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Citation: Bobula, M.; Michalak, P.;
Wołoszyn, J. Influence of the TABS
Material, Design, and Operating
Factors on an Office Room’s Thermal
Performance. Energies 2024,17, 1951.
https://doi.org/10.3390/en17081951
Academic Editor: Boris Igor Palella
Received: 18 March 2024
Revised: 16 April 2024
Accepted: 17 April 2024
Published: 19 April 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
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Attribution (CC BY) license (https://
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4.0/).
energies
Article
Influence of the TABS Material, Design, and Operating Factors
on an Office Room’s Thermal Performance
Mikołaj Bobula †, Piotr Michalak †and Jerzy Wołoszyn *,†
AGH University of Krakow, Faculty of Mechanical Engineering and Robotics, Department of Power Systems and
Environmental Protection Facilities, al. A. Mickiewicza 30, 30-059 Krakow, Poland; mbobula@agh.edu.pl (M.B.);
pmichal@agh.edu.pl (P.M.)
*Correspondence: jwoloszy@agh.edu.pl
†These authors contributed equally to this work.
Abstract: Reducing energy consumption in residential and commercial buildings is an important
research topic. Thermally activated building systems are a promising technology for significantly
reducing energy consumption. The high thermal inertia, large surfaces, and radiative nature are
advantages of these systems, but, on the other hand, this makes the system control and design
complex. A transient simulation is also required to address the dynamic behavior of the system. The
influence of 19 factors (material, design, and operating parameters) on the air temperature and mean
radiant temperature inside the room as well as the required cooling equipment power were analyzed
to better understand the system. The screening experiment was conducted using the random balance
design method, and measurement data were used to validate the resistance–capacitance model. The
analysis was performed using the Plackett–Burman design and a design with randomly selected
points from a full factorial experiment. The results show that internal heat gains and the inlet water
temperature have a significant influence on the system, and the influence of the screed’s properties is
insignificant compared to other parameters. It should be borne in mind that the obtained results and
conclusions are valid for the assumed range of factors’ variability.
Keywords: TABS; concrete core activation; resistance–capacitance model; sensitivity analysis; validation;
measurement
1. Introduction
Thermally activated building systems (TABS) are commonly used for heating and cool-
ing multi-story buildings. They cover a wide range of various constructions [
1
], including
one with pipes embedded in the concrete core of the slab. This type of TABS was intro-
duced in Switzerland in the early 1990s and, since then, it has been installed in numerous
buildings around the world [
2
]. TABS are known in German as Betonkerntemperierung
(BKT) systems, or in English as Concrete Core Activation (CCA) or Concrete Core Cooling
(CCC) [
3
–
5
]. During periods of high thermal load, heat is transferred through the floor
and ceiling and stored in concrete; it can then be removed by water flowing in pipes when
the occupants are absent [
6
]. Spreading the removal of heat over a longer period results in
lower peak power requirements for cooling systems, which can lead to energy savings up
to 50% [7].
The high thermal inertia, large surfaces, and radiative nature are advantages of TABS;
however, on the other hand, this makes the system control and design complex. A transient
simulation is also required to address the dynamic behavior of the system [
8
,
9
]. In [
10
],
thermal comfort issues in a room located in an office building with TABS were experi-
mentally investigated. Measurements performed during the everyday operation of the
room revealed very low differences in indoor air temperature (between 22.5
◦
C and 23.1
◦
C
during the working days) in its vertical profile and good thermal conditions provided by
TABS cooperating with a balanced ventilation system. The average temperature of the
Energies 2024,17, 1951. https://doi.org/10.3390/en17081951 https://www.mdpi.com/journal/energies
Energies 2024,17, 1951 2 of 22
floor’s surface ranged from 20.6
◦
C to 26.2
◦
C. However, this study was not oriented to
dynamic thermal analysis of TABS. Such works are very rare because multi-floor buildings
with thermally activated slabs exchanging heat between upper and bottom adjacent zones
are, in general, large commercial facilities. Hence, they are normally very difficult to access,
and measurements are very troublesome for occupants during their normal operation. That
is why most of the experimental studies on TABS concern control-oriented applications in
terms of energy use [
11
–
14
] or were performed under laboratory conditions in simple test
rooms [15,16].
One way of estimating system performance is through computational fluid dynamics
(CFD). It can provide detailed information about the system, but it is time-consuming
and therefore impractical [
17
,
18
]. Simplified methods based on ordinary differential equa-
tions can be an alternative to detailed simulations because they require less time to solve.
Nageler et al. [18]
compared the results of CFD simulations and simplified physical models
with measurement data. They found that simplified models can provide satisfying results.
Sharifi et al.
[9]
used a simplified resistance–capacitance model of TABS to develop the con-
trol algorithm for optimal load splitting between TABS and the secondary cooling system.
The utilization of the simplified model allowed authors to run the optimization algorithm
for a one-year period (8760 h long time steps) within 2 h, which would not be possible with
detailed simulations. To make the calculations easier, the method for simulating a room
with TABS was standardized in ISO 11855-4 [
19
]. This standard proposes a one-dimensional
simplified resistance–capacitance mathematical model of the room and slab, which is solved
with the finite difference method (FDM). The method has been utilized by Behrendt
[20]
to develop a computer program for simulating TABS. Catalano
[6]
has modified the ISO
11855-4 method to deal with unrealistic behavior of the system in the case of high thermal
load and low cooling power, which resulted in internal temperature exceeding 40
◦
C. The
author has proposed a correction factor that was calculated based on air temperature inside
the room and was used to modify heat gain value. However, simplified methods still
require detailed information on room design as well as on internal and external conditions.
Therefore, identifying parameters with the highest influence on the performance of TABS
would simplify the calculations and result in a better understanding of the system.
Due to the complexity of TABS, many studies have been conducted to establish
the influence of various parameters on conditions in the TABS-equipped building and
control strategy. Lu et al.
[21]
examined building energy flexibility under the influence of
various parameters that included thermal transmittance of the external wall (U-value), total
structural thermal mass, internal heat gains, and methods of cooling. They found that the U-
value of the external wall had a slight effect on cooling performance when compared to other
parameters. It should be kept in mind that this is valid for the assumed input parameters’
variability range. Saelens et al.
[22]
evaluated the influence of occupants’ behavior on
internal heat gains. They concluded that changes in various aspects of occupants’ behavior,
such as their mobility, the probability that they appear in the office during the day, or
manual operation of the lights and shading devices, have a significant influence on cooling
demand and thermal comfort in the office. Their results show that switching off the lights
reduces cooling demand by 8% and shortens the time that the temperature is outside the
thermal comfort zone by 15%. Rijksen et al.
[23]
examined the influence of internal heat
gains and window area on the peak-shaving performance of cooling in an office building
with TABS and without it. The authors discovered that TABS combined with a smaller area
of the windows resulted in a reduction of required cooling power by 50% when compared
to a system without energy buffering. Samuel et al.
