Thermal transmittance of a composite lightweight wall panel with integrated load-bearing structure: Experimental versus numerical approach

Full text

Case Studies in Construction Materials 19 (2023) e02631
Available online 2 November 2023
2214-5095/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Case study
Thermal transmittance of a composite lightweight wall panel with
integrated load-bearing structure: Experimental versus
numerical approach
Mergim Gaˇ
si
*
, Bojan Milovanovi´
c, Domagoj Tkalˇ
ci´
c, Marija Jelˇ
ci´
c Rukavina
Department of Materials, Faculty of Civil Engineering, University of Zagreb, Croatia
ARTICLE INFO
Keywords:
Lightweight steel structures
Thermal transmittance
Experimental measurements
Numerical simulations
U-values
Heatow method
ABSTRACT
One of the most important parameters when it comes to heat losses in buildings is the thermal
transmittance or U-value. Therefore, great importance should be given to the determination of U-
values, especially for elements where there is a high thermal bridge effect, as is the case with
lightweight steel frame (LSF) structures. Since LSF structures are usually geometrically more
complex, especially when diagonal elements are present, the determination of the overall U-value
of these elements is usually done either on scale models in the laboratory or by numerical
methods. This paper compares different methods for determining the total U-value for four
different polyurethane foam-lled LFS walls and a reference wall made of EPS. Analytical (ISO
6946), experimental (Guarded Hot Box Method and HFM) and numerical 2D and 3D calculations
were used to determine the U-value. The aim of the comparison was to verify which methods can
be used for more complex geometries of LSF walls when there is a stronger inuence of point
thermal bridges due to the additional diagonal bracing. All methods showed similar U-values with
the highest absolute deviation of 17.18% between the HFM and the 3D numerical calculations.
The analytical method for inhomogeneous building elements given in ISO 6946 agrees well with
all methods with the maximum absolute deviation of 8.83% between the analytical and HFM
method. The work showed the importance of the placement of the HFM sensor for the determi-
nation of the surface heat ux, as incorrect placement of the sensor can result in inadequate U-
values that deviate up to 167% from the true value.
1. Introduction
Recently, the focus has largely been on sustainability, reducing CO
2
emissions, and improving energy efciency. Approximately
40% of the total energy consumption and 36% of CO2 emissions can be attributed to the building sector [1]. The European Union has a
large number of buildings that are over 50 years old, and unfortunately, many of these buildings are not energy efcient. [2]. To reduce
these statistics, the European Union has issued a directive stating that starting from 2019, all public buildings must meet near-zero
energy building (nZEB) standards, and from 2021 onwards, all new buildings must be constructed as nZEBs [3].
In order to align EU policies with the climate goals established by the Council and the European Parliament, the Fit for 55 package
was introduced [4]. This comprehensive plan includes various measures aimed at reducing CO2eq emissions from buildings by 2030
* Corresponding author.
E-mail address: mgasi@grad.hr (M. Gaˇ
si).
Contents lists available at ScienceDirect
Case Studies in Construction Materials
journal homepage: www.elsevier.com/locate/cscm
https://doi.org/10.1016/j.cscm.2023.e02631
Received 26 June 2023; Received in revised form 27 September 2023; Accepted 29 October 2023

Case Studies in Construction Materials 19 (2023) e02631
2
compared to 2005. The proposed actions involve improving energy performance of new and renovating existing buildings to enhance
their energy performance. These initiatives are in line with the European Commission’s long-term plan to create a low-carbon Europe
by 2050 [5,6].
The European Parliament has endorsed draft measures to accelerate the rate of building renovations and minimize energy con-
sumption and CO2eq emissions from buildings. These targets have been legally enshrined in the European Climate Law, making them
binding obligations under European legislation [7]. According to the approved measures, all new buildings will need to be
zero-emission buildings (ZEBs) by 2028. According to the approved measures, by 2028, all newly built buildings must be zero-emission
buildings (ZEBs). Additionally, new buildings owned or used by public authorities should meet this requirement by 2026 [8], sur-
passing the standards set by nZEBs.
In the construction industry, lightweight steel frame (LSF) structures have continued to gain momentum in recent years. The
advantages of LSF structures over traditional concrete and masonry structures include reduced weight, faster construction time, high
potential for recycling and reuse, and lower greenhouse gas emissions over the building lifetime [9–14].
One of the major drawbacks of LSF elements is the increased risk of thermal bridging due to the use of thermally conductive
materials such as steel [15–19]. For this reason, an emphasis should be placed on the analysis of thermal bridging and water vapor
diffusion. Due to the more pronounced effect of thermal bridges, LSF elements require more thermal insulation to achieve minimal
requirements set by the different standards in terms of U-values.
Another issue with LSF elements is quality control after the building is completed. Some quality control methods mostly used in
practice are infrared thermography (IRT) [20,21] and the heat ow meter method (HFM). These methods can be used to determine
surface temperatures and heat ows on site to verify the extent of thermal bridges and calculate the actual energy consumption.
One of the most important parameters in building energy consumption assessment is the thermal transmittance or U-value of each
building component. The main method for determining the U-value is described in the ISO 6946 standard [22]. This standard contains
methods for calculating the U-value of both homogeneous and inhomogeneous building elements, i.e., building elements with
embedded load-bearing structure such as LSF elements.
