tempe-
rature field is assumed. In this study, the daily thermal
behaviours of six basic masonry (brick, lightweight and
reinforced concrete) wall constructions are simulated.

3652 Sci. Res. Essays

Figure 2. Composite wall of M layers showing node arrangement.

The one-dimensional transient heat conduction equation
is solved by employing an explicit finite-differences
procedure taking into account the thermo-physical
characteristics of the layers. The composite wall of M
layers is separated into a number of nodes (Figure 2).
Using the energy balance method, the explicit finite-
difference equations are derived for the boundary node
on the outside surface, interface nodes between layers,
interior nodes inside the layers and the boundary node on
the outside surface (Al-Sanea, 2002; Ozel and Pıhtılı,
2007). The resulting finite-difference equations are given
as follows:

The boundary node (0) on the outside surface:

( ) [ ]Sp p pTBi Fo TFo Bi Fo T T1 1 11 1 1 01
0 2 2 1 21 + + + – =+
[21]

where xt Fo DD= /1 1a and 1 1 /kx h BioutD = and sol-air
temperature TS is defined as follows (Kuehn et al., 1998):

out g out S htI tTT /)( )(a+ = . [22]

Interface node (i) between layers (K) and (K+1):

Bx k x k BT Tx k Tx kTK Kp
ip
i Kp
i K p
i)] / ()/( [ )/ ( )/(1 1 1 1 1 D +D + – D + D=+ + + – +
[23]

where t x C x C BK K K K D D +D =+ + 2/) (1 1r r .

Interior node (j) inside the layer (M):

( ) ( )p
jp
j M Mp
jp
j T T Fo Fo T T1 1121+ -++ + – = [24]

where xt FoM M DD = / a .

The boundary node (n) on the inside surface: ( ) [ ]p
in N Np
n N N Np
np
n TBi Fo TFo Bi Fo T T 2 2 1 2111+ + + – =-+
[25]

where

xt FoN N DD = / a and N in N kxh Bi /D= . [26]

The set of the finite-differences equations is solved
iteratively by using the Gauss-Seidel iteration method
(Incropera and DeWitt, 1996; Ozısık, 1980). Taking the
distance between nodal points x = 0.01 m, the stability
criterion belonging to every layer, has been taken into
account in solutions. Hourly changing of temperature
distribution in the wall construction is obtained by the
explicit approach, and simultaneous solution of the finite-
differences equations is written for all nodal points. It is a
common practice in air conditioning calculation to use
standard values for the indoor and outdoor heat transfer
coefficient and for the solar radiation absorption
coefficient of the outer surface of the wall; in this study,
those values are determined to be 8.141 W/m2K, 23.26
W/m2K and 0.6 respectively in this study (Antonopoulos
and Valsamakis, 1993).

RESULTS

The energy loss gets decreased by increasing the
insulation thickness on building walls. In consequence of
applying insulation, heat load and fuel costs get
decreased.
However, increasing the insulation thickness causes
the insulation cost to increase. On the other hand, the
optimum insulation thickness is proportional with climatic
conditions, feature of insulation materials and economic
parameters (Çomakli and Yuksel, 2003; Soylemez and
Unsal, 1999). The total cost of the much thicker insulation
is assumed to increase again than the optimum one. The
variation of total cost, fuel and insulation costs in
accordance with the insulation thickness is displayed in
Figures 3a, b and c for reinforced concrete, brick,

Ozbalta and Ozbalta 3653

0.05 0.1 0.2 0.15 0.25 0.3 0.35

Figure 3a. The effect of insulation thickness on total cost – Wall I reinforced concrete.

Figure 3b. The effect of insulation thickness on total cost – Wall IV brick.

lightweight concrete walls, respectively and natural gas
which are widely used in Eskisehir. The optimum
insulation thicknesses of different wall types were
calculated by equation 13. The results for different fuel
types and for insulation material are shown in Table 4. It
was found out that the optimum insulation thicknesses for investigated wall materials vary between 0.082 – 0.157
m for reinforced concrete wall, 0.069 – 0.143 m for brick
wall and 0.070 – 0.150 m for lightweight concrete wall.
Since discount and inflation rates affect P1, the
optimum insulation thickness is affected by the
mentioned economical criteria. When thermal resistance Cost ($/m2) Cost ($/m2)

3654 Sci. Res. Essays

0.3 0.1 0.2

Figure 3c. The effect of insulation thickness on total cost – Wall VI lightweight concrete.

Table 4. The optimum insulation thickness, energy saving and payback period for different fuel and wall types.