[24]
experimentally assessed the effect
of parameters on thermal comfort in a room with TABS installed. The authors concluded
that increasing the number of cooling surfaces had a positive effect on thermal comfort
and that, with all surfaces cooled (ceiling, floor, and four walls), thermal comfort was
maintained throughout the day. They also found out that the use of ventilation could
result in rapid temperature changes as external air was mixed with internal.
Ning et al. [25]
examined the influence of geometric and thermal parameters on the system response
Energies 2024,17, 1951 3 of 22
time. They found that concrete thickness and pipe spacing have a significant impact on
TABS response time.
Samuel et al. [26]
performed a sensitivity analysis based on CFD
simulations to investigate the influence of pipe diameter, pipe thermal conductivity, and
slab thickness on thermal comfort in a room with TABS. They found that increasing pipe
thermal conductivity from 0.14 to 1.4
W
m·K
and increasing its inner diameter from 9 to 17 mm
reduced the operative temperature by 2.8
◦
C and 1.8
◦
C, respectively. However, increasing
the floor and ceiling slab thickness from 0.1 to 0.2 m reduced the operative temperature
by only 0.3
◦
C.
Chandrashekar and Kumar [27]
experimentally studied the influence of
various floor covering materials on TABS performance. They found that using a granite
floor resulted in lowering air temperature in the room by 1.5
◦
C and reduced cooling load
by 10% compared to the vinyl floor, which had lower thermal conductivity than granite.
Rakesh et al.
[28]
experimentally evaluated the influence of inlet water velocity on the
temperature in a room with TABS. They found that increasing the water velocity from 0.35
to 1
m
s
reduced internal air temperature by 1.5
◦
C; however, further a increase in the water
velocity to 1.5
m
s
reduced air temperature by only 0.2
◦
C. The review presented in this
section has been summarized in Table 1.
Table 1. Literature review summary.
Reference Method 1Examined Parameters Findings
[21] S
external wall thermal transmittance,
total thermal mass,
internal heat gains,
cooling method
little effect of thermal transmittance of the wall
[22] S internal heat gains (occupants’ behavior)
significant influence on internal conditions,
encouraging occupants to switch off lights may
reduce cooling demand by 8%
[23] E, S window area,
internal heat gains
internal heat gains have a significant effect on
cooling power
[24] E number of cooled surfaces,
use of other cooling system
cooling all surfaces allows for maintenance of
thermal comfort in the room throughout the day
(tropical climate)
[25] S
concrete thickness,
pipe spacing,
concrete type,
pipe diameter,
water flow pattern,
water temperature,
room operating temperature
concrete thickness and pipe spacing have the most
significant influence on TABS response time
[26] S
pipe diameter,
pipe thermal conductivity,
slab thickness
increasing pipes’ thermal conductivity and
diameter is more influential on operative
temperature than increasing slab thickness
[27] E floor covering properties
granite floor with higher thermal conductivity
reduces cooling load by 10% and air temperature
in the room by 1.5 ◦C
[28] E water inlet velocity
increasing the water velocity from 0.35 to 1 m
s
reduced internal air temperature by 1.5 ◦C, but
further velocity increase has little effect on the
temperature
1E—Experiment, S—Simulation
As presented above, materials, design, and operating parameters have important
effects on the performance of TABS. However, the influence of these parameters has not
been widely discussed in terms of the internal air and mean radiant temperature, which
Energies 2024,17, 1951 4 of 22
is very important in terms of thermal comfort. Moreover, the researchers examined the
influence of a limited number of factors at the same time (all factors at a time analysis).
Therefore, the possibility of comparing the influence of the parameters is limited. To fill
those gaps, we conducted a sensitivity analysis based on a random balance design and
found which parameters significantly affect the temperature inside a room with TABS and
required cooling power. We examined the influence of 19 parameters, including the slab
material properties, properties of walls, circuit operating parameters, and heat gains. The
calculations were performed using the modified method presented in ISO 11855-4 [
19
] and
validated using measurement data.
2. Details of Research Objective
The experimental part of this study was performed in a single office room in the
passive office building (Figure 1) located in Katowice in south Poland. This facility has been
described recently [
10
,
29
]. It has a total and usable area of 8100 m
2
and 7500 m
2
, respectively.
Figure 1. General view of the building from the south.
Ceiling slabs (Figure 2b) and the basement floor were made from 30 cm thick reinforced
concrete with embedded modules and with polymer pipes with a total area of 4500 m
2
and
1870 m
2
, respectively. This is the main heating and cooling system in the building. It is
supported by five air handling units with heating and cooling coils, creating a complete
heating, ventilation, and air conditioning (HVAC) system. Four units have a common
intake and exhaust collector on the roof, and they supply fresh air to office and social rooms.
The fifth unit supplies fresh air to sanitary facilities and toilets and is equipped with a
separate air intake and exhaust on the roof. The HVAC system is supplied with water from
the set of six water/water heat pumps with a total heating and cooling capacity of 244 kW
and 187 kW, respectively. Additionally, 10 vacuum solar collectors are used to support the
heating and tap water systems. As a peak cooling source, two chillers can be used.
The office rooms are located around the outer perimeter of the building, facilitating the
use of daylight. The large area of triple-glazed external windows (U = 0.7
W
m2·K
) increases
the share of solar energy in the thermal balance of the building. External blinds, on the other
hand, make it possible to reduce excessive solar gains during the summer. The corridors
are located on the inner perimeter of the building and, thanks to the glazing in its central
part, they are naturally illuminated. Photovoltaic modules with a total power of 107 kW
p
mounted on the roof and on the facade, as well as the three trackers in front of the building,
reduce electricity consumption in the building. For effective energy management and data
analysis, a building management system (BMS) is used. An office room (Figure 2a), located
on the west side of the second floor of the building was chosen for the research. It has a
floor area of 46.11 m2and a height of 3.10 m. During measurements, it was not occupied.
Energies 2024,17, 1951 5 of 22
(a) (b)
Figure 2. Experimental room: (a) General view; (b) Cross-section of the floor and the ceiling slabs
(dimensions in mm, 1-carpet, 2-cement screed, 3-reinforced concrete, 4-gypsum plaster).
3. Research Strategy
A sensitivity analysis for 19 (material, design, and operating) parameters for the
real TABS is impossible due to the high cost and the long time needed to perform each
experiment. One solution is to perform a series of simulation experiments. There are basic
CFD-based calculations that are detailed and accurate but time-consuming, so reduced-
order methods for the calculation of such complex systems are required. However, even
the use of supercomputers and distributed computing to perform sensitivity studies for
19 parameters is time-consuming. Therefore, there is a need to utilize an efficient research
strategy by using effective and time-reducing methods.