Other methods for determining U-values include experimental and numerical methods. Experimental methods such as the pro-
tected heater box method according to the ISO 8990 standard [23] can be used in the laboratory to determine the steady-state U-value
Fig. 1. Examined wall segments, (a) Hotbox sample, (b) EPS reference sample (RS-EPS), (c) With diagonal stiffeners, (d) Without diago-
nal stiffeners.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
3
of the entire building element [24], while other methods such as the heat ux meter (HFM) method [25] according to the ISO 9869–1
standard and the infrared thermography (IRT) method [26] according to the ISO 9869–2 standard can be used in the eld to verify the
performance of the installed building elements [20,27–30]. Numerical methods as dened in the ISO 10211 standard [31] can be two-
or three-dimensional, but require the use of specially designed thermal bridge numerical analysis software, such as AnTherm [32],
Flixo [33], CRORAL [34], Therm [35], or other numerical thermal analysis software that passes the ISO 10211 and ISO 10077–2
reference tests [31]. Numerical methods are among the most accurate methods for determining the thermal bridge effect [13,17,24,27,
28,36–39], but due to the sometimes complex geometries of structural elements, especially in the case of windows and LSF walls, and
the need for higher computational power, their application is not very common in practice.
Since the presence of steel columns in LSF elements causes a higher heat transfer rate and more profound structural thermal
bridges, it is a general rule that higher dimensional heat transfer calculations are required [19,40,41]. The objective of this work is to
compare different methods for calculating the total U-value of the element – experimental, numerical, and analytical methods – and to
see which of these methods can be used for calculating the U-value in the case of LSF elements.
Another objective of this work is to highlight the effect of the lightweight steel structure on the surface heat ux, especially for the
HFM method since the location where the heat ow meter sensor is placed has a great inuence on the measured U-value.
2. Wall samples description
Four different wall segments (Fig. 1a) and one EPS reference sample (Fig. 1b) were tested (Table 1). The wall samples consisted of a
steel structure lled with polyurethane foam and a double and triple cladding of re protection panels. An EPS reference sample with
known thermal conductivity was tested to validate the test results. Fig. 2.
The load- bearing structure of the tested wall segments consists of steel C-sections with and without diagonal stiffeners (Fig. 1c and
d). Two different wall thickness were examined because the examined samples were optimized for better sound insulation with
additional reboard panels on both sides of the sample. The thickness of the wall segments is 185 and 210 mm respectively, and the
thickness of the reference sample is 185 mm. The overall external dimensions of all samples were 1130 ×2000 mm (width ×height)
(Table 2).
3. Experimental setup
3.1. Hotbox method
All samples described in Section 2 were tested in the hotbox chamber according to the ISO 8990 standard. The setup consists of one
hot and one cold climatic chamber and a movable steel frame used for the installment of the test samples (Fig. 3a and b). A total of 18
thermocouples were attached to each sample to measure the surface temperature (9 on the cold side and 9 on the hot side) (Fig. 3c). Six
additional thermocouples were used to measure air temperature, three on each side of the chamber, and six thermocouples were used
to measure the surface temperature of the chamber screen parallel to the tested surfaces. All data acquisition was done with an
automated system centrally controlled by software.
The adiabatic boundary condition about the perimeter of the sample was approximated by EPS with the same thickness as the
samples and known thermal conductivity.
Thermocouples were placed on the surface of the tested samples near the steel studs to capture the effects of three-dimensional heat
ow, and further away from the steel studs where the heat ow can be assumed as one-dimensional.
After installing the sample and test equipment, the environment on both sides of the sample is heated/cooled to reach 20 ◦C on the
hot side and 0 ◦C on the cold side. The sample is held at these temperatures for 36 h. Air temperatures, surface temperatures, relative
humidity and air velocities were measured during the measurement period. The hot side of the chamber is heated with a heating coil
and fan that blows hot air over the tested surface. The cold side of the chamber is cooled with a split system air conditioners.
3.2. Heatow method
The heat ow method (HFM) is used for in-situ determination of U-value by simultaneous measurement of heat ow with a
owmeter and indoor and outdoor temperature with a pair of thermocouples (Fig. 4) according to the ISO 9869 standard. Generally,
the heat ux is averaged over a long-enough period of time to compensate for the daily variations in air temperature and heat ux over
the area under the examined surface. If the heat ux and temperatures are semi-stationary during the measurement, the measurement
Table 1
Sample name and description.
Sample name Sample description
W1-DS d =185 mm, with diagonal stiffeners and with two reboards on both sides.
W1 d =185 mm, without diagonal stiffeners and with two reboards on both sides.
W2-DS d =210 mm, with diagonal stiffeners and with three reboards on both sides.
W2 d =210 mm, without diagonal stiffeners and with three reboards on both sides.
RS-EPS d =185 mm, EPS with known thermal conductivity.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
4
time can be shortened, as is the case in this research. The equipment used in this work is the TRSYS01 heat ux measurement system
from Hukseux, whose specications (Table 3) meet all the requirements of the ISO 9869 standard.
The heat ow sensors were positioned on the surface of the warmer side of the samples, whereas the thermocouples measuring the
internal and external air temperature were placed on both sides of the samples (two on the warmer side and two on the colder side).
Fig. 5 shows the placement of the heat ow meter sensors for wall without diagonal stiffeners and the overlap with the load bearing
structure. The exact location of the heat ux sensors for each sample is shown in Fig. 6.
Measurement aimed to determine the maximum heat ux at the junction of 6 steel studs and the minimum heat ux at the point
where there are no studs but only a cross-section with polyurethane foam.
Heat ux and temperatures were measured over a 36-hour period, from which the average values of the heat ux and air tem-
peratures were calculated. The average method of the ISO 9869 standard was used for the analysis. According to the average method,
the U-value is calculated as follows:
Fig. 2. Cross-sections, (a) W1-DS and W1, (b) W2-DS and W2.