 

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of wall construction in a determined degree-day gets
increased, the insulation requirement gets decreased
(Tables 3 – 4). The optimum insulation thickness
increases in the countries such as Turkey where fuel cost
is high. However, applying optimum insulation thickness
on external walls provides significant energy saving.
Annual saving per meter square of external wall area
was computed as the difference between the cost of
heating the insulated and uninsulated buildings. Energy
saving depends on fuel cost, climatic conditions and
thermal characteristics of external wall materials. The
effect of different energy types on energy savings is
presented in Figures 4a, b and c. Table 4 illustrates the
annual saving obtained by the application of the optimum
insulation thickness on external wall rather than unin-
sulated wall. The values vary between 11.695 – 43.005
$/m2 for reinforced concrete wall, 4.092 – 15.505 $/m2 for
brick wall, 4.543 – 22.972 $/m2 for lightweight concrete
wall when XPS is applied. On the other hand, it is
essential to mention here that energy saving is more important for the expensive fuels such as electricity and
fuel oil. The payback periods for different walls and fuel
types are also shown in Table 4. The values vary
between 0.464 – 0.896 years for reinforced concrete wall,
1.343 – 2.194 years for brick wall, 0.850 – 2.021 years for
lightweight concrete wall. With respect to payback period,
the lowest value is obtained from reinforced concrete
walls.
When the evaluation is done by taking the thermal
characteristic of wall materials into consideration, it is
seen that (Tables 3 and 5) time lag and decrement factor
change between 6.744 – 6.143 h and 0.0082 – 0.0107
respectively for the reinforced concrete walls (Wall 1 – 3)
whose heat storage capacity (1745.593 – 1285.671
kJ/m3K) is high and thermal diffusivity (0.597*10-7-
0.810*10-7 m2/s) is low. The values for time lag and
decrement factor of the brick wall (Wall 4) was found out
to be 5.743 h and 0.0176 respectively whose heat
storage capacity is 560.061 kJ/m3K and thermal diffusivity
is 1.783*10-7 m2/s. For the lightweight concrete walls Cost ($/m2)

Ozbalta and Ozbalta 3655

0.3 0.1 0.2

Figure 4a. For different fuel types, the variation of annual saving with regard to
insulation thickness – Wall I reinforced concrete.

0.35 0.05 0.1 0.15 0.2 0.25 0.3

Figure 4b. For different fuel types, the variation of annual saving with regard
to insulation thickness – Wall IV brick.

(Wall 5 – 6), time lag and decrement factor vary between
4.343 – 4.963 h and 0.0227 – 0.0204, respectively; heat
storage capacity (493.765 – 500.475 kJ/m3K) is low and
thermal diffusivity (2.065*10-7 – 2.006*10-7 m2/s) is high.
All values displayed above for time lag and decrement
factor belong to the insulated wall on which insulation is
placed in the outer surface of the walls. For the insulated
wall on which insulation is placed in the inner surface of
external wall, time lag and decrement factor vary between 5.244 – 5.856 h and 0.0194 – 0.0224 for
reinforced concrete walls (Wall 1 – 3), 5.000 h and 0.0224
for brick wall (Wall 4), 3.642 – 4.309 h and 0.0289 –
0.0224 for lightweight concrete walls (Wall 5 – 6),
respectively.
It seen that thermal mass has maximum efficiency
when insulation is placed in the outer surface of external
wall in heating season. Furthermore, from outside
climatic condition, isolated thermal mass is directly in Annual saving ($/m2)
Annual saving ($/m2)

3656 Sci. Res. Essays

Figure 4c. For different fuel types, the variation of annual saving with regard to insulation
thickness – Wall VI lightweight concrete.

contact with the indoor conditioned air, whereby it gained
higher inner surface temperature. Thus, it contributes
positive effect to the thermal comfort. Besides, outer
insulated external wall has better ability to reduce inner
surface temperature fluctuations due to thermal capacity
of wall materials.
When insulation is placed in the inner surface of
external wall, it is seen that thermal mass has less
effective utilization. Because thermal mass is isolated
from the indoor conditioned air and is exposed to the
outside climatic conditions as ambient temperature, wind
and humidity etc (Tavil, 2004).
In this study (Vijayalaksmi et al., 2006), it was found out
that decrement factor values are lower and time lag
values are longer for the walls with insulation on the
exterior side. If time lag is longer, the temperature
fluctuation on the inner surface is delayed in comparison
with the outer surface; and hence, heat can be
penetrating into the indoor space the desired time by
suitably selecting the wall material. The decrement factor
indicates the reduction in amplitude of the inner surface
temperature fluctuation. The lower decrement factor is
desirable, because the inner surface temperature can be
maintained fairly at the constant temperature irrespective
of fluctuating outer surface temperature.
Energy efficiency of external wall depends on not only
the position of insulation but also the thermal diffusivity
and heat capacity of the wall materials. As displayed in
Table 5, the increase in heat storage capacity affects the
time lag and decrement factor positive, which means
increasing time lag, decreasing decrement factor. Hence,
the ability of the material is to store more heat so as to delay the heat conduction. The higher thermal diffusivity
increases the heat conduction rate and, thus, reduces the
time lag and increases the decrement factor. The time lag
and decrement factor are affected by the thermo-physical
properties of wall material and their position. As a result,
to obtain energy efficient external walls, it is necessary to
combine different materials so as to get effective thermal
diffusivity and heat storage capacity as the best option.