3.1. Research Algorithm
According to the research algorithm outlined in Figure 3, the initial phase of the
study involved meticulous identification of design specifications, material properties, and
operational parameters of the building room with TABS (Section 2). Simultaneously, a
decision was made to adopt a reduced computational model, aligning with the established
methodology outlined in ISO 11855-4 [19] (Section 5). The assumed computational model
of the office room with TABS was verified and validated (Section 5.2) using measurement
results (Section 4). The mean air temperature and mean radiant temperatures of the room
were compared in the validation analysis. For a full factorial design experiment, there was
a need to conduct 2
19
= 524,288 computational experiments. It is still impossible to conduct
the full experiment due to time-consuming calculations.
Figure 3. The research algorithm.
It was decided to conduct research using the random balance design method, and
experiments were generated by the use of the Plackett–Burman (PB) design. The PB designs
are mainly used for screening research. This design is efficient, but the main effects are, in
general, heavily confounded with two-factor interactions. For this reason, we decided to
Energies 2024,17, 1951 6 of 22
extend this research and conduct 512 randomly selected experiments from a full factorial
design. This allowed the results to be confirmed or rejected. Consequently, we assess
the impact of 19 factors on five output parameters. This screening experiment has been
performed using scripts written in Python 3.10, and the pyDOE3 version 1.0.1 [
30
] library
has been used to prepare the design of the experiments.
3.2. Assumptions
Using data from diverse sources, an extensive array of cases within the TABS across
varied geographical locations can be analyzed. The ranges of variability (Table 2) in the
parameters under analysis were determined by synthesizing information based on existing
literature. Consequently, we assumed parameters such as a cooling surface area (
P
1
=AF
)
equal to 50% and 100% of the total floor area on low and high levels, respectively, and the
material parameters’ variability values. The thermal conductivity of the concrete layer
(
P
2
=λcon
) and pipe spacing (
P
13
=L
) are limited by the assumptions of the method
described in [
19
]; the thermal conductivity, the specific heat, the density of the screed layer
(
P
3
=λsc
,
P
5
=csc
,
P
7
=ρsc
), the specific heat, and the density of the concrete layer
(P4=ccon ,P6=ρcon) are based on [31].
The construction of the slab is based on Figure 2b, and properties of the 2nd layer
(screed) and the 3rd layer (concrete) have been considered as parameters in the sensitivity
analysis. The water pipes were always located in the middle of the concrete layer. The 1st
layer (carpet) has been ignored due to its negligible thermal capacity; hence, it has not been
considered a slab layer in the numerical model (there is no node representing the carpet
layer). However, the influence of the thermal resistance of the carpet has been examined
by introducing additional thermal resistance (
P
11
=RAddF
) at the floor. We have assumed
that, at the high level, the value of
RAddF
is equal to the thermal resistance of the carpet in
the considered room, and the low level of the parameter represents the situation where the
carpet is not present and therefore the additional thermal resistance is equal to 0
W
m2·K
. The
properties of the 4th layer (plaster gypsum) have been considered constant in the sensitivity
analysis, and they are presented in Table 3.
The internal building walls consist of two layers of plasterboard and a layer of min-
eral wool between them. Their structure is the same as in the building for which the
measurements were made. The high level for the internal wall thickness parameter
P
10
=dIW
decomposed into layers equaled 25 mm for plasterboard and 200 mm for
the mineral wool layer (
dIW =
25
mm +
200
mm +
25
mm =
250
mm
) and, for the low
value,
dIW =
8
mm +
50
mm +
8
mm =
66
mm
. To calculate internal walls’ thermal re-
sistance and specific heat capacity, which are the parameters in the mathematical model,
we have evaluated the substitute values of walls’ thermal conductivity (
λIW
) and specific
thermal capacity (CIW ) according to the following equations:
λIW =∑di
∑di
λi
(1)
CIW =∑di·ci·ρi
∑di
(2)
where
di
is thickness of the
i
th layer [m],
λi
is the thermal conductivity of the
i
th layer
[
W
m·K
],
ci
is the specific heat of the
i
th layer [
J
kg·K
], and
ρ
is the density of the
i
th layer [
kg
m3
].
The thermal properties of the walls’ materials were determined according to [
31
]. The
values of λIW and CIW are presented in Table 3.
The values of water flow (
P
12
=˙
mH
) and inlet water temperature (
P
19
=θWaterIn
)
have been estimated according to measurement results. The values of the parameters at
low and high levels denote the minimum and maximum values provided by the building
management system (BMG), respectively.
Thermal transmittance of window
P
15
=UW
variability is based on values provided
by [
32
]. We have assumed that the values of the window area (
P
14
=AW
) equaled 30%
Energies 2024,17, 1951 7 of 22
and 70% of the external wall area at the low and high levels, respectively. Additionally, we
have assumed that the area of glazing (
Ag
) used in the process of calculating solar heat
gains equals 90% of the total window area (AW).
Thermal transmittance of the opaque part of the external wall (
P
16
=UEW
) is calcu-
lated according to [
33
]. The wall consists of four layers: (i) plaster, (ii) styrofoam with a
thickness of 300 mm, (iii) hollow bricks, and (iv) plaster. The values of the parameter were
determined by changing the thickness of the styrofoam layer, and for low and high values,
the thickness was equal to 50 mm and 300 mm, respectively.
The values of primary air gains (
P
17
=QPrim Air
) have been based on the results
of measurements conducted in the considered room. The ventilation system provided
constant airflow of 95
m3
h
between 3 a.m. and 7 p.m.; however, the difference between
supply and exhaust air temperature was greatest between 3 a.m. and 9 a.m. After 9 a.m.,
the difference between the supply and exhaust air temperature was reduced significantly;
hence, the heat gain was considered to be 0 W despite the ventilation system still working.
To simplify the model, we have assumed that the ventilation system provides constant
airflow of 240
m3
h
, which is the maximum value that can be provided by the HVAC system.
To estimate the value of the parameters, we have assumed that the difference between
supply and exhaust air temperature equals
−
4.5
◦
C and 0
◦
C at low and high levels,
respectively, which results in the value of QPri mAir equal to −350 W and 0 W, respectively.
Internal heat gains (
P
18
=QInt
) originate from occupants, office equipment, and
lighting in the room. In a sensitivity analysis, we have assumed that the occupants are
present and that they use the equipment between 7 a.m. and 5 p.m.; otherwise, the internal
heat gains are equal to 0 W. We have determined that the value of the parameter at a low
level, assuming that the room is not used, is 0 W. For the high level, the value of internal
heat gains was estimated according to [
34
]. To carry out the calculations, we have assumed
that five people work in the room and that each person uses a personal computer with two
monitors; additionally, there is one printer in the room. The internal heat gains estimated
according to those assumptions are equal to 1500 W. We have assumed that half of the
internal heat gain is transferred through radiation (
QInt Rad
) and the other half is through
convection (
QIntConv
) [
22
]. All parameters considered in the sensitivity analysis along with
their variability ranges are presented in Table 2.
Table 2. Variability ranges of the input parameters.