Table 2
Thermal characteristics and thickness of the used materials.
Material Thermal conductivity Thickness
[W/ (m K)] [mm]
Polyurethane foam 0.036 135
Fireboard 0.38 12.5
Steel 50.0 89
EPS 0.0326 ±0.0010 185
Fig. 3. Hotbox apparatus, (a) hot and cold chamber, (b) hotbox sample, (c) thermocouples position.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
5
U=
n
i=1
qi

n
i=1Ti
int −Ti
ext
(1)
In the equation (1), q
i
represents the heat ux density in W/m
2
, T
int
and T
ext
represent the internal and external air temperature in
◦C, respectively, and n indicates the total number of measurement points utilized to compute the average values.
4. Numerical simulations
4.1. Boundary conditions
Surface resistances were calculated according to ISO 8890 standard for each tested sample (Table 4). Different values of surface
resistances for each sample are the result of different air velocities on both sides of the samples.
Fig. 4. Heatow meter apparatus, (a) TRSYS01 system, (b) heat ux sensor.
Table 3
Heatow system specications.
Measurement range -2000 to +2000 W/m
2
Sensitivity 60.77/61.68
μ
V/(W/m
2
)
Sensor thermal resistance 71 ×10⁻⁴ K/(W/m
2
)
Sensor thickness 5.4 mm
Uncertainty of calibration ±3% (k =2)
Rated operating temperature range -30 to +70 ◦C
Acceptance interval temperature difference measurement ±0.1 ◦C
Fig. 5. Installation of the heatow meter apparatus, (a) hot side, (b) cold side.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
6
4.2. 3D numerical simulation
The three-dimensional thermal calculations were performed in AnTherm, a software specialized in the calculation of heat loss in
building physics. Geometric models consist of the steel structure lled with polyurethane foam and all one-dimensional layers
(reboard and polyurethane foam), as shown in Fig. 7. The geometric models did not take into account the spacer between the steel
structure and the reboard plate, or the holes in the steel structure that serve to homogenize the polyurethane foam across the sample
Fig. 6. Heat ux sensor location, (a) W1-DS, (b) W1, (c) W2-DS, (d) W2, (e) RS-EPS.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
7
volume.
AnTherm uses the control volume method (CVM) to calculate the unknown temperatures in the numerical grid. The temperatures
are calculated for the center of each nite volume. Two different grid sizes were used for the calculation, one for the Samples 1–4 and
one for submodels. Different grid sizes were used to show the accuracy of the numerical analysis for coarse and ne mesh. For Samples
1–4 the grid size was 25–50 mm with 25 mm step growth and for submodels the mesh size was 6–50 mm with 6 mm step growth.
Another reason for coarse mesh size for Samples 1–4 is due to the limitation of software of 300000 cells for system of equations. Since
the numerical calculations are done for a steady state heat transfer they can be done in matter of minutes on a personal computer that
meets software requirements. The bigger problem is the limitation of the software to 300000 cells which leads to limitations in the
mesh size.
To validate the results of the 3D calculation four different submodels were made for the samples with diagonal stiffeners (W1-DS
and W2-DS) to validate coarse mesh used for the whole 3D model (Fig. 8).
The most important parameter of the 3D numerical calculation is the thermal coupling coefcient L
3D
in W/K. In this case, L
3D
is
calculated as the total heat ux transferred through the cross-section dividing the two environments. If L
3D
is known, then the U-value
is calculated as:
U=L3D
A(2)
Where A is the area of the sample in m
2
.
4.3. 2D numerical simulation
Because of complexity of 3D calculations in term of geometry and tools needed for the numerical calculation [19,40], another
approach to calculating total heat ux without a 3D numerical calculation is to assume that total heat ux is the sum of 1D heat ux, 2D
heat ux (linear thermal bridges), and in general case, 3D heat ux (point thermal bridges):
Qtotal =Q1D+Q2D+Q3D(3)
Q1D=U1D•A
Table 4
Surface resistances.
Sample name Internal heat transfer coefcient R
si
External heat transfer coefcient R
se
(m
2
K)/W (m
2
K)/W
W1-DS 0.07 0.04
W1 0.05 0.06
W2-DS 0.11 0.05
W2 0.11 0.05
EPS reference sample 0.08 0.04
Boundary condition temperature used for the calculation were 20 ◦C on the hot side and 0 ◦C on the cold side.
Fig. 7. Geometrical models, (a) Steel structure, (b) With diagonal stiffeners, (c) without diagonal stiffeners.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
8
Q2D=
N
i=1
ψ
i•Li
Fig. 8. Submodels, (a) W1-DS (junction), (b) W1-DS (stiffener), (c) W2-DS (junction), (d) W2-DS (stiffener).
Fig. 9. Geometrical models for 2D numerical calculations, (a) W1-DS and W1 (TM1), (b) W1-DS and W1 (TM2), (c) W2-DS and W2 (TM1), (d) W2-
DS and W2 (TM2).
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
9
Q3D=
N
i=1
χ
i
Where U1D is the 1D thermal transmittance of the whole sample in W/(m
2
K), A is the surface area of the sample in m
2
,
ψ
is the linear
thermal transmittance in W/(m K), L is the thermal bridge length for which the
ψ
-value applies in m and
χ
is the point thermal
transmittance in W/K.
Numerical calculations for 2D heat transfer were performed using CRORAL software. This software uses the same method as
AnTherm to calculate the unknown temperatures (Control Volume Method).
