Equivalent wall method for dynamic characterisation of thermal bridges

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 EQUIVALENT WALL METHOD FOR DYNAMIC CHARACTERIZATION OF THERMAL BRIDGES K. Martín1, C. Escudero2, A. Erkoreka1, I. Flores2, J.M. Sala1 1Department of Thermal Engineering – University of the Basque Country (UPV/EHU), Alameda Urquijo s/n. 48013 Bilbao, Spain 2Laboratory for the Quality Control in Buildings – Basque Government C/Agirrelanda n. 10, 01013 Vitoria-Gasteiz, Spain E-mail: [email protected] Tel.: + (34) 94 601 7378, Fax: + (34) 94 601 4283 ABSTRACT Although there are specific rules in the standard ISO 10211 for the characterization of thermal bridges, they are mainly focused on steady state calculations to obtain the linear thermal transmittance () or the temperature factor at the internal surface (fRsi). These parameters are respectively indicators of the additional heat flow and the risk of internal surface condensation of thermal bridges. However, in the calculations of building energy demand the dynamic thermal aspects of the envelope take a very important role. Moreover, a high percentage of the envelope is influenced by thermal bridges. Therefore it is necessary to take into account the implicit inertia of thermal bridges for accurate calculations. This paper presents a methodology based on thermoelectric analogy to calculate an equivalent wall of three homogeneous layers, which have the same dynamic thermal behaviour as the thermal bridge. Furthermore, each thermal bridge is associated with an influence area within the envelope, so that they can be easily implemented in building energy simulation programs where the heat flow is usually considered onedimensional. KEYWORDS: Thermal bridges, equivalent wall, thermoelectric analogy, unsteady state, inertia. This is the accepted manuscript of the article that appeared in final form in Energy and Buildings 55 : 704-714 (2012)), which has been published in final form at https:// doi.org/10.1016/j.enbuild.2012.08.024. © 2012 Elsevier under CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1. Introduction There are three main aspects that can be used for energy impact reduction: the control of emissions, use of renewable energy sources and increased energy efficiency. Energy conservation, defined as the strategy to adjust and optimize the energy use per person without affecting the socio-economic development, leads to a secure energy and desirable environmental goals. The greatest potential for energy conservation in buildings is based on the reduced use of heating and cooling systems, which in Spain is more than 47% of building energy consumption [1], being even higher in the European Union. There are three main characteristics which complicate the calculation of the energy demand: variables that change unsteadily, heat flow associated with non-linear temperature expressions and different heat transfer mechanisms which interact between them in complex ways [2]. To overcome these difficulties, building energy simulation (BES) programs have evolved, in part due to advances in computer technologies, adjusting the mathematical algorithms to achieve more accurate energy efficient design. It is necessary to conduct a comprehensive building analyse, because different aspects to consider are closely related, such as indoor air quality, noise or energy saving. However, today is the day that is not yet properly calculated the impact of thermal bridges (TBs) in buildings energy demand. As far as energy saving is concerned it can only be asserted that the proportion of TBs impact increases when the insulation level of the envelope grows [3]. On the other hand, the influence on the phenomena related to the internal surface condensation and mould growth must also be considered [4]. Implementing correctly TBs in buildings energy demand models means a major effort by the designer that often is not rewarded. The research community in BES is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 constantly working to reduce energy demand differences between simulated values using computer tools and the real ones based on the use of the dwelling. There have been several studies to verify that these predictive tools offer high quality results [5]. Mainly there are two ways for the correct implementation of TBs in BES. On the one hand there is the possibility of incorporating 2D or 3D heat conduction capabilities into the existing programme structure [6]; although further improvements in solution speed and ease of problem specification is required before it can be routinely applied. On the other hand a homogeneous multilayer equivalent wall can be calculated that behaves similarly to the TB constructive solution. This latter option is analysed in this paper. Thus one-dimensional heat flow can be calculated instead implementing more complex models. 2. Objectives The main goal is to introduce a methodology to implement TBs in the BES dynamic calculations taking into account the effects of thermal mass of each TB. Usually as a first approximation for the estimation of TBs, the value of linear thermal transmittance () is used, which computes the additional heat flow of a specific TB, Eq. (1). But  is a parameter calculated in steady state, so it does not consider the inertial aspects of TBs. Similarly it would be like trying to calculate the energy demand of a building considering only the thermal transmittance values (U) of the envelope elements. However, nowadays it is totally analysed and demonstrated the importance of thermal inertia in the calculation of energy demand [7],[8].    