CONCLUSIONS

In this study, the optimum insulation thickness, annual
energy saving and payback periods are investigated for
six different types of external walls, for XPS as insulation
material and four various fuel types for Eskisehir which is
one of the coldest cities in Turkey. The calculations are
carried out through the P1-P2 method over the 10-year
lifetime. In consequence of the study, insulation thick-
nesses were determined between 0.068 – 0.157 m with
the amount of 4.1 – 43.0 $/m2 energy saving and 0.46 –
2.20 years payback period depending on various fuel and
wall types. These results show that energy saving is
more significant when costly fuel is used. The most
suitable fuels for Eskisehir are determined as natural gas
and coal.
The position and thickness of each layer in a multi-
layered wall construction has significant influences on
time lag and decrement factor. The time lag and
decrement are very important thermal inertia parameters
to evaluate and interpret the heat storage capabilities of
building envelopes. The one-dimensional transient heat Annual saving ($/m2)

Ozbalta and Ozbalta 3657

Table 5. The effect of wall material properties on the decrement factor and time lag.

Equivalent thermal
conductivity Equivalent heat
storage capability Equivalent thermal
diffusivity Outer Insulation Inner Insulation
keq
(W/mK) keq
(W/mK) eq*107
(m2/s) Decrement
factor Time lag
(h) Decrement
factor Time lag
(h)
Wall 1 0.1042 1745.5925 0.5972 0.0082 6.7442 0.0194 5.8558
Wall 2 0.1041 1482.1922 0.7023 0.0095 6.3426 0.0206 5.6226
Wall 3 0.1041 1285.6705 0.8097 0.0107 6.1432 0.0224 5.2442
Wall 4 0.0998 560.0613 1.7827 0.0176 5.7426 0.0224 5.0000
Wall 5 0.1004 500.4751 2.0060 0.0204 4.9635 0.0224 4.3094
Wall 6 0.1020 493.7646 2.0654 0.0223 4.3426 0.0289 3.6416

conduction equation is solved by employing an explicit
finite-differences procedure by taking the thermophysical
characteristics of the layers into account. It was found out
that time lag vary between 4.34 – 6.74 on the outer
insulated walls and 3.64 – 5.86 on the inner insulated
walls. The least decrement factor was computed between
0.008 – 0.023 and 0.019 – 0.029, respectively. As a result,
for the effectiveness of the thermal mass, insulation
should be placed on the exterior of external walls. The
large heat storage capacity increases time lag and
decreases decrement factor. Higher thermal diffusivity
decreases time lag and increases decrement factor. The
result of this study would be useful for the design of
energy efficient buildings.

NOMENCLATURE

Bi, Biot number; C, flag indicating income producing or
non-income producing; Ci, insulation material cost $/m3;
Cf, fuel cost ($/kg, $/m3, $/kWh); Ch, annual heating cost
per unit area ($/m2); Cins, building insulation cost ($/m2);
Ct, total heating cost of insulated building ($/m2); D, down
payment fraction; d, discount rate; DD, degree-days (°C-
days); EA, annual heating energy (J/m2 year); f,
decrement factor (-); Fo, Fourier number; H, lower
heating value of fuel depending on the fuel type (J/kg,
J/m3, J/kWh); h, convection heat transfer coefficient
(W/m2 K); I, inflation rate; k, thermal conductivity (W/mK);
MF, fuel consumption; MS, ratio of first year miscellaneous
costs to the initial investment; N, lifetime (year); P1, ratio
of the life cycle fuel savings to first-year fuel energy cost;
P2, ratio of owning cost to initial cost; PWF, present
worth factor; R, thermal resistance (m2 K/W); Ri, inside
air-film thermal resistance (m2 K/W); Rins, insulation
thermal resistance (m2 K/W); Ro, outside air-film thermal
resistance (m2 K/W); Rw, total thermal resistance of the
wall layers without insulation (m2 K/W); Rtw, sum of Ri,
Rw, Ro (m2 K/W); RV, Ratio of resale value at end period
of analysis to initial investment; T, temperature (°C); t,
time (s); qA, heat loss (J/m2 year); q, heat flux (W/m2);
U, overall heat transfer coefficient (W/m2K); x, thickness
(m), rectangular coordinate (m); xopt, optimal insulation thickness (m).

Greek letter

= thermal diffusivity (m2/s), g= solar, absorbtivity (-),
f= time lag (h), h=efficiency of the heating system, r=
density (kg/m3), x=internodal distance (m), t=time
step (s).

Subscripts

A= annual, eq = equivalent, f= fuel, i= inside, Ins=
insulation, o=outside, opt= optimum, t= total, tw= total
wall excluding insulation material, w= wall material.

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APPENDIX

Heat capacity represents the wall heat storage capability,
is expressed as the mass times the specific heat capacity
of the wall. The equivalent heat capacity of a multi-layer
wall which is composed from parallel layers of thickness
is calculated by the expression (Tsilingiris, 2002):

( )
=
=







=n
ii pi i n
iieqp xc
xc
1
11) ( r r

The equivalent thermal conductivity of a multi-layer wall is
given by the expression:

Ozbalta and Ozbalta 3659


==





=
n
i iin
ii
eq
kxx
k
11

The equivalent thermal diffusivity is a very important
property of a multi-layer wall and determines how fast the
heat diffuses through the wall materials. The equivalent
thermal diffusivity is defined as:

()()eqpeq
eqck
ra =