ψ
-value is calculated as the difference between the 2D heat ux (or L
2D
) and 1D heat ux as follows:
ψ
=L2D−
M
j=1
Uj•Lj(4)
If the inuence of 3D thermal bridges is ignored in the calculation, then the U-value is calculated as:
Usample =
U1D•A+
N
i=1
ψ
i•Li
A(5)
The aim of this calculation is to test how ignoring the effect of point thermal bridges on the U-value compares to 3D numerical
calculations and experimental methods.
A two-dimensional calculation is performed for all thermal bridges that affect the U-value. All 2D thermal bridges for all 4 samples
can be reduced to 4 geometric models (Fig. 9 and Fig. 10), but since all 4 samples have different surface resistances, these results in 8
different numerical calculations.
ψ
-value is calculated using external dimensions by procedure given in ISO 10211.
5. U-value calculation using analytical approach
The method most commonly used in practice to calculate the design U-value of LSF walls is the method described in the ISO 6946
standard for structural members with non-uniform layers. This method is based on a simplied procedure for calculating the thermal
resistance of inhomogeneous building components. The method is applicable when the ratio between the upper and the lower limit of
thermal resistance is less than 3/2. The total thermal resistance of a wall component is calculated as:
Fig. 10. 2D thermal bridges schemes and lengths, (a) W1-DS and W2-DS, (b) W1 and W2.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
10
Rtot =Rtot,upper +Rtot,lower
2
Utot =1
Rtot
(6)
Where Rtot is the total thermal resistance in (m
2
K)/W, Rtot,upper and Rtot,lower are the upper and lower limits of the total thermal
resistance and Utot is the total U-value in W/(m
2
K).
5.1. Upper limit calculation
The upper limit is calculated by assuming the 1D heat ow through the surface of the component (Fig. 11):
1
Rtot,upper
=fa
Rtot,a
+fb
Rtot,b
+…+fo
Rtot,o
(7)
In the Eq. (7), Rtot,a, Rtot,b and Rtot,o represent the overall thermal resistances from one environment to another for each 1D segment,
while fa, fb and fo denote the respective fractional areas of each segment.
Upper U-value limit is calculated for W1-DS using Eq. 2 (Table 5) where L
i
are the dimensions shown in Fig. 12 for each part of the
cross section.
5.2. Lower limit calculation
The minimum threshold is computed by assuming that all layers within the component are uniform in temperature. However, when
accounting for individual non-uniform layers to establish the equivalent thermal resistance for each of them, the thermal resistance is
calculated as follows:
1
Rj
=fa
Rj,a
+fb
Rj,b
+…+fo
Rj,o
(8)
Where Rj is the equivalent thermal resistance of the inhomogeneous layer “j” and Rj,a, Rj,b and Rj,q are the thermal resistances of each
part of the inhomogeneous layer denoting to fractional surfaces fa to fo (Fig. 12).
When all the equivalent thermal resistances of the component are known the lower limit is calculated as:
Rtot,lower =Rsi +Ra+Rb+…+Ro+Rse (9)
Lower U-value limit is calculated for W1-DS using Eq. 2 (Table 6) where L
i
are the dimensions shown in Fig. 13 for each part of the
cross section. Surface resistances are taken from Table 4.
5.3. Total analytical U-value
By using the same procedure for the calculation of upper and lower U-value limit for all LSF samples, analytical U-values for all four
samples are calculated as the mean value between the upper and lower value (Table 7).
6. Results
6.1. Thermal transmittance (U-values)
6.1.1. Hotbox results
Results of the hotbox testing are measured heat uxes and interior and exterior temperatures as shown in Table 8.
Fig. 11. Example of dimensions and 1D U-values used for the calculation of the upper limit (W1-DS).
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
11
6.1.2. HFM results
Table 9 shows the results of the HFM measurements. These results show the minimum and maximum heat uxes and the average
values of internal and external air temperatures, from which the minimum, maximum and average U-values are calculated using the
average method as described in Section 3.2. Results of the measurement are shown in Fig. 13 together with the average U-values
calculated for two different location (HFM1 and HFM2).
6.1.3. 3D numerical calculation
3D numerical calculation results are shown in Table 10 and Table 11, while Table 12 shows the difference between the L
3D
thermal
conductivity coefcient calculated for a coarse and a ne mesh. The maximum difference of 2.10% shows that the coarse mesh size is a
good approximation for samples 1 and 3, which have diagonal stiffeners and are numerically more complex, i.e., a ne mesh would
Table 5
Upper U-value limit for analytical approach (W1-DS).
Cross section U R L f f/R
W/ (m
2
K) (m
2
K)/W mm – (m
2
K)/W
a 0.657 1.522 0.950 0.001 0.001
b 0.254 3.937 40.100 0.035 0.009
c 0.296 3.378 0.950 0.001 0.000
d 0.251 3.984 502.000 0.444 0.112
e 0.657 1.522 0.950 0.001 0.001
f 0.254 3.937 40.100 0.035 0.009
g 0.296 3.378 0.950 0.001 0.000
h 0.251 3.984 230.000 0.204 0.051
i 0.657 1.522 0.950 0.001 0.001
j 0.254 3.937 40.100 0.035 0.009
k 0.296 3.378 0.950 0.001 0.000
l 0.251 3.984 230.000 0.204 0.051
m 0.296 3.378 0.950 0.001 0.000
n 0.254 3.937 40.100 0.035 0.009
o 0.657 1.522 0.950 0.001 0.001
1/Rtot,upper =0.253 W/(m
2
K)
Fig. 12. Example of inhomogeneous layer dimensions and 1D U-values for the calculation of equivalent thermal resistance.
Table 6
Lower U-value limit for analytical approach (W1-DS).