No Parameter Symbol Value Unit
Low High
P1 Cooling surface area AF23 46 m2
P2 Concrete thermal conductivity λcon 1.15 2 W/(m·K)
P3 Screed thermal conductivity λsc 1.4 1.8 W/(m·K)
P4 Concrete-specific heat ccon 900 1100 J/(kg·K)
P5 Screed-specific heat csc 900 1100 J/(kg·K)
P6 Concrete density ρcon 1800 2400 kg/m3
P7 Screed density ρsc 1800 2000 kg/m3
P8 Concrete layer thickness dcon 0.2 0.4 m
P9 Screed layer thickness dsc 0.005 0.03 m
P10 Internal wall thickness dIW 0.066 0.25 m
P11 Floor additional resistance RAdd F 0 0.032 m2·K/W
P12 Water flow ˙
mH0.028 0.08 kg/s
P13 Pipe spacing L0.15 0.3 m
P14 Window area AW5.4 12.5 m2
P15 Thermal transmittance of window UW0.5 3.3 W/(m2·K)
P16 Thermal transmittance of external wall (opaque) UEW 0.088 0.203 W/(m2·K)
P17 Primary air heat gain QPrim Air −350 10 W
P18 Internal heat gains QI nt 01500 2W
P19 Inlet water temperature θWaterIn 16 22 ◦C
1Between 3 a.m. and 9 a.m.; otherwise 0 W. 2Between 7 a.m. and 5 p.m.; otherwise 0 W.
Energies 2024,17, 1951 8 of 22
To provide information about thermal comfort inside the room and the cooling power
necessary for maintaining constant water temperature in the circuit, we have selected the
following output parameters:
• Maximum and minimum air temperature (θMax
A,θMin
A),
• Maximum and minimum mean radiant temperature (θMax
MR ,θMin
MR ),
• Maximum power received by the circuit (QMax
Circuit).
The maximum/minimum air temperature (
θMax
A
,
θMin
A
) and maximum/minimum
mean radiant temperature (
θMax
MR
,
θMin
MR
) have been considered only between 7 a.m. and
5 p.m. when occupants are present, while power (
QMax
Circuit
) received by the circuit has been
considered throughout the day.
Other parameters that have not been considered in the sensitivity analysis but that are
necessary for calculations are presented in Table 3.
Table 3. Other system parameters.
Parameter Symbol Value Unit
Room width X5.8 m
Room length Y7.95 m
Room height Z3.1 m
Convection coefficient on the floor hAF 2.37 W/(m2·K)
Convection coefficient on the ceiling hAC 0.54 W/(m2·K)
Convection coefficient on the internal walls hAW 1.79 W/(m2·K)
Radiant heat transfer coeff. between floor and ceiling hFC 2.79 W/(m2·K)
Radiant heat transfer coeff. between floor and internal walls hFW 2.07 W/(m2·K)
Ceiling additional resistance RAddC 0m2·K/W
Water-specific heat cw4183 J/(kg·K)
Plaster layer thickness dpl 0.005 m
Plaster thermal conductivity λpl 0.43 W/(m·K)
Plaster-specific heat cpl 1000 J/(kg·K)
Plaster density ρpl 1200 kg/m3
Internal wall thermal conductivity λIW 0.06 W/(m·K)
Substitute internal wall-specific thermal capacity CI W 321, 710 J/(m3·K)
Pipe external diameter da0.02 m
Pipe wall thickness s0.002 m
Pipe wall thermal conductivity λr0.35 W/(m·K)
Time step ∆t3600 s
Maximum iteration error allowed ξMax 0.00001 ◦C
Maximum number of iterations allowed nMax 10, 000 -
4. Details of Measurements
The measurements were carried out in a specially prepared office room with 46.11 m
2
(Figure 2a). All sensors were placed in the room according to the layout presented in
Figure 4a,b. For the sake of clarity, supply and exhaust channels of the ventilation system
were indicated only for the ceiling.
All air and surface temperature measurements were performed using Pt100 platinum
resistance sensors. Heat flux of the ceiling and the floor was measured using the HFP01
sensors of Hukseflux [
35
]. Global solar irradiance entering the room was measured by the
LP PYRA03 pyranometer of DeltaOhm [
36
]. At the center of the room, a tripod was placed
with a globe temperature sensor (diameter of 150 mm) at a height of 1.5 m. Based on [
37
,
38
],
it was assumed that the mean radiant temperature is the same as the measured globe
temperature. However, as noted in [
39
,
40
], this assumption may result in underestimation
of the mean radiant temperature. As the room was unoccupied during measurements, this
effect was minimized, but its precise assessment requires further analysis. Additionally,
three air temperature sensors were attached to a tripod at heights of 0.2 m, 0.6 m, and 1 m
above floor level. They were covered with low-emissivity (
ε=
0.1) coating to minimize
Energies 2024,17, 1951 9 of 22
the impact of heat transfer by radiation. The wall temperature sensors were placed 1.5 m
above the floor. All sensors are listed in Table 4. All sensors were connected directly to the
Fluke 2638A data logger [41].
(a) (b)
Figure 4. Location of the measurement equipment in the room (all dimensions in meters): (a) Floor;
(b) Ceiling.
Table 4. Measurement sensors.
Symbol Type, Class Measured Variable
QF1,QF2HFP01 Floor heat flux
QC1,QC2HFP01 Ceiling heat flux
TF1,TF2,TF3,TF4Pt100, class AA Floor surface temperature
TF5,TF6Pt1000, class A Floor surface temperature
TC1,TC2Pt1000, class A Ceiling surface temperature
TIWS1,TIWS2Pt1000, class A Internal wall surface temperature
Texh Pt1000, class A Exhaust ventilation air temperature
Tsup Pt1000, class A Supply ventilation air temperature
Tglobe Pt100, class A Globe temperature
T0.2 Pt100, class AA Indoor air temperature at 0.2 m above the floor
T0.6 Pt100, class AA Indoor air temperature at 0.6 m above the floor
T1.0 Pt100, class AA Indoor air temperature at 1.0 m above the floor
Isol LP PYRA03 Global solar irradiance entering the room
Accuracy classes of Pt100 and Pt1000 follow IEC 60751 [42].
According to [
43
], combined uncertainty of measured variable
x
, when using a mea-
surement sensor and a signal processing and display unit (device), is given by:
u(x) = qu2
sens +u2
dev. (3)
Both sensor and device uncertainties can be obtained from the relevant standards or
manufacturer documentation. Following IEC 60751 [
42
] for the known temperature (
T
), the
tolerances of the A and AA class sensors are given by the following relationships, respectively:
∆T= (0.15 +0.002|T|), (4)
∆T= (0.01 +0.0017|T|). (5)
At 25
◦
C for the A class sensor, we obtain from Equation (4):
usens =∆T
√3
= 0.116
◦
C.