N jjjD lUL 1 2 (1) To include the effect of TBs taking into account not only the additional heat flow, but also their intrinsic inertia, a methodology to obtain a dynamic equivalent wall is defined, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 as well as its corresponding influence area (area of the envelope to which the thermal properties of the equivalent wall is assigned), which allows a simple implementation in BES software. Summarizing, the issues discussed are as follow: Analyse the variety of TBs in a real building placed in Vitoria-Gasteiz (Basque Country). Steady state thermal characterization of the TBs by calculating the linear thermal transmittance (). For each type of TB its influence area is defined. Definition of a methodology to achieve a dynamic equivalent wall for a TB. 3. Equivalent wall method Basically the concept of equivalent wall is based on defining a multilayer wall with the same steady and dynamic thermal behaviour as the original solution to be modelled. So the aim would be to calculate the equivalent thermal properties, such as conductivity (), density () and specific heat (cp) for the different homogeneous layers of the equivalent wall. These data could be entered in BES programs for a direct response factors or conduction transfer coefficients calculation. Once the equivalent wall is calculated, one-dimensional heat flow can be assumed for the TB. After getting the average value of parameters such as heat flow or surface temperatures in the influence area, a similar behaviour of the TB is achieved. The creator of the equivalent wall concept Kossecka defines it as follows: "The thermally equivalent wall is a simple structure that has the same dynamic behaviour of a complex structure and can be used as a substitute for it in building energy simulation design" [9]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Currently there are different methods for obtaining the characteristic parameters of the equivalent wall. Kossecka uses the definition of the structural factors to get response factors, and from them to calculate if necessary, the conduction transfer function coefficients [10]. In [3], Mao defines different types of TBs in the frequency domain. A method based on finite differences is used here to characterize TBs by amplitude and phase lag when it is excited by sinusoidal temperatures with different frequencies. Then an equivalent electrical circuit is defined through a frequency and lumped parameters transformation (-RC), from which the thermal properties can be obtained. 4. Preliminary considerations To characterize a TB by numerical calculation, taking into account not only the heat loss that would result in steady state but also the inertial effect, the cut-off planes of the constructive solution must be fixed for the geometry definition. The standard ISO 10211 [11] locates the cut-off planes at least to 1 m distance from the central element if there is no nearer symmetry plane. It will be shown that shorter distance of these cut-off planes to a certain limit does not decrease accuracy in the  value calculation, although it has influence on the dynamic response. If only  is used for characterizing the TB in BES programs there is no problem to identify the length which corresponds to the TB, but the error of a dynamic calculation using stationary parameters must be consider [12]. On the other hand, if the TB inertial properties are going to be implemented, the difficulty stays in the definition of its influence area. ISO 13786 [13] indicates that for the dynamic characterization of a TB cut-off planes should be placed according to the specifications of the ISO 10211. The problem is to define the area to be assigned in the BES software to implement the TB. For example to characterize a 0.3x0.3 m2 pillar TB, 2.3 m wide geometry is needed according to the standard. If a smaller surface is assigned in the BES software, such as the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 corresponding to the width of the pillar (0.3 multiplied by the pillar length), it would be an error of under estimating the real impact of the TB. This is because when considering large distance for the cut-off planes, the influence of the homogeneous part of the wall over the TB has much weight, so the average heat flow is lower than if closer cut-off planes are chosen. When the area of influence assigned in the BES program is different to that used for the dynamic characterization of the TB an error is made [12]. 5. Tools used in the study 5.1. Thermal bridge characterization in steady state To obtain the linear thermal transmittance () for each TB found around the building envelope, there are some possibilities: I. Use of TB catalogues or handbooks that collect many constructive solutions with the corresponding  values [14]. II. Use finite element, finite difference or finite volume programs where the calculation methodologies are more complex, but the achieved accuracy and flexibility are much higher. III. Use of specific programs for the calculation of TBs. The most common are THERM or KOBRA. The option of using catalogues with different construction details is initially the most attractive because of its simplicity. However, the variety of TBs in buildings is large, so taking  values from catalogues normally leads to deviations from the real ones. Summarizing, the main drawback is that catalogues do not offer the flexibility to fit  values to the real TBs details given in a building. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 The possibility of using numerical methods programs such as FLUENT, FEMLAB, HEAT3, VOLTRA... allows any type of TB characterization from the point of view of material properties, geometry and boundary conditions. This fact results in a wide range of possibilities for heat transfer analysis considering steady or unsteady states and obtaining highly accurate values. The problem is the time consuming task of learning and familiarizing with the program user environment. The last option is to employ specific software for the calculation and review of TBs. This combines the advantages of the above two alternatives, being more rigid than the numerical programs and not as simple as the use of a catalogue. In addition, some TB configurations that appear in buildings are not described neither in the catalogue or the KOBRA program itself, which limits the possibilities to choose a simpler tool. Since it is necessary to develop the equivalent wall transient methodology simulations, the Computational Fluid Dynamics FLUENT 6.2 program [15] is to be used. 5.2. System identification methods Thermoelectric analogy is used in the proposed methodology to obtain an equivalent RC circuit of the TB. From the analog electric circuit the thermal properties of the equivalent wall can be calculated. The resistances and capacities of the electric circuit are estimated by means of a system identification tool. Therefore, after the transient simulations are carried out by FLUENT, a system identification tool is used to estimate the parameters of the equivalent RC circuit. For the latter purpose there are several tools available. The most used identification software is the Matlab ”System identification toolbox”, although there are more specific tools applied to heat transfer models. This is the case of Continuous Time Stochastic Modelling (CTSM) and Logical R Determination (LORD) tools. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 In the case of CTSM, the system identification process is performed by searching the objective function that with the highest probability fits to the objective function dependent on the parameters to be identified. For this purpose the prediction error method is applied. LORD is based on a similar process, but in this case the search of dependent function parameters which minimize residuals respect to the objective function is made by applying the output error method. In both cases it is necessary to define the lower and upper limits of the identification parameters. Regarding to the searching of minimum residuals, LORD presents a methodology based on Nelder-Mead and Monte Carlo methods [16] which allow fixing broader initial ranges, resulting in more robustness for the system identification process. For this reason the chosen program for this study is LORD [17]. 6. Simulation characteristics Numerical calculations are performed through the finite volume software FLUENT 6.2, which solves the simplified equation of energy Eq. (2) for each time step and at each node defined by the mesh. The mesh is generated using GAMBIT 2.2. The simplicity of the geometries allows rectangular and structured 5 mm size elements achieving optimal mesh quality.     Th t    (2) where, is the density [kg/m3] h is the enthalpy [J/kgK] is the thermal conductivity [W/mK] T is the temperature [K] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6.1. Steady state The calculation consists of applying a temperature difference of 20K between inner and outer environments using as surface thermal resistances the ones specified in ISO 6946 [18]. The aim of simulations in steady state is double. Firstly is to calculate the value of  for the geometry under ISO 10211 standard (hereafter referred as standard) and then compare it with the value obtained in the geometry where the cut-off planes are redefined according to the proposed methodology (hereafter referred as proposed). The condition is that both solutions must have similar  value to consider that they have the same behaviour in steady state. Secondly the same simulation is used for the definition of the proposed cut-off planes. The evolution of the inner surface contour temperature is analysed in section 7. 6.2. Unsteady state A dynamic simulation is carried out in each TB analysing both the standard and proposed solutions. The simulation consists on exciting the outer surface according to the temperature of the Fig. 1 and keeping the indoor environment at the constant temperature of 293K. The outer temperature excitation, composed by a set of harmonic signals of different periods and amplitudes, is used to optimize the process of system identification method. This type of temperature is represented by a variety of excitations under which the building envelope may be affected and simplifies the data analysis to obtain the thermal properties of the equivalent wall due to its variability. Moreover, the sudden variations of the transient excitation signals makes that the parameter estimation results will be conservative compared to more conventional outer temperature excitations. This is, if the equivalent wall behaves like the TB under the excitement of Fig. 1, it will in