Cross section L f R =d/λ f/R
mm – (m
2
K)/W (m
2
K)/W
a 0.950 0.001 0.002 0.472
b 40.100 0.035 2.419 0.015
c 0.950 0.001 1.864 0.000
d 502.000 0.444 2.472 0.180
e 0.950 0.001 0.002 0.472
f 40.100 0.035 2.419 0.015
g 0.950 0.001 1.864 0.000
h 230.000 0.204 2.472 0.082
i 0.950 0.001 0.002 0.472
j 40.100 0.035 2.419 0.015
k 0.950 0.001 1.864 0.000
l 230.000 0.204 2.472 0.082
m 0.950 0.001 1.864 0.000
n 40.100 0.035 2.419 0.015
o 0.950 0.001 0.002 0.472
1/Rtot,lower +Rsi +Rse=0.511 W/(m
2
K)
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
12
result in a large system of equations that cannot be solved by AnTherm’s solver.
For mesh sizes smaller than 5 mm, it becomes necessary to address the issue of point thermal bridges, a challenge encountered in
the computational process. It should be emphasized that when using such ne mesh sizes, AnTherm’s solver encounters difculties in
providing accurate results. Therefore, for the purpose of the numerical calculation in this research, these limitations have been taken
into account and a coarse mesh was chosen for all numerical models for Samples 1–4 and more ne mesh was chosen for submodel
numerical calculations.
The heat ux densities shown in Table 11 are calculated for the same location as the HFM method (Fig. 5), where q
1
corresponds to
HFM1 and q
2
to HFM2 when stationary boundary conditions are achieved. The overall distribution of heat ux densities on the inner
surfaces are shown in Fig. 14. A horizontal cross-section through the undisturbed section and the junction is shown in Fig. 15.
6.1.4. 2D numerical calculation
Results of the 2D numerical calculation are shown in Table 13 and Fig. 16. U-values are calculated by the procedure described in
Section 4.3.
6.1.5. Verication of heatbox and HFM measurement
As mentioned in Section 2, an EPS reference wall sample was tested to validate the hotbox and HFM results. The wall sample
consists of 185 mm thick EPS insulation with a known thermal conductivity of 0.0326 ±0.0010 W/(m K) and a U-value of 0.171
±0.005 W/(m
2
K) calculated according to EN ISO 6946 for vertical walls. The U-values calculated by the hotbox and HFM methods are
0.173 and 0.181, respectively, which is less than 5% difference. Since the deviation of the design U-value (0.171) is about 3.2%, it is
concluded that both the heatbox and HFM results outperform the reference measurement.
Fig. 13. HFM measurement results (red dashed line is the beginning of average method), (a) W1-DS, (b) W1, (c) W2-DS, (d) W2, (e) RS-EPS.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
13
6.1.6. Comparison of results and discussion
Fig. 17 through Fig. 20 show the comparison of results for all four different wall samples. Fig. 17 shows calculated U-values for all
calculation methods, while Fig. 18 shows the difference between the calculated U-values compared to all calculation methods,
respectively. Fig. 18 and Fig. 19 show the total and relative difference of the calculated heat ux densities.
Minimal and maximal differences between the calculated U-values are shown in Table 14. The maximum absolute difference for all
Fig. 13. (continued).
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
14
samples is 17.18% between the HFM and the 3D numerical calculation.
If hotbox and 3D numerical calculation results are compared, the maximum absolute difference is 13.82%. The maximum absolute
difference between the calculated U-values is 6.15% between the 2D and the 3D numerical calculation.
Fig. 20 shows the comparison of heat ux between HFM and 3D numerical calculations for two locations shown in Fig. 5:
dq1=q1,3D−q1,HFM
q1,HFM
(10)
dq2=q2,3D−q2,HFM
q2,HFM
The maximum difference between the heat ux at the location without steel studs (q
1HFM
) is 30.9%, while the difference between
the heat ux at the junction of steel studs (q
2HFM
) is 17.6%. If the HFM method is to be used to validate the design U-value of
lightweight steel frame walls, the location for placing the HFM sensor is critical, as the difference between the heat uxes q
1HFM
and
q
2HFM
ranges from 90% to 167%. If the device is installed in a location where there is a steel stud, the result may be misleading. The
measurement should only be performed if the stud placement scheme is known, and at least two heat ow meters should be used. One
over the location without steel studs and one over the location with the maximum heat ux. In this work, the location with maximum
heat ux is above the intersection of seven steel studs. The average of these two values is a good approximation of the nal U-value, as
shown in this research.
Fig. 21 shows the comparison of the analytically calculated U-value with the method described in the standard ISO 6946 (Section 5)
and all other methods used in this research. The analytical U-value agrees well with the values determined both experimentally and
numerically. The maximum absolute difference between the analytical U-value and all other methods is 8.83% for the HFM method.
Another aspect of this research was to show how numerical methods can be used to nd the best location for placing the HFM
Table 7
Total U-value for analytical approach.
U
tot,lower
U
tot,upper
U
tot
W/(m
2
K)
0.511 0.253 0.382
0.484 0.252 0.368
0.483 0.245 0.364
0.458 0.244 0.351
Table 8
Hotbox results.
Quantity Unit W1-DS W1 W2-DS W2 RS-EPS
q
HB
[W/m
2
] 7.810 7.660 7.180 7.660 3.430
T
int
[◦C] 20.260 20.32 20.210 20.210 20.00
T
ext
[◦C] 0.500 0.510 0.490 0.510 0.410
U-value [W/(m
2
K)] 0.395 0.387 0.364 0.364 0.173
Table 9
HFM results.