According to the manufacturer [
41
], for a 4-wire Pt100 sensor, uncertainty
udev
= 0.024
◦
C
Energies 2024,17, 1951 10 of 22
at 25
◦
C. Hence, from Equation (3):
u(x) =
0.12
◦
C. Apart from variables listed in Table 4,
inlet water temperature and flow rate were obtained from the heat meter connected to the
BMS. For the second class heat meter [
44
] the maximum permissible error (MPE), expressed
in %, is defined for the flow rate (
Ef
) and for the temperature difference measured by the
pair of sensors (ET) by the following relationships:
Ef= (2+0.02 ˙
mper /˙
m), (6)
ET= (0.5 +3∆T/∆Tmin), (7)
where
˙
m
means flow rate,
˙
mper
is the maximum permissible flow rate,
∆T
is the current
inlet/outlet temperature difference, and
∆Tmin
is the minimum temperature difference
(
∆Tmin
= 5 K in the considered case). Based on available data, it was established that
both
ET
and
Ef
do not exceed 3%. Finally, according to the manufacturer’s data, it was
assumed that the ventilation flow rate was measured with an accuracy of
±
5%. The most
troublesome to assess is the accuracy of heat flux sensors. Following the manufacturer’s
recommendations [
35
] in buildings physics, it varies from
±
6% in ideal conditions to
±
20% in typical on-site applications. In the presented case, the second value seems to be
reasonable in the analysis of the measurement results.
5. Computational Model Description
5.1. Mathematical Model Description
The mathematical model of the room is based on resistance–capacitance simplification
introduced in ISO 11855-4 [
19
]. The mathematical model includes the slab, internal walls
(walls between the considered room and adjacent ones), and air filling the room, which are
divided into thermal nodes and, in each node, the heat balance is calculated according to
the following equation:
Cdθ
dt =∑Q, (8)
where
C
is the thermal capacity of the node [
J
K
], and the right-hand side of the equation is
the sum of heat transfer rates received or delivered to the considered node in [W].
The RC representations of the slab and the room are presented in Figure 5a and
Figure 5b, respectively. The heat transport in the slab is simplified by the use of the thermal
resistance method provided in ISO 11855-2 [
45
], where
Rt
is the thermal resistance between
inlet water and concrete at the pipe level. It is introduced to calculate heat transfer between
water flowing in pipes and concrete. In the part of the mathematical model representing
the room, nodes representing the floor, ceiling, and internal wall surface are connected,
which represents radiant heat transfer between them. The convective heat transfer is also
present, and it is represented by connections between surface nodes and air nodes. Several
simplifying assumptions were also made:
•
The heat transport in the perpendicular direction to the floor is taken into considera-
tion,
• Water mass flow in the pipes is constant throughout the simulation time,
• Radiant heat gains are distributed evenly to all surfaces,
• Conditions in rooms above and below are the same as in the considered room,
• All thermophysical properties are constant and independent of temperature.
The mathematical model is solved through the implicit scheme of the finite difference
method, and the equation used for calculating temperature in the considered node can be
written as follows:
θh
p=
HA·θh
A+HIWS ·θh
IWS +HF·θh
F+HC·θh
C+HRad ·Qh
Rad +HCo nv ·Qh
Conv +
+HCondU p ·θh
p−1+HCond Down ·θh
p+1+HInertia ·θh−1
p+HCircuit ·θh
WaterIn
HA+HIWS +HF+HC+HCondU p +HCondDown +HInertia +HCircuit
, (9)
Energies 2024,17, 1951 11 of 22
where
θh−1
p
is the temperature of the considered node in the previous time step [
◦
C],
θh
p−1
is the temperature of the previous node [
◦
C],
θh
p+1
is the temperature of the next node [
◦
C],
Qh
Rad
is total radiant heat gain [W],
Qh
Conv
is total convective heat gain [W], and
θh
Water,In
is inlet water temperature [
◦
C].
H
represents the heat transfer coefficients, which depend
on the type of node that is currently being considered. An iterative method is used for
determining temperatures in the nodes, and with each iteration, the error is calculated
as follows:
ξ=∑
p|θh
p−θh′
p|, (10)
where
θh′
p
is the temperature calculated in the previous iteration. Calculations are carried
out until the iteration error
ξ
is smaller than the maximum allowed error (
ξMax
) or until the
maximum number of iterations (
nMax
) is achieved. The values of maximum iteration error
and maximum iterations allowed are presented in Table 3.
(a) (b)
Figure 5. Scheme of the model (based on [
19
]): (a) Resistance network representing the slab; (b) Resis-
tance network representing the room.
The initial and specific conditions have to be determined before calculating the heat
delivered or received from the considered room. Specific conditions can be divided into
three categories:
•
Radiant heat gains delivered to surface nodes (floor, ceiling, and internal wall surface
(Figure 5b)),
• Convective heat gains delivered to the air node,
• Heat received by the circuit from the pipe-level node.
Both radiant and convective heat gains depend on internal and external conditions and
are calculated for every time step of the simulation according to the following equations:
Qh
Rad =0.85 ·Qh
Transm +Qh
Sun +Qh
Int Rad (11)
Qh
Conv =0.15 ·Qh
Transm +Qh
Prim Air +Qh
IntConv (12)
where
Qh
Transm
is the transmission heat gain [W],
Qh
Sun
is the solar heat gain [W],
Qh
Prim Air
is
the primary air heat gain [W], and
Qh
Int Rad
and
Qh
IntConv
are internal radiant and convective
heat gains [W], respectively. The value of each term in Equations (11) and (12) has to be
known for every time step of the simulation. Primary air and internal heat gains have been
Energies 2024,17, 1951 12 of 22
determined according to measurement data and the literature (see Section 3.2). The solar
heat gains have been determined according to the following:
Qh
Sun =Isol ·Ag, (13)
where Isol is total solar irradiance entering the room [ W
m2], and Agis the area of glazing [m2].
According to Catalano
[6]
, adopting the value of transmission heat gain independent
of temperature may lead to errors. Hence, the value of the transmission heat gain has been
determined using the difference between external and internal temperatures according to
PN-EN 12831-1 [46], and it is equal to the following:
Qh
Transm = (UEW ·AEW +UW·AW)(θh
Ex −θh
A)(14)
where
UEW
is the thermal transmittance of the opaque part of the external wall [
W
m2·K
],
UW
is the thermal transmittance of the window [
W
m·K
],
AEW
is the area of the opaque
surface [m
2
],
AW
is the area of the window [m
2
], and
θh
Ex
is the external temperature
[
◦
C]. Since transmission heat gain is dependent on air temperature, it has to be calculated
with every iteration. The external temperature has been obtained from weather data. To
examine the influence of external conditions on the room, the weather data chosen for the
experiment contained outside temperatures differing from measured room temperatures.
The maximum value of the external temperature considered in the experiment was equal
to 18 ◦C.
Convective heat transfer coefficients on the surfaces in the room were calculated
according to equations developed by Awbi
[47]
, presented in Table 5. It is assumed that the
difference between the surface and air temperatures (
∆T
) in each case is constant and equal
to 1.5 K, so the coefficients are constant.
Table 5. Convective heat transfer coefficient for the surfaces [47].
