buildings with double brick wall onstructions: impact of thermal bridges on the energy demand

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The impact of thermal bridges on the energy demand of buildings with double

brick wall constructions

T.G. Theodosiou a,*, A.M. Papadopoulos b,1

a Department of Engineering and Management of Energy Resources, University of Western Macedonia, GR-50100 Kozani, Greeceb Laboratory of Heat Transfer and Environmental Engineering, Department of Mechanical Engineering, Aristotle University Thessaloniki, GR-54124 Thessaloniki, Greece

1. Introduction

The European Directive 2002/91/EC on the Energy Performance

of Buildings (EPBD) [1] is probably the most important single

action towards the improvement of energy efficiency in the

building sector throughout Europe since the 1970s when, in the

aftermath of the energy crisis, most national building regulations

introduced mandatory thermal insulation requirements. The

implementation of the Directive 2002/91/EC in the form of

national laws by each member state, gradually leads to the need

to adopt advanced standards, techniques and technologies while

designing and constructing new buildings, but also in applying

energy renovation measures in existing ones, in order to comply

with the updated energy efficiency requirements. The features of

the urban built environment in many European countries impose

limitations, or at least restrictions, on implementing other

advanced renovation measures like the use of passive or active

solar systems, passive cooling techniques, etc. This is mostly due to

factors like the overshadowing of buildings in winter, the

unfavourable orientation and the architectural typology of

buildings facades [2]. Still, even in cases where such measures

can be implemented, it is still rather impossible to achieve a

satisfactory degree of energy efficiency, as long as the buildings

present high thermal losses trough their external envelope. In that

sense, the less glamorous but still most effective measures, such as

the buildings envelope thermal insulation and the heating

systems upgrading remain prerequisites for a realistic approach

towards the improvement of the buildings energy efficiency.

Contemporary national regulations throughout the world

specify requirements for the insulation of the various buildings

elements, according to specific thermophysical properties and the

calculation procedures adopted, based on various standards,

varying from simple one-dimensional steady state considerations

to more sophisticated two-dimensional dynamic ones, which

inevitably lead to executing building simulation procedures. Still,

the problem of thermal bridges, appearing for example at the

junction between two separately insulated elements, or between a

vertical and a horizontal element, is not always dealt with

properly. This leads to underestimated thermal losses during the

design process, the insulation study or the various calculation

Energy and Buildings 40 (2008) 20832089

A R T I C L E I N F O

Article history:

Received 11 April 2007

Received in revised form 7 April 2008

Accepted 2 June 2008

Keywords:

Thermal bridges

Insulation

Double brick walls

Thermal facade

A B S T R A C T

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. However, even in cases

where impressive measures can be implemented in the densely built urban environment, the less

glamorous measure of buildings envelope thermal insulation remains a prerequisite towards the

improvement of the buildings energy efficiency. Despite the insulation requirements specified by

national regulations, thermal bridges in the buildings envelope remain a weak spot in the constructions.

Moreover, in many countries construction practices tend to implement only partially the insulation

measures foreseen by regulations. As a result, thermal losses are in practice greater than those predicted

during the design stage. This paper presents a study on representative wall thermal insulation

configurations used in Greek buildings, in order to investigate the impact of the thermal bridges on the

energy consumption. The double wall construction, used widely in Greece and not only there, is rather

susceptible to the occurrence of thermal bridges, in contrast to a typical thermal insulating facade, like

the one applied in Central Europe. The analysis of the thermal bridges impact will in that sense also

highlight the potential for energy renovation measures in older buildings.

2008 Elsevier B.V. All rights reserved.

* Corresponding author. Tel.: +30 2461 056695; fax: +30 2461 056601.

E-mail addresses: [email protected] (T.G. Theodosiou), [email protected]

(A.M. Papadopoulos).1 Tel.: +30 2310 996015; fax: +30 2310 996012.

Contents lists available at ScienceDirect

Energy and Buildings

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n b u i l d

0378-7788/$ see front matter 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2008.06.006
mailto:[email protected]:[email protected]://www.sciencedirect.com/science/journal/03787788http://dx.doi.org/10.1016/j.enbuild.2008.06.006http://dx.doi.org/10.1016/j.enbuild.2008.06.006http://www.sciencedirect.com/science/journal/03787788mailto:[email protected]:[email protected]


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methods in general, and, consequently, to higher (in comparison to

the estimates) energy requirements in practice. Moreover, in many

countries actual construction practices tend to only partially

implement the insulation foreseen by regulations, because of

construction difficulties, the conflicting stability issues of the

various building elements, the lack of properly trained/qualified

personnel and, finally, because of minimal or inefficient controls on

behalf of the authorities. The aforementioneddiscrepancy between

estimated and actual thermal losses appears despite the fact that

both analytical and simulative methods enable the designing

engineer to achieve a very good approximation of the thermal

losses [3,4].

Nowadays, more than ever in thepast,the need forconvergence

between the predicted and the actual buildings energy consump-

tion has proven to be an essential factor in the design and

construction processes. The energy performance certificate intro-

duced by theEPBD,which will be mandatory fornew constructions

and for existing ones in order to be sold or rented, is going to affect

the building sector in a variety of ways. The certification

introduced, be it asset or rating-based, raises, from the earliest

design stages already, the necessity for accurate prediction of

thermal losses through the buildings envelope, if the actual

consumption is expected to reasonably converge with thepredicted one. Unfortunately, many European countries still base

their thermal insulation requirements and legislations on simpli-

fied calculation methods that neglect or reduce the impact of

thermal bridges. This, in many cases, may lead to significant

deviation between predicted and actual thermal losses through the

buildings envelope, depending on the thermal insulation solution

opted for. Consequently, the design process is likely to provide an

underestimation of the actual energy demand compared to the

values to be later on identified and reported in an energy audit,

carried out in the frame of EPBD.

The study discussed in the present paper looks into the typical,

representative buildings thermal insulation configurations used in

wall structures in Greece. In particular, this study examines how

and to what extent the inclusion of the thermal bridges effects, as

they occur in vertical building elements, affects the calculations

during the design process and also the actual energy efficiency of a

building, as this can be measured during an energy audit. The main

reason for focusing on vertical building elements is that the double

wall construction, which is used in Greece but also in other

Mediterranean countries, is rather susceptible to allowing thermal

bridges, in contrast to a typical thermal insulating facade, like the

one applied in Central and Western Europe. At the same time, the

analysis of the thermal bridges impact aims to shed light on the

potential for energy renovation measures to be applied in older

buildings. Last but not least, the efficiency of each thermal

insulation configuration is examined with respect both to its

economic feasibility and to its environmental impact.

2. Methodology

In order to conduct this study, a typical three-storey apartment

building with an open ground-floor space (pilotis), normally used

as a parking lot, and a flat roof was chosen as a representative

urban residential building type. Each storey consists of two

identical apartments with a total area of 200 m2 (Fig. 1). All

apartments are equipped with autonomous heating and cooling

systems. The building is located in the city of Thessaloniki, in

northern Greece. The main climatic data for this area, which are

summarised in Table 1, are similar to those prevailing in Southern

France, Northern Italy and the Mediterranean coastal area of Spain.

During the heating period, each apartments indoor tempera-

ture is thermostatically kept to 21 8C, with a night set back

temperature of 19 8C (00:0008:00). During the cooling period

each apartments indoor temperature is thermostatically kept to

24 8C at day-time (08:0024:00), whilst natural ventilation is

opted for at night, or when the ambient temperature drops below

24 8C. The latter policy seems to be the most reasonable and

realistic one for the case of partially air-conditioned buildings [5].

All simulative calculations were carried out using the TRNSYS 16

simulation software, which has an established reliability for

calculating two-dimensional heat fluxes through building ele-

Fig. 1. Plan view of the building.

T.G. Theodosiou, A.M. Papadopoulos / Energy and Buildings 40 (2008) 208320892084


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ments and also of HVAC systems [6,7]. These calculations are in

accordance with the relevant standards concerning the thermal

bridge heat flows [810]. This approach can therefore highlight the

discrepancy between the typical analysis method and the 2Danalysis for thermal bridging. The complexity of various envelope

details further exacerbates the inaccuracy of using simple methods

and requires 3D analysis to truly account for all the heat flow paths

[11,12].

Four different scenarios are examined (Fig. 2). The first three

scenarios represent typical wall constructions in Greek buildings.

The forth scenario (D) represents, as far as the Greek context is

concerned, a novel approach, applied after 2004, which may well

constitute the main renovation strategy in order to apply

additional thermal insulation to existing buildings envelopes. In

detail, scenario A represents a large proportion of the Greek

building stock constructed during the 1980s, after the introduction

of the Thermal Insulation Regulation (TIR) in 1979. Although

thermal insulation of all external envelope elements is, accordingto TIR, mandatory, theapplicationof thermal insulation during this

period has proven to be problematic, mainly because of the lacking

construction experience and the absence of adequate and

appropriate insulation materials in the Greek market. The outlined

situation led to only a partial application of insulation, namely in

the cavity between the two brick walls, leaving, as a rule, the load-

bearing structure, consisting of armed concrete elements, unpro-

tected. Whilst the insulation materials dominating the market inthe 1980s were expanded polystyrene and, initially, glass wool, in

the mid-1990s, when armed concrete elements were insulated

more systematically, extruded polystyrene became very popular

and glass wool almost disappeared from the market, and was

substituted by expanded polystyrene. Since 2003, when the

production of stone wool began in Greece, this inorganic material

is increasingly becoming popular. The aforementioned develop-

ments are reflected in the following figures for the year 2006,

whereby extruded polystyrene accounted for 35%, expanded

polystyrene for 45% and stone wool for 15% of the market, with

the last one rising and largely replacing expanded polystyrene

mainly in the double brick masonry construction. The remaining

5% of themarket is covered by other materialsand insulating bricks

[13]. In addition to these elements, double-glazed windows andthermal insulation of the flat roof and pilotis have been found to be

applied in most cases during the construction process or after-

wards as a refurbishment action. Unfortunately, even nowadays,

buildings of similar, poor quality of thermal protection are still

Table 1

Climatic data for Thessaloniki

Month Mean daily ambient temperature (8C) Mean relative humidity (%) Total horizontal radiation (kWh/m2) Heating degree days (18 8C)

Minimum Mean Maximum

January 2 5 10 75 45 367

February 1 7 13 72 54 319

March 4 10 16 72 87 263

April 8 14 20 68 125 143May 14 20 25 64 159 35

June 20 24 28 57 172 0

July 22 27 30 53 175 0

August 22 26 30 55 159 0

September 17 22 26 62 120 0

October 9 16 22 69 78 76

November 4 11 17 77 48 208

December 1 7 14 77 37 330

Total 1259 1741

Fig. 2. Insulation configuration among the examined scenarios.

T.G. Theodosiou, A.M. Papadopoulos / Energy and Buildings 40 (2008) 20832089 2085


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constructed. In many cases, parts of the load-bearing structure are

still left un-insulated and so result in excessive thermal losses

during the winter [14]. As far as the applied thicknesses are

concerned, and despite the fact that in the coldest climatic zone of

Greece a minimum of 5 cm of insulation thickness is required

(scenario C), in practice thinner insulation layers (3 cm or thinner)

are used on concrete elements during the construction, mostly

because of stability reasons of masonry wall and in order to

simplify the construction demands. This practice is represented by

scenario B, whilst external envelope insulation, by means of the

thermal insulating facade is represented by scenario D. This

insulation approach has the advantageof significantlyreducing theeffect of thermal bridges andis applicable to both new andexisting

buildings when energy renovation works take place.

With the exception of scenario A, where thermal insulation is

obviously insufficient,simulation of the other cases was performed

twice, considering and not considering the effects of thermal

bridges. This was done, because the thermal insulation regulation,

still valid in Greece, does not address the thermal bridges effect.

Consequently, it is of interest to estimate the approximation error

resulting from this oversimplification, as well as the extent to

which the existing methodology leads to underestimating the

actual thermal losses through the buildings envelope. The mean U-

value for a 1-m-long wall construction in every scenario for both

methodologies examined is shown in Table 2. It is obvious that

ignoring the thermal bridges effect has a great impact on most ofthe examined wall constructions, with the exception of scenario D,

whereas in the latter case D, where the facade is not interrupted by

an overhang, the U-value is the same for both methodologies.

For all the examined scenarios double-glazed insulated

windows were assumed to be the case of all openings of the

buildings envelope. This assumption is in accordance with most

Greek buildings reality, since even older buildings have been

retrofitted with this type of windows. In addition, insulation of

both the flat roof and the pilotis is regarded as identical in every

scenario, according to the requirements of the prevailing regula-

tion [15].

3. Results

Theresults discussedfocus on both theheating andcooling load

requirements and on the corresponding power demand for each

storey of the building, as well as for the entire building.

3.1. Heating load

The specific heating load requirements for each examined

scenario are shown in Fig. 3. It becomes obvious that in every case

the intermediate floor apartments present the smaller heating

requirements. The first and the last floor of the building, whichhave more exposed surfaces to the ambience (floor of the first

storey to the pilotis and the last floor to the flat roof) suffer from

higher thermal losses and consequently feature a higher heating

consumption than the intermediate ones. Moreover, the first

storey is in a more disadvantageous position, since, on the one

hand, it does notreceive solar irradiation and, on theotherhand,its

thermal transmittance is higher than that of the last storey,

because of the more demanding U-value requirements for the flat

roof foreseen by the regulations. Due to the thermostatic control of

the apartments internal air temperature, there are no significant

vertical heat fluxes among them, despite the lack of horizontal

insulation in the intermediate floors.

The absence of thermal protection on the load-bearing

elements on scenario A, results in high heating requirements(153 W/m2 and 131 W/m2 for the cases of including or neglecting

thermal bridge calculations, respectively) especially in the lower

storey where the insulation is restricted to the masonry walls and

is obviously inadequate, even for the relatively mild Greek climate.

The more effective approach of the thermal protection of the entire

envelope (scenarioB) even when therequirements of thethermal

insulation regulations in terms of thickness are not fully adopted

is obviously an important step towards reducing heating energy

requirements. This is true even in the case where the thermal

bridge effect is included in the calculations. Still, this reduced/

restricted insulation (scenario B), which is the case for the

Table 2

Average U-value for a 1-m-long external wall construction for both the examined methodologies

Scenario Average U-value for a 1-m-long wall construction (W/m2 K)

Excluding thermal

bridge effect

Including thermal bridge effect

(in the place of overhangs)

Including thermal bridge effect

(without obstruction by overhangs)

A 0.64 3.64 3.91

B 0.56 3.56 3.83

C 0.49 3.49 3.77D 0.52 1.07 0.52

Fig. 3. Specific annual heating load requirements for each examined scenario.



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majority of the existing buildings, leads to an increase of actual

heating consumption by almost 15% compared to a full adoption of

the insulation requirements, as represented by scenario C

(109 kWh/m2 year instead of 92 kWh/m2 year when including

thermal bridge effects and 87 kWh/m2 year instead of 71 kWh/

m2 year when ignoring thermal bridge effects). The results of the

partially adopted thermal insulation case, combined with the fact

that thermal bridges are not included in the insulation calculation

procedure, clearly indicate that the actual thermal losses are 35%

higher more than the estimated ones, according to the existing

requirements (109 kWh/m2 year compared to 71 kWh/m2 year in

scenarios B and C, respectively). Considering the fact that, even

nowadays, this deviation applies to the majority of the newly

constructed buildings in Greece, it becomes obvious that currently

applied thermal insulation measures are rather inadequate and fail

to contribute, to the expected extent, to energy conservation in

buildings. When it comes to the reduction of thermal losses,

external insulation as represented by scenario D is approximately

identicalwith theone in the previouscase (scenarioC). Theslightly

higher heating requirements in scenario D are due to the higher

thermal transmittance of the masonry wall elements. According to

a more accurate calculation scheme, which includes the 2D

thermal bridge effect, this configuration proves to be the mostefficient one, as external insulation enables the reduction of

thermal bridges located at the junction between different

structural elements. Given that the shape of Greek buildings leads

to a large number of such junctions, due to the presence of

balconies and overhangs, this configuration can be efficiently

adopted in such constructionpractices. This last remarkshowsthat

the calculation methods currently used in Greece lead to

misleading results, since a highly effective insulation configura-

tion, as this of external insulation, is considered to be less efficient

than cavity insulation.

The deviation between the two calculation methods highly

depends on the buildings insulation efficiency, as it is shown in

Fig. 4. Thermallybetter protectedbuildings show a wider deviation

between the two approaches, since thermal bridges losses accountfor a larger proportion of the total conductive thermal losses. In

that sense, the existing calculation methodology becomes less

accurate,the betterinsulateda building is. In thecase of scenario C,

the underestimation of the heating requirements is significant,

reaching approximately 30%, whilst in the case of the poorly

insulated building of scenario A the error is not exceeding 16%

approximately.

It is worth mentioning that these types of calculation errors are

not limited to simple calculation methods but can also appear in

advanced calculation methods, like FEM or nodal based energy

simulations, when thermal bridge effects are not included in the

calculation model. In the process of an energy audit, this would

mean that more efficient buildings will prove to have bigger

deviation between estimated and actual heating consumption

values. Obviously, the current regulations and their effects greatly

contradict the target of designing and constructing more energy

efficient buildings, since the more efficient the building is, the

more misleading and erroneous the results become.

Amongst all the insulation configurations examined, the case of

external insulation (scenario D) results in the minimum deviation

(5.5%), dueto the limited length of thermal bridges. In this case, the

decision whether to include or not the thermal bridge losses in the

calculation method becomes less important. With the exception of

the external insulation configuration, whereby the majority of

thermal bridges are located in the pilotis ceiling, the calculation

error is more evident in the case of the intermediate storey, in

which thermal losses occur only through the external envelope.

Apparently, in the case of multi-storey buildings, or of buildings

with a high ratio of vertical to horizontal external surfaces in

general, the deviation shown in Fig. 4 is expected to be of greater

importance.

The maximum heating power the heating system has to provide

is another important factor affected by the insulation configuration.In partially insulated buildings, the need for maintaining the air

temperature at 21 8C, especiallyin the early morning orlate at night,

results in an increasedrating of the heating system, whencompared

toan adequately insulated building(this canbe seen in Fig.5).Inthe

casewhere thermal bridges are ignored, the requiredheatingpower

is similaramongall theadequatelyinsulatedbuilding scenarios. This

holdsnot true in the case of themoreaccurate approach,i.e. theone

including the calculation of thermal bridge effects, where external

insulation configuration leads to a decrease in required heating

power by up to 21% compared to the most common type of

insulation configuration presented by scenario B (26.5 kW in

scenario D compared to 33.4 kW in scenario B).

3.2. Cooling load

In the case of cooling load requirements differences among the

examined scenarios appear to be less significant (see Fig. 6). The

main reason being that during the cooling season heat flows,

caused by conduction through the building envelope, contribute to

a lesserextent to thebuildings energy balance andhave, therefore,

a smaller effect on the cooling load demands.

In almost every case it is the buildings last storey which

presents the higher energy demands, because the flat roof accepts

high values of solar irradiation during summer. Despite the small

differences, external insulation still provides an efficient solution

Fig. 4. Deviation of calculated heating load demand with and without the inclusion

of thermal bridge effects. Fig. 5. Maximum heating power requirement during the heating season.



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in terms of energy conservation, because of the decreased heat

flows through the opaque elements of the buildings envelope. Onthewhole, considering the seasonal cooling demand, it is of limited

importance whether to include or not the thermal bridge effect in

the calculation method.

In contrast to the case of the annual cooling demand, the

thermal insulation effect on the required cooling power of the

cooling system is more evident (Fig. 7). A comparison of scenarios

A and D indicates that the difference varies between 21% (15.5

19.6 kW) and 16% (15.218.2 kW), depending on whether the

thermal bridge effects are included or not.

4. Energy cost and carbon dioxide emissions

The primary energy consumption for each examined scenario

was calculated for the cases of two different heating systems, anoil-fired and a gas-fired boiler distributing the heat to hydronic

radiators. The former is the traditional heating system installed in

the majority of current building stock and the latter is a rather new

option introduced in the late 1990s in many Greek cities, with a

rapid retrofitting takingplace since 2003. Thenominal efficiency of

the boiler is 85% and 90% for each fuel type, respectively. When it

comes to cooling, an air to air heat pump, with an average seasonal

coefficient of performance (COP) equal to 2.7, is typical for Greek

climatic conditions. On the basis of these assumptions, the annual

consumption for each type of fuel is presented in Table 3. For the

calculation of the annual heating and cooling costs, data for the

year 2006 were considered with respect to fuel prices and the

national energy mixture as presented in Table 4 [16]. The results

are presented in Table 5. All values reflect energy consumption

resulting from thermal losses calculations including thermal

bridge effects, since this was proven to be a more accurateapproach.

The total annual carbon dioxide emissions for the apartments

heating and cooling are presented in Fig. 8. The most representa-

tive case among the current building stock-fired of scenario B is

compared to an oil-fired boiler, which is the typical heating

equipment over the last decades and is therefore considered to be

the reference case.

In the cases of a buildings construction or renovation, the

combination of external insulation and a state of the art gas-fired

boiler would result in an almost 50% annual running cost

reduction, compared to the most common combination of cavity

insulation with oil-fired boiler (22294508s, respectively). This is

mainly due to the heating consumption reduction, since the

cooling demands are not significantly affected by the thermalinsulation configuration. The environmental impact of this

optimum combination is also significant since an approximately

Fig. 6. Specific annual cooling load requirements for each examined scenario.

Fig. 7. Maximum cooling power demand during the cooling season for the entire

building and for each storey.

Table 3

Annual consumption for each type of fuel

Fuel type Annual consumption for each scenario

A B C D

Heating

Fuel oil (kg) 9130 6513 5514 4515

Natural gas (m3) 7432 5302 4489 3676

Cooling

Electricity (kWh) 7362 7307 7435 6684

Table 5

Total annual running costs for heating and cooling

Fuel type Annual running cost for each scenario (s/

year)

A B C D

Heating

Fuel oil 5478 3908 3309 2709

Natural gas 3398 2424 2052 1680

Cooling

Electricity 604 600 610 549

Total

Fuel-fired boiler and heat pump 6083 4508 3919 3258

Gas-fired boiler and heat pump 4003 3024 2663 2229

The scenarios presented here were calculated by taking into account the thermal

bridge effects.

Table 4

Fuel and electricity tariffs and emission factors

Energy source Tariffs Emission factor (kg/kWh)

Natural gas 0.0456s/kWh 0.181

Fuel oil 0.600s/lt 0.247

Electricity 0.08211s/kWh 0.368



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27% reduction in carbon dioxide emissions can be achieved on an

annual basis (3.124.29 t/year).

5. Conclusions

The study of representative wall insulation configurations inGreek buildings, applying both the currently valid calculation

methodology and the more accurate approach which takes the

thermal bridge effect into consideration, shows that the existing

legislative frame is inadequate, leading to a significant under-

estimation of actual energy consumption, especially in the case of

cavity insulation.

Considering the fact that the majority of the buildings

constructed in the last twenty years are partially insulated and

that thermal bridges are not considered by the calculation

procedure, actual thermal losses in the cases of such buildings

are by up to 35% higher than the initially estimated ones. The

double brick wall construction used widely in Greece is

particularly susceptible to allowing thermal bridges. Even when

the actual construction fully implements the insulation study,heating requirements are in reality by 30% higher than the ones

calculated by the current methodology which does not take

thermal bridge effects into account. Interestingly enough, the

underestimation of thermal losses is more misleading in the cases

of fully insulated buildings than in the cases of partially insulated

ones. It was also shown, that the current legislation disfavours the

more effective configuration of external insulation, when com-

pared to the cavity insulation, despite the fact that the former can

minimise thermal losses in thethermal bridges andis also themost

appealing solution when it comes to renovating existing buildings.

Thus, there is an obvious contradiction between the target of

designing more energy efficient buildings and the current

legislative framework, which needs to be addressed and redeve-

loped and which was still debated in April 2008.

Apart from the improved heating and cooling demands of

buildings, there are two further benefits to be considered, namely

the not negligible environmental impact and the reduction of the

buildings running costs. Such aspects should not be overlooked

when revising the existing building codes.

References

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[3] A.B. Larbi, Statistical modelling of heat transfer for thermal bridges of buildings,Energy and Buildings 37 (2005) 945951.

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[14] S. Chadiarakou, M. Santamouris, A. Papadopoulos, The importance of insulationon the buildings thermal losses, in: Proceedings of the CLIMAMED Congress,Lyon, November 2021, 2006, (2006), pp. 325332.

[15] A.M. Papadopoulos, T. Theodosiou, K. Karatzas, Feasibility of energy savingrenovation measures in urban buildings: the impact of energy prices andthe acceptable pay back time criterion, Energy and Buildings 34 (2002) 455466.

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buildings with double brick wall onstructions: impact of thermal bridges on the energy demand