Quantity Unit W1-DS W1 W2-DS W2 RS-EPS
q
HFM1
[W/m
2
] 3.883 3.887 4.815 4.052 3.677
q
HFM2
[W/m
2
] 10.221 9.542 9.144 10.839 3.518
T
int
[◦C] 19.734 19.817 19.618 19.814 20.104
T
ext
[◦C] 0.298 0.290 0.310 0.304 0.236
U
min
[W/(m
2
K)] 0.200 0.199 0.249 0.208 0.185
U
max
[W/(m
2
K)] 0.526 0.489 0.474 0.556 0.177
U
avg
[W/(m
2
K)] 0.363 0.344 0.361 0.382 0.181
Table 10
Results of the 3D numerical calculation.
Quantity Unit W1-DS W1 W2-DS W2
L
3D
[W/K] 0.846830 0.768692 0.809656 0.737786
A [m
2
] 2.2600 2.2600 2.2600 2.2600
U-value [W/(m
2
K)] 0.375 0.340 0.358 0.326
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
15
Fig. 14. Calculated surface heat ux density, (a) W1-DS, (b) W1, (c) W2-DS, (d) W2.
Table 12
Submodel results of the 3D numerical calculation.
Quantity Unit Submodel 1 Submodel 2 Submodel 3 Submodel 4
L
3D,FM
[W/K] 0.281104 0.301362 0.273857 0.292941
L
3D,CM
[W/K] 0.275207 0.295757 0.268214 0.288084
ΔL
3D
[%] 2.10 1.86 2.10 1.66
Table 11
Heat ux densities results of the 3D numerical calculation.
Quantity Unit W1-DS W1 W2-DS W2
q
1
[W/m
2
] 5.230 4.970 4.880 4.930
q
2
[W/m
2
] 11.540 10.710 10.990 9.160
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
16
(caption on next page)
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
17
sensor. If one wants to accurately measure the U-value in situ then at least two heatowmeter sensors should be used. One sensor
should be placed at the location where the maximum heat ux is expected to occur. This location can be found either by examining the
schematics of the installed steel framing or, if schematics are not known, by using nondestructive techniques such as infrared
Fig. 15. Heat ux density proles, (a) W1-DS (junction), (b) W1-DS (undisturbed heat ux), (c) W1 (junction), (d) W1 (undisturbed heat ux), (e)
W2-DS (junction), (f) W2-DS (undisturbed heat ux), (g) W2 (junction), (h) W2 (undisturbed heat ux).
Table 13
Results of the 3D numerical calculation.
Quantity Unit W1-DS W1 W2-DS W2
Ψ
TM1
[W/(m K)] 0.020 0.020 0.019 0.019
L
TM1
[m] 6.260 6.260 6.260 6.260
Ψ
TM2
[W/(m K)] 0.025 0.025 0.025 0.025
L
TM2
[m] 7.660 4.260 7.660 4.260
U
1D
[W/(m
2
K)] 0.251 0.251 0.243 0.243
A [m
2
] 2.260 2.2600 2.260 2.260
U-value [W/(m
2
K)] 0.391 0.354 0.380 0.343
Fig. 16. Results of the 2D numerical calculation for W1-DS, (a) W1-DS (TM1), (b) W1-DS (TM2).
Fig. 17. Calculated U-values for all methods.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
18
thermography or rebar locators. The second sensor should be placed on the surface where the heat ow is considered to be one-
dimensional. A good approximation of the total U-value of the LSF wall is the average of the maximum and minimum U-values, as
shown in this research.
Fig. 18. U-value comparison for all methods, (a) W1-DS, (b) W1, (c) W2-DS, (d) W2.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
19
7. Conclusion
Four different lightweight steel frame walls were experimentally tested alongside a reference wall made of EPS. Numerical cal-
culations were conducted using AnTherm for 3D and CRORAL for 2D scenarios. The standard ISO 6946 was used for analytical
approximation of the U-value. The main conclusions and new ndings of this research are given below.
Objectives:
•The primary aim of this research was to compare U-values and surface heat uxes obtained through various methods, including
experimental, numerical, and analytical approaches.
•Secondary objective of this research was to, by comparing the results of the numerical and experimental results, give guidelines for
calculating the U-value in-situ using the HFM method.
Experimental method comparison:
Fig. 19. Calculated heat ux densities for all methods.
Table 14
Minimal and maximal differences between calculation methods.
Minimal difference [%] Methods Maximal difference [%] Methods
W1-DS 1.01 2D/HOTBOX -8.82 HOTBOX/HFM
W1 1.16 3D/HFM -13.82 HOTBOX/3D
W2-DS 0.82 HFM/HOTBOX -6.15 2D/3D
W2 4.71 HOTBOX/HFM -17.18 HFM/3D
Fig. 20. Heat ux comparison for all methods.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
20
•Both the hotbox and the HFM (Heat Flux Measurement) methods successfully passed a reference test, with a maximum U-value
difference of less than 5% between them.
3D vs. 2D numerical calculations:
•When comparing 3D and 2D numerical calculations for all four samples, the maximum absolute difference was found to be 6.15%.
Efciency of HFM method:
•The research demonstrated that the placement of HFM sensors for lightweight steel frame walls in-situ is crucial. The location
should align with the steel frame installation scheme, as the difference in heat uxes over the sample surface can be as high as
167%.
Placement of the HFM sensors:
•One of the main conclusions in this research is that if HFM is to be used for determining the U-value of the LSF walls in-situ the
following procedure should be used:
1. At least two HFM heatowmeter sensors should be used.
2. First sensor should be placed on the location on the surface where the maximum heat ow is expected. This location can be found
either by inspecting the schematics of the frame installation or by using the nondestructive technique such as infrared thermog-
raphy or rebar locators to nd the framework scheme.
3. Second sensor should be placed on the surface on the location where the heat ow is minimal, i.e. one-dimensional.
4. A good approximation of the Total U-value is the average of the maximal and minimal U-value calculated from heat ux densities 2
and 3 as shown in this research.
Analytical U-Values:
•Analytical U-values, as per ISO 6946, closely matched the values obtained experimentally and numerically, with a maximum
difference of 8.83%.
•The analytical approach described in ISO 6946 can be considered a reliable reference point for designing U-values for polyurethane
lightweight steel frame elements. This applies not only to simpler congurations but also to elements with more complex structural
geometry, such as steel frames with diagonal stiffeners.
Declaration of Competing Interest
I acknowledge that the research conducted for this manuscript was partially funded by the EU project KK.01.1.1.07.0060, titled
"Composite lightweight panel with integrated load-bearing structure (KLIK-PANEL)." This project provided nancial support for the
research activities, including data collection, analysis, and interpretation.
Data availability
Data will be made available on request.
Acknowledgements
This research was funded by the European Union through the European Regional Development Fund’s Competitiveness and
Cohesion Operational Program, grant number KK.01.1.1.07.0060, project “Composite lightweight panel with integrated load-bearing
structure (KLIK-PANEL)”.
Fig. 21. Comparison of analytical U-value with experimental and numerical results.
M. Gaˇ
si et al.

Case Studies in Construction Materials 19 (2023) e02631
21
References
[1] European Commission, In focus: Energy efciency in buildings, n.d. 〈https://commission.europa.eu/news/focus-energy-efciency-buildings-2020–02-17_en〉
(accessed on 23 June 2023).
[2] L.C. a M. Economidou a, V. Todeschi a b, P. Bertoldi a, D. D’Agostino a, P. Zangheri a, Review of 50 years of EU energy efciency policies for buildings, 2020.
https://doi.org/https://doi.org/10.1016/j.enbuild.2020.110322.
[3] European Commission, Energy performance of buildings directive, 2023. 〈https://energy.ec.europa.eu/topics/energy-efciency/energy-efcient-buildings/
energy-performance-buildings-directive_en〉(accessed on 23 June 2023).
[4] European Parliament, BRIEFING Towards climate neutrality: Fit for 55 package, 2021.
[5] EU Monitor, The European Green Deal, 2019. 〈https://www.eumonitor.eu/9353000/1/j9vvik7m1c3gyxp/vl4cnhyp1ort〉(accessed on 23 June 2023).
[6] EU Monitor, Annex to the communication from the commission to the european parliament, the european council, the council, the european economic and
social committee and the committee of the regions The European Green Deal, 2019. 〈https://www.eumonitor.eu/9353000/1/j9vvik7m1c3gyxp/vl4d8dfd2dye〉
(accessed on 23 June 2023).
[7] European Commission, European Climate Law, Off. J. Eur. Union. 2021, 2021: 17. 〈https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:
32021R1119〉.
[8] P.A. Fokaides, A. Kylili, I. Kyriakides, Boundary conditions accuracy effect on the numerical simulations of the thermal performance of building elements,
Energies 11 (2018), https://doi.org/10.3390/en11061520.
[9] N. Soares, P. Santos, H. Gerv´
asio, J.J. Costa, L. Sim˜
oes, Energy e f ciency and thermal performance of lightweight steel-framed ( LSF) construction: A review,
78, 2017: 194–209. https://doi.org/10.1016/j.rser.2017.04.066.
[10] D. Perera, I.R. Upasiri, K. Poologanathan, P. Gatheeshgar, P. Sherlock, T. Hewavitharana, T. Suntharalingam, Energy performance of re rated LSF walls under
UK climate conditions, J. Build. Eng. 44 (2021), 103293, https://doi.org/10.1016/j.jobe.2021.103293.
[11] M.J. Rukavina, D. Skeji´
c, A. Kralj, T. ˇ
Sˇ
capec, B. Milovanovi´
c, Development of lightweight steel framed construction systems for nearly-zero energy buildings,
Buildings 12 (2022), https://doi.org/10.3390/buildings12070929.
[12] B. Milovanovi´
c, M. Bagari´
c, M. Gaˇ
si, N. Vezili´
c Strmo, Case study in modular lightweight steel frame construction: thermal bridges and energy performance
assessment, Appl. Sci. 12 (2022), https://doi.org/10.3390/app122010551.
[13] I.A. Atsonios, I.D. Mandilaras, D.A. Kontogeorgos, M.A. Founti, Two new methods for the in-situ measurement of the overall thermal transmittance of cold frame
lightweight steel-framed walls, Energy Build. 170 (2018) 183–194, https://doi.org/10.1016/j.enbuild.2018.03.069.
[14] L. Kempton, G. Kokogiannakis, A. Green, P. Cooper, Evaluation of thermal bridging mitigation techniques and impact of calculation methods for lightweight
steel frame external wall systems, J. Build. Eng. 43 (2021), 102893, https://doi.org/10.1016/j.jobe.2021.102893.
[15] P. Santos, P. Lopes, D. Abrantes, Thermal performance of lightweight steel framed facade walls using thermal break strips and ETICS: a parametric study,
Energies 16 (2023), https://doi.org/10.3390/en16041699.
[16] P. Santos, D. Abrantes, P. Lopes, Experimental and numerical performance evaluation of bio-based and recycled thermal break strips in LSF partition walls,
Buildings 12 (2022), https://doi.org/10.3390/buildings12081237.
[17] L. Moga, I. Petran, P. Santos, Thermo-energy performance of lightweight steel framed constructions: a case study, Buildings 1 (2022), https://doi.org/10.3390/
buildings12030321.
[18] P. Santos, The importance of stud anges size and shape on the thermal performance of lightweight steel framed walls, Sustainability 13 (2021) 1–22, https://
doi.org/10.3390/su13073970.
[19] P. Santos, G. Lemes, D. Mateus, External Facade LSF Walls: A Parametric Study, Energies (2019) 1–20, https://doi.org/10.3390/en12142671.
[20] M. Gaˇ
si, B. Milovanovi´
c, S. Gumbarevi´
c, Comparison of infrared thermography and heat ux method for dynamic thermal transmittance determination,
Buildings 9 (2019) 132, https://doi.org/10.3390/buildings9050132.
[21] A. François, L. Ibos, V. Feuillet, J. Meulemans, In situ measurement method for the quantication of the thermal transmittance of a non-homogeneous wall or a
thermal bridge using an inverse technique and active infrared thermography, Energy Build. 233 (2021), https://doi.org/10.1016/j.enbuild.2020.110633.
[22] EN ISO 6946, Building components and building elements — Thermal resistance and thermal transmittance — Calculation methods, 2017.
[23] The International Organization for Standardization, ISO 8990:1994 Thermal insulation — Determination of steady-state thermal transmission properties —
Calibrated and guarded hot box, 1994.
[24] P. Santos, G. Lemes, D. Mateus, Analytical methods to estimate the thermal transmittance of LSF walls: Calculation procedures review and accuracy comparison,
Energies 13 (2020), https://doi.org/10.3390/en13040840.
[25] International Organization for Standardization, ISO 9869–1:2014 - Thermal insulation – Building elements – In-situ measurement of thermal resistance and
thermal transmittance – Part 1: Heat ow meter method, 2014: 36. 〈https://www.iso.org/standard/59697.html〉(accessed June 3, 2019).
[26] The International Organization for Standardization, ISO 9869–2:2018 Thermal insulation — Building elements — In-situ measurement of thermal resistance and
thermal transmittance — Part 2: Infrared method for frame structure dwelling, 2018.
[27] P. Santos, D. Mateus, D. Ferrandez, A. Verdu, Numerical simulation and experimental validation of thermal break strips’ improvement in facade LSF walls,
Energies 15 (2022), https://doi.org/10.3390/en15218169.
[28] P. Santos, M. Gonçalves, C. Martins, N. Soares, J.J. Costa, Thermal transmittance of lightweight steel framed walls: Experimental versus numerical and
analytical approaches, J. Build. Eng. 25 (2019), 100776, https://doi.org/10.1016/j.jobe.2019.100776.
[29] S. Gumbarevi´
c, B. Milovanovi´
c, M. Gaˇ
si, M. Bagari´
c, Application of multilayer perceptron method on heat ow meter results for reducing the measurement time
†, Eng. Proc. 2 (2020) 1–6, https://doi.org/10.3390/ecsa-7-08272.
[30] S. Gumbarevi´
c, B. Milovanovi´
c, B. Dalbelo Baˇ
si´
c, M. Gaˇ
si, Combining Deep Learning and the Heat Flux Method for In-Situ Thermal-Transmittance Measurement
Improvement, Energies 15 (2022), https://doi.org/10.3390/en15145029.
[31] The International Organization for Standardization, ISO 10211:2017 Thermal bridges in building construction — Heat ows and surface temperatures —
Detailed calculations, 2017.
[32] Kornicki, An.Therm (Thermal Heat Bridges), 2023. 〈http://www.antherm.at/〉(accessed on 23 June 2023).
[33] Infomind GmbH, The thermal bridge analysis and reporting application, 2023. 〈https://www.ixo.com/〉(accessed on 23 June 2023).
[34] M. Gaˇ
si, CRORAL-Computer Program for Thermal Bridge Analysis and Vapour Analysis, 2023. https://www.croral.org/ (accessed on 23 June 2023).
[35] Windows and Daylighting, THERM, 2023. 〈https://windows.lbl.gov/〉(accessed on 23 June 2023).
[36] M. Pomada, J. Adamus, A. Boruszewski, Numerical and experimental analysis of heat ow at window-to-wall interface, Energies 15 (2022), https://doi.org/
10.3390/en15103837.
[37] M. Rahiminejad, D. Khovalyg, Numerical and experimental study of the dynamic thermal resistance of ventilated air-spaces behind passive and active façades,
Build. Environ. 225 (2022), 109616, https://doi.org/10.1016/j.buildenv.2022.109616.
[38] R. Hart, Numerical and experimental validation for the thermal transmittance of windows with cellular shades, Energy Build. 166 (2018) 358–371, https://doi.
org/10.1016/j.enbuild.2018.02.017.
[39] U. Berardi, T. Kisilewicz, S. Kim, A. Lechowska, J. Paulos, J. Schnotale, Experimental and numerical investigation of the thermal transmittance of PVC window
frames with silica aerogel, J. Build. Eng. 32 (2020), 101665, https://doi.org/10.1016/j.jobe.2020.101665.
[40] E. Roque, P. Santos, The effectiveness of thermal insulation in lightweight steel-framedwalls with respect to its position, Buildings 7 (2017), https://doi.org/
10.3390/buildings7010013.
[41] P. Santos, D. Abrantes, P. Lopes, D. Mateus, Experimental and numerical performance evaluation of bio-based and recycled thermal break strips in LSF partition
walls, Buildings 12 (2022), https://doi.org/10.3390/buildings12081237.
M. Gaˇ
si et al.