Surface Convective Coefficient Range
Floor h=2.175
D0.076 ∆T0.308 9·108<Gr <7·1010
Ceiling h=0.704
D0.601 ∆T0.133 9·108<Gr <1·1011
Walls h=1.823
D0.121 ∆T0.293 9·108<Gr <6·1010
The initial temperature of the nodes has been set to 22
◦
C by default. However, due to
the high thermal inertia of the system, the time required by the node temperatures to reach
their final distribution may exceed the simulation time. For that reason, a startup period
has been added to the simulation [
20
]. During the startup period, node temperatures can
reach their final values without altering the solution. To verify whether the final results
are achieved, the difference between the maximum temperatures of the considered and
the previous day is calculated. If the difference is smaller than 0.005 K, the solution is
considered valid.
5.2. Validation and Verification
The mathematical model was validated using experimental data to assess whether
the model parameters and the specific conditions are properly set. During the process, a
six-day-long period was simulated, and the results were compared with data collected
during measurements. The specific conditions were based on measurements of solar
irradiation, external temperature, and air temperature delivered by an air conditioning
system. Since there were no occupants in the room during the measurements, the internal
heat gains resulted from measurement equipment only. They were assumed to have a
constant value of 10 W throughout the simulation time. The specific conditions used in the
simulation have been doubled to form a startup period; therefore, the total simulation time
was equal to 12 days, but only the second half of it was considered valid and not affected
Energies 2024,17, 1951 13 of 22
by initial conditions. The simulation was performed with a time step (
∆t
) equal to 1 h and
a maximum iteration error (ξMax ) equal to 10−5K.
A comparison of simulation results and measurements for air temperatures is pre-
sented in Figure 6a. The mean absolute error is equal to 0.16
◦
C, and the maximum error is
0.65
◦
C, which are acceptable values. In the case of mean radiant temperature, the error
values were higher when compared to the air temperature mean, and the maximum abso-
lute errors are equal to 0.18
◦
C and 2.02
◦
C, respectively. The high value of the maximum
error may result from high sun radiation entering the room and heating the thermometer
responsible for collecting the data. Despite the relatively high maximum error for the
mean radiant temperatures, both air and radiant temperatures show good agreement with
experimental data.
(a) (b)
Figure 6. Comparison of simulation and experimental results. (a) Air temperature. (b) Mean radiant
temperature.
To assess that the results would converge, a grid independence study was conducted.
A calculation with the number of nodes varying from 13 to 55 was considered. The grid
independence study was performed for the air temperature at 12 a.m. and at 11 a.m. on
the first day of the simulation time (1st and 12th time steps, respectively, after rejecting the
startup period). The results are shown in Figure 7a and Figure 7b, respectively. In both
cases, temperatures reach a steady value, with the number of nodes equal to 35. Beyond
this value, no significant change in the solution can be reported; thus, we have chosen
the model with approximately 35 nodes for sensitivity analysis. However, the number of
nodes may differ depending on the experiment, since the geometry of the slab varies, as
the thickness of the screed and concrete layer are parameters in the sensitivity analysis.
(a) (b)
Figure 7. Results of grid independence analysis: (a) Results for the beginning of the simulation;
(b) Results for the 12th hour of the simulation.
Energies 2024,17, 1951 14 of 22
6. Results of Sensitivity Analysis
The sensitivity analysis was conducted using two experimental design methods—
Plackett–Burman and full factorial design—from which 512 experiments were randomly
selected. The medians of the appropriate output parameters were calculated for a series of
design points when the specific factor assumed low or high levels. Scatter diagrams with
marked medians (dashed lines) for all design points and medians for low and high levels
(point) for both methods are presented in Figures 8–12. The influence of the parameters’
changes on maximum air temperature (
θMax
Air
) is presented in Figure 8. According to both
experiment designs, the area of the cooling surface (
P
1), internal heat gains (
P
18), and
inlet water temperature (
P
19) have a significant impact on
θMax
A
, as the differences in their
medians have values greater than 2.2
◦
C. In the case of water flow (
P
12), the difference in
the medians obtained with the full factorial design is at the same level as the difference
in the area of the cooling surface (
P
1). However, the value obtained with the PB design
is lower and equals 0.6
◦
C. Since the full factorial design contains more experiments, it is
considered to be more informative in the case of uncertainty; therefore, parameter
P
12 is
also considered to have an impact on
θMax
A
. The influence of the specific heat of concrete
(
P
4) cannot be confirmed, since its influence should be considered according to PB design.
In contrast, according to full factorial design, its influence is negligible. The discrepancy
between the two methods suggests that further study may be necessary to evaluate the
impact of the concrete-specific heat.
Figure 8. Results of sensitivity analysis for maximum air temperature.
In the case of minimum air temperature (
θMin
A
) presented in Figure 9, the assumed
DOEs show more inconsistency compared to the case of
θMax
A
. According to the PB design
(dark lines), only the inlet water temperature (
P
19) has a significant impact on
θMin
A
, with
the difference in the medians equal to 4.1
◦
C, while for other parameters, the difference in
the medians is smaller than 1
◦
C. However, according to the full factorial design, the area
of the cooling surface (
P
1), internal wall thickness (
P
10), floor additional resistance (
P
11),
water flow (
P
12), thermal transmittance of the window (
P
15), primary air heat gains (
P
17),
internal heat gains (
P
18), and inlet water temperature (
P
19) have considerable influence on
θMin
A
, with the difference in the medians above 1
◦
C. Due to the more informative nature of
the full factorial design, we consider parameters
P
1,
P
10,
P
11,
P
12,
P
15,
P
17,
P
18,
P
19 as
influences on θMin
A.
The result of sensitivity analysis for the maximum value of mean radiant temperature
(
θMax
MR
) is presented in Figure 10. Both methods indicate that the cooling surface area (
P
1),
Energies 2024,17, 1951 15 of 22
internal heat gains (
P
18), and inlet water temperature (
P
19) have a significant influence
on the results, with differences in the medians greater than 1
◦
C. The results of the PB
design indicate that the specific heat of concrete (
P
4), screed density (
P
7), and the window
area (
P
14) also have considerable influence on the maximum value of the mean radiant
temperature. However, this is not confirmed by the results of the full factorial design,
according to which the differences in the medians for parameters
P
4,
P
7, and
P
14 are
smaller than 1
◦
C. Therefore, the influence of parameters
P
4 and
P
7 is not considered
significant. The significance of the window area (
P
14) cannot be confirmed. According to
the PB design, the difference in the medians is equal to 2.3
◦
C; however, the value obtained
with a randomly selected design from a full factorial experiment equals 0.7
◦
C. Due to the
inconsistency between the results of both methods, further study is necessary to confirm
the influence of parameter P14.
Figure 9. Results of sensitivity analysis for minimum air temperature.
Figure 10. Results of sensitivity analysis for maximum mean radiant temperature.
Energies 2024,17, 1951 16 of 22
The results for minimum mean radiant temperature (
θMin
MR
) are presented in Figure 11.