general do it for any excitement, as will be demonstrated in section 9.1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 After verifying the similarity in steady state response, the dynamic simulation is carried out to supply data for the system identification program LORD. The software gives the values of resistances and capacities of the equivalent wall and then thermal properties of the layers can be calculated (Table 3). Results are checked by repeating the transient simulation for the equivalent wall and comparing with the proposed TB (Fig. 8). Surface temperatures and interior heat flow of the equivalent wall line up with those obtained from the TB constructive solution. The deviations in the results can be analysed more accurately with the residuals values of Fig. 8d. When the whole procedure is finished, all the information needed to implement the corresponding TB to a BES program is achieved. The area of influence to be implemented would be the corresponding to the product between the length along which the slab face TB is given and the height of the proposed geometry (0.655 m). The methodology has been developed for an atypical dynamic temperature excitation. A typical exterior temperature excitation used in building physics calculations is the solair temperature Error! Reference source not found.. It is therefore advisable to check that the equivalent wall works not only to the excitation of Fig. 1, but also does for other transient conditions. This verification is carried out with the weather data from Vitoria-Gasteiz for an average day of summer and winter (Fig. 9). After confirming that interior heat flow and surface temperatures fit to the real constructive solution for sol-air excitation (Fig. 10), the defined equivalent wall methodology for TBs is validated to evaluate their real impact in BES programs. 9.2. Other thermal bridges It has been demonstrated the validity of the methodology to characterize the equivalent wall for the slab face TB. The next step is to analyse the results for other types of TBs. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Below there are other 10 constructive solutions of TBs with the same basis wall of the slab face TB (Fig. 11). Firstly the steady state thermal performance is analysed and the  value is compared with that obtained according to standard ISO 10211 (Table 4). Secondly the residuals of the interior heat flow and surface temperatures are shown in Fig. 12 due to the dynamic response to the excitation of Fig. 1. In the residual results the same scale for axes have been used when possible for an easier analysis, but in the low inertia TBs heat flow and temperatures are higher, leading to greater values of residuals. To compare the different magnitudes of interior heat flow, Fig. 13 shows the response of all the evaluated TBs and also the response of the basis wall (homogeneous) as reference. Each TB has different characteristics, resulting in different responses to the same excitation (Fig. 13). When the impact of TBs are assessed in BES using the value of , two different constructive solutions with the same  involve the same thermal behaviour. However, it has been shown that the inertia of the TBs plays an important role in energy calculations, so it is necessary to include its effect. 10. Conclusions A methodology has been developed to calculate an equivalent wall with the same dynamic thermal behaviour of a TB. The calculated equivalent wall has the same average interior heat flow and surface temperatures of the analysed TB, but with onedimensional heat flow which allows implementing this solution in BES programs. Thus, not only the additional heat flow of the TB would be taken into account, but also its inertial effects. The methodology can be applied to any type of TB. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 One of the innovations of the proposed methodology is that for the dynamic characterization of a TB, cut-off planes must be relocated modifying ISO 10211 specification. By comparison of linear thermal transmittance () it is shown that the proposed geometry behaves similarly to the standard geometry at steady state. The highest deviation is given in the meeting between façade and the roof TB with a difference of =0.019 W/mK (3.5% error). Furthermore, relocating the cut-off planes the influence area of the TB is defined so that the simulated geometry corresponds to the area to be implemented in BES programs. On the other hand, despite the proposed and standard geometries have the same behaviour in steady state, it is shown that in dynamic regime it is different. In conclusion ISO 13786 approach for the dynamic characterization of the TBs under estimates their dynamic impact. Summarizing, if the cut-off planes are replaced according to the proposed method and thus the influence of the homogeneous part of the constructive solution is reduced, differences are noticed in the transient behaviour of the TB, but stationary properties are kept. The thermal properties of the equivalent wall are calculated using thermoelectric analogy and solving the state equations by system identification methods. For any TB a generic equivalent wall of three layers is assigned with five resistances and four capacities in each layer. Notice that for each TB a different electrical circuit can be designed, simpler or more complicated, but the aim is to make the method general. The residuals of interior heat flows and surface temperatures for different TBs are presented to a random outdoor temperature excitation. The worst result occurs in the blind box and lintel TB, which is a low inertia TB. In this case, the average residual for inner surface temperature, outer surface temperature and interior heat flow are 0.5 K, 1.4 K and 4.06 W/m2 respectively. In the rest of TBs the residuals are much lower, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 being respectively the inner surface temperature, outer surface temperature and interior heat flow residuals, 0.1 K, 0.6 K and to 0.45 W/m2. The next step would consist of implementing the equivalent wall thermal properties in BES programs to analyse the TB impact in a building. Results could be compared with other methodologies which use  as a parameter to evaluate TBs impact. References [1] IDEA, Practical energy guide: Efficient and responsible consumption, Institute for Energy Diversification and Saving, 3th edition, Graficas Monterreina, Madrid, 2011. [2] J.A. Clarke, Energy Simulation in Building Design, 2nd edition, ButterworthHeinemann, Oxford, 2001. [3] G. Mao, Thermal Bridges. Efficient Models for Energy Analysis in Buildings, Department of Building Sciences, Kunglika Tekniska Högskolan, Stockholm, 1997. [4] G.H. dos Santos, N. Mendes, P.C. Philippi, A building corner model for hygrothermal performance and mould growth risk analyses, International Journal of Heat and Mass Transfer, 52 (2009) 4862-4872. [5] D.B. Crawley, J. Hand, M. Kummert, B.T. Griffith, Contrasting the capabilities of building energy performance simulation programs Building and Environment 43 (2008) 661-673. [6] P. Strachan, A. Nakhi, C. Sanders, Thermal bridge assessments, Energy Systems Research Unit, University of Strathclyde, Glasgow, Scotland, 2009. [7] S.A. Al-Sanea, M.F. Zedan, S.N. 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Martin, A. Erkoreka, I. Flores, M. Odriozola, J.M. Sala, Problems in the calculation of thermal bridges in dynamic conditions, Energy and Buildings, 43 (2011) 529-535. [13] ISO 13786, Thermal Performance of Building Components. Dynamic Thermal Characteristics. Calculation Methods, 1999. [14] ISO 14683, Thermal Bridges in Building Construction. Linear Thermal Transmittance. Simplified Methods and Default Values, 1999. [15] FLUENT 6.2, User Manual. ANSYS Inc., 2005. [16] C. Borgelt, G.G. Rodriguez, W. Trutschnig, M.A. Kubiano, M.A. Gil, P. Grzegorzewski, O. Hryniewics, Combining soft computing and statistical methods in data analysis, 1st edition, Springer-Verlag, Berlin, Germany, 2010. [17] O. Gutschker, LORD 3.2. PASLINK European Economic Interest Grouping, Bruselas, Belgium, 2002. [18] ISO 6946, Building components and building elements. Thermal resistance and thermal transmittance. 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TABLES CAPTION Electrical circuit Heat Transfer Parameter Symbol Units Parameter Symbol Units Electrical current I A Heat flux Q W Potential difference V V Temperature difference T K Electrical resistance R  Thermal resistance Rt K/W Capacitance C F Thermal capacity C J/K Table 1 – Thermoelectric analogy Layer Material Thickness [m]  [W/mK]  [kg/m3] cp [J/kgK] 1 Perforated brick 0.115 0.667 1140 1000 2 Mortar 0.015 1.000 1700 1000 3 Polyurethane 0.040 0.028 30 800 4 Air cavity 0.020 0.118 1.23 1006 5 Ceramic block 0.045 0.445 1000 1000 6 Plaster 0.015 0.300 900 1000 7 Parquet 0.010 0.130 500 1600 8 Glass fiber 0.020 0.050 104 840 9 Mortar 0.050 1.000 1700 1000 10 Long hollow brick 0.310 1.128 1040 1000 Table 2 – Thermal characteristics of the slab face TB Layer Thickness [m]  [W/mK]  [kg/m3] cp [J/kgK] 1 0.083 0.650 1459.2 1000 2 0.083 0.158 1958.4 1000 3 0.083 0.067 0.5 1000 Table 3 – Thermal properties of the equivalent wall for the slab face TB Table(s) with Caption(s) TB 1 2 3 4 5 6 7 8 9 10 standard [W/mK] 1.30 0.15 0.08 0.64 0.53 0.07 -0.07 0.36 0.26 0.47 proposed [W/mK] 1.29 0.14 0.08 0.65 0.51 0.06 -0.08 0.36 0.26 0.47 ·103 [W/mK] 0.89 9.01 0.57 -4.05 18.8 12.6 9.98 1.42 1.37 -0.08 Table 4 –  comparison between the standard and proposed geometry FIGURES CAPTION Figure 1 – Thermal boundary conditions for dynamic calculations Figure 2 – Electric circuit model for three layers equivalent wall Figure 3 – Constructive solution of the slab face TB Figure 4 – Inner surface temperature distribution in the slab face TB Figure 5 – Slab face geometry for the proposed method Figure 6 – Interior heat flow comparison between the standard and proposed geometry Figure 7 – Isotherms in the slab face TB a) standard geometry b) proposed geometry Figure 8 – Comparison between the proposed slab face TB and its equivalent wall a) outer temperature b) inner temperature c) interior heat flow d) residuals Figure 9 – Winter and summer typical sol-air temperature in Vitoria-Gasteiz Figure 10 – Residual comparison between the slab face TB and its equivalent wall for a sol-air excitacion Figure 11 – Constructive solutions of the analyzed TBs Figure 12 – Residuals of the analysed TBs Figure 13 – Interior heat fluxes of the thermal bridges and the homogeneous wall List of Figure Captions An equivalent wall methodology for thermal bridges is developed. The influence area of the thermal bridges is redefined by the cut-off planes. The equivalent wall can easily be implemented in building energy simulations. Eleven types of thermal bridges have been evaluated for the methodology validation. *Highlights (for review)