Similarly to the case of minimum air temperature (
θMin
A
), the results obtained with the
PB design indicate that only the influence of the inlet water temperature (
P
19) can be
considered significant, with the difference in the medians equal to 5
◦
C. The significance of
parameter
P
19 is confirmed by the results of the full factorial design, with the difference in
the medians equal to 5.7
◦
C. The results obtained with the full factorial design indicate that
the parameters
P
1,
P
8,
P
10,
P
12,
P
15,
P
17, and
P
18 should also be considered significant.
However, further study may be necessary to establish the influence of these parameters.
According to both methods, the differences in the medians for thermal conductivity of
concrete (
P
2), concrete-specific heat (
P
4), and distance between pipes (
P
13) are smaller
than 0.6 ◦C, which means that the influence of these parameters on θMin
MR is negligible.
Figure 11. Results of sensitivity analysis for minimum mean radiant temperature.
The last output parameter examined in this study was the maximum power received
by the circuit (
QMax
Circuit
). Its value corresponds with the power required by water cooling
equipment to maintain the constant inlet water temperature. According to the results
presented in Figure 12, both DOEs indicate that the cooling surface area (
P
1), thermal
transmittance of the window (
P
15), and internal heat gains (
P
18) have a significant impact
on the value of
QMax
Circuit
, with the differences in the medians greater than 120 W. The
results of both methods show that the properties of the screed layer (parameters
P
3,
P
5,
and
P
7) and thermal transmittance of the opaque part of the external wall (
P
16) have
insignificant influence on the cooling power demand. In the case of the window area (
P
14)
and primary air heat gains (
P
17), the PB design indicates a significant influence on the
results, with a difference in the medians greater than 110 W. However, according to the
results of the full factorial design, parameters
P
14 and
P
17 have no impact on the value of
QMax
Circuit
, as differences in the medians are smaller than 15 W. The inconsistency between
the two methods indicates that further study may be necessary to evaluate the influence of
parameters P14 and P17.
A comparison of the results shows that the internal heat gains (
P
18) have the most sig-
nificant influence on
θMax
A
,
θMax
MR
, and
QMax
Circuit
, which is consistent with the results presented
in [
22
]. However, in this study, we have assumed that the internal heat gains are constant
within working hours and that their value is independent of the temperature inside the
room, which is a considerable simplification. According to [
22
], even minor changes in
occupants’ presence and behavior (such as switching off the lights) might notably influence
Energies 2024,17, 1951 17 of 22
the temperature inside the room and the demand for cooling power. Therefore, designers
should pay particular attention to properly evaluate the value of internal heat gains.
The results show that the inlet water temperature (
P
19) has a significant impact on
both air and mean radiant temperature in the room, while the impact of water flow has
been considered significant only in the case of
θMin
A
. The amount of water delivered to the
pipes and its temperature is controlled by the cooling system. Therefore, developing the
proper control strategy for the cooling system is essential for maintaining the temperature
inside the room at comfortable levels. However, keeping the appropriate value of the inlet
water temperature is more important than the water flow, since the water temperature has
a greater influence on the internal room temperature than does the water flow.
Figure 12. Results of sensitivity analysis for maximum power received by the circuit.
In every experiment, the influence of the screed properties (parameters
P
3,
P
5,
P
7,
and
P
9), the thermal conductivity of concrete (parameter
P
2), and pipe spacing (
P
13)
is insignificant when compared to other parameters. This means that, in the process of
dimensioning the room with TABS, designers do not have to pay particular attention to
those parameters, since their influence on internal conditions is negligible; instead, they
should focus on more influential ones.
The results show that the primary air gain (
P
17) does not influence
θMax
A
or
θMax
MR
, which
may be an effect of the assumption that the ventilation cools the room only in the hours
following its activation. In the case of high thermal load, the air temperature delivered
by the ventilation system and the air temperature in the room may differ significantly.
Therefore, the primary air gain would have a non-zero value throughout the time the
ventilation system is on. To consider the influence of the internal temperature on the
primary air gain, a further modification of the numerical model of the room is necessary.
The results of both the PB and full factorial design methods show that the transmittance
of the opaque part of the external wall (
P
16) has no significant influence on temperatures
inside the room nor on the power received by the circuit. The insignificant influence of the
parameter
P
16 may be caused by the fact that its values are approximately one order of
magnitude lower than the values of the thermal transmittance of the window (
P
15). This
resulted in low heat flux transmitted by the opaque part of the external wall and low heat
loss to the environment, which is consistent with the results obtained by Lu et al.
[21]
. It
should be borne in mind that the obtained results and conclusions are valid for the assumed
range of factors’ (P1–P19) variability.
Energies 2024,17, 1951 18 of 22
7. Conclusions
In this study, we performed a sensitivity analysis to find which of the selected 19
factors (material, design, and operating parameters) affect the maximum/minimum air
temperature, maximum/minimum mean radiant temperature inside the room, and the
maximum required cooling equipment power. The analysis was performed using the PB
design and a randomly selected design from a full factorial experiment. The resistance–
capacitance model introduced in ISO 11855-4 was used for simulation research. The
specific conditions considered in the mathematical model and parameters assumed in the
sensitivity analysis were based on the measurement results collected in the office building.
The measurement data were also used to validate the mathematical model. Below, we
provide a summary of the key findings from the research:
•
The internal heat gains (
P
18) and the inlet water temperature (
P
19) significantly influ-
ence the maximum/minimum air temperature, maximum/minimum mean radiant
temperature, and the maximum required cooling equipment power. Therefore, special
attention should be paid to the internal heat gain model and control strategy for TABS
while it is being designed.
•
The impact of the analyzed factors on the mean radiant temperature, however, is
influenced by simplifications resulting from the set of the experimental equipment
used. Hence, in the study, the globe temperature was assumed to be equal to
θMR
.
Precise measurement of air velocity near the globe sensor would be of special interest
in terms of obtaining the correct value of θMR.
•
The primary air heat gains (
P
17) significantly influence the minimum air temperature.
•
The influence of the screed’s properties (
P
3,
P
5,
P
7) is insignificant compared to other
parameters, and it does not need to be considered in the process of dimensioning the
cooling system or in the cooling control strategy. However, it should be borne in mind
that this is valid for the assumed range of factors’ (P1–P19) variability.
•
Thermal transmittance of the external wall does not have a significant effect on internal
conditions because, even at a high level, its value is small compared to the thermal
transmittance of the window.
•
The water inlet temperature (
P
19) has a considerably larger influence on the tempera-
ture in the room than does the water mass flow rate (P12) in the pipes.
The simulation conditions have been simplified and are based on measurement data,
which may limit the results to specific situations. The authors of this study propose to ex-
tend the research, such as by making primary air heat gains dependent on air temperature.
Author Contributions: Conceptualization, J.W. and P.M; investigation, M.B., J.W. and P.M.; methodol-
ogy, M.B., P.M. and J.W.; software, M.B.; supervision, J.W.; validation, M.B. and P.M.; writing—original
draft, M.B., J.W. and P.M.; writing—review & editing, M.B., J.W. and P.M. All authors have read and
agreed to the published version of the manuscript.
Funding: This research project was partly supported by the program “Excellence initiative—research
university” for the AGH University of Science and Technology and by Poland national subvention,
Poland no. 16.16.130.942.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding authors.
Conflicts of Interest: The authors declare no conflicts of interest.
Energies 2024,17, 1951 19 of 22
Abbreviations
The following abbreviations are used in this manuscript:
BMS Building management system
DOE Design of experiment
FDM Finite difference method
HVAC Heating, ventilation, and air conditioning
MPE Maximum permissible error
PB Plackett–Burman
TABS Thermally activated building systems
Nomenclature
ASurface area, m2
cSpecific heat, J
kg·K
CSpecific thermal capacity, J
m2·K; Substitute specific thermal capacity, J
m3·K
dThickness, m
daPipe outer diameter, m
DCharacteristic dimension, m
EMaximum permissible error, [-]
Gr Grashof number, [-]
h,HHeat transfer coefficient, W
m2·K
Isol Solar irradiance, W
m2
LPipe spacing, m
˙
mFlow rate, [kg
s]
˙
mHWater flow in pipes, [kg
s]
nNumber of iterations, [-]
PParameter
QHeat gain, W
RThermal resistance, m·K
W
RAddC Ceiling additional thermal resistance, m·K
W
RAddF Floor additional thermal resistance, m·K
W
RtThermal resistance between inlet water and concrete at pipe level, m·K
W
sPipe wall thickness, m
tTime, [s]
TTemperature, ◦C
uUncertainty
UThermal transmittance, W
m2·K
X,Y,ZRoom dimensions, m
Greek symbols
εEmissivity, [-]
θTemperature, ◦C
λThermal conductivity, W
m·K
λrPipe wall thermal conductivity, W
m·K
ξIteration error, K
ρDensity, kg
m3
Subscripts
AAir
CCeiling
con Concrete layer
CondDown Conduction to next node
CondUp Conduction to previous node
Conv Convective
dev Device
EW External wall (opaque)
Ex External
exh Ventilation exhaust
fFlow
FFloor
Energies 2024,17, 1951 20 of 22
gGlazing
hTime step number
Int Internal
IntConv Internal convective
IntRad Internal radiant
IW Internal walls
IWS Internal wall surface
MR Medium radiant
pNode number
per Permissible
pl Plaster gypsum layer
Rad Radiant
sens Sensor
sc Screed layer
sup Ventilation supply
TTemperature
Transm Transmission
WWater
WWindow
WaterI n Water inlet
References
1.
Kalz, D.E. Heating and Cooling Concepts Employing Environmental Energy and Thermo-Active Building Systems for Low-Energy
Buildings—System Analysis and Optimization. Ph.D. Dissertation, Karlsruhe Institute of Technology, Karlsruhe, Germany, 2010.
2. Olesen, B. Using Building Mass To Heat and Cool: Thermo Active Building Systems (TABS). ASHRAE J. 2012,54, 44–52.
3.
Stefan, W.; Dentel, A.; Madjidi, M.; Dippel, T.; Schmid, J.; Gu, B. Design Handbook for Reversible Heat Pump Systems
with and without Heat Recovery. Final Report of the IEA-ECBCS Annex 48 Project. February 2010. Available online: https:
//iea-ebc.org/Data/publications/EBC_Annex_48_Final_Report_R4.pdf (accessed on 26 January 2024).
4.
Kalz, D.; Pfafferott, J.; Koenigsdorff, R. Betriebserfahrungen mit thermoaktiven Bauteilsystemen. Bauphysik 2021,34, 66–75.
[CrossRef]
5.
van der Heijde, B.; Sourbron, M.; Arance, F.; Salenbien, R.; Helsen, L. Unlocking flexibility by exploiting the thermal capacity of
concrete core activation. Energy Procedia 2017,135, 66–75. [CrossRef]
6.
Catalano, L. Development of a Simplified Method for Sizing Thermo-Active Building Systems (TABS). Master’s Thesis, University
of Padua, Padua, Italy, 2014.
7.
Villar-Ramos, M.M.; Hernández-Pérez, I.; Aguilar-Castro, K.M.; Zavala-Guillén, I.; Macias-Melo, E.V.; Hernández-López, I.;
Serrano-Arellano, J. A Review of Thermally Activated Building Systems (TABS) as an Alternative for Improving the Indoor
Environment of Buildings. Energies 2022,15, 6179. [CrossRef]
8.
Romaní, J.; Gracia, A.D.; Cabeza, L.F. Simulation and control of thermally activated building systems (TABS). Energy Build. 2016,
127, 22–42. [CrossRef]
9.
Sharifi, M.; Mahmoud, R.; Himpe, E.; Laverge, J. A heuristic algorithm for optimal load splitting in hybrid thermally activated
building systems. J. Build. Eng. 2022,50, 104160. [CrossRef]
10.
Michalak, P. Selected Aspects of Indoor Climate in a Passive Office Building with a Thermally Activated Building System: A Case
Study from Poland. Energies 2021,14, 860. [CrossRef]
11.
Hu, R.; Li, X.; Liang, J.; Wang, H.; Liu, G. Field study on cooling performance of a heat recovery ground source heat pump system
coupled with thermally activated building systems (TABSs). Energy Convers. Manag. 2022,262, 115678. [CrossRef]
12.
Li, Z.; Zhang, J. Study of distributed model predictive control for radiant floor heating systems with hydraulic coupling. Build.
Environ. 2022,221, 109344. [CrossRef]
13.
Mork, M.; Xhonneux, A.; Müller, D. Nonlinear Distributed Model Predictive Control for multi-zone building energy systems.
Energy Build. 2022,264, 112066. [CrossRef]
14.
Sui, X.; Huang, L.; Han, B.; Yan, J.; Yu, S. Multi-objective optimization of intermittent operation schemes of thermally activated
building systems using grey relational analysis: A case study. Case Stud. Therm. Eng. 2023,45, 102987. [CrossRef]
15.
Krajˇcík, M.; Šimko, M.; Šikula, O.; Szabó, D.; Petráš, D. Thermal performance of a radiant wall heating and cooling system with
pipes attached to thermally insulating bricks. Energy Build. 2021,246, 111122. [CrossRef]
16.
Junasová, B.; Krajˇcík, M.; Šikula, O.; Arıcı, M.; Šimko, M. Adapting the construction of radiant heating and cooling systems for
building retrofit. Energy Build. 2022,268, 112228. [CrossRef]
17.
Feng, J.; Borrelli, F. Design and Control of Hydronic Radiant Cooling Systems. Ph.D. Thesis, University of California, Berkeley,
CA, USA, 2014.
Energies 2024,17, 1951 21 of 22
18.
Nageler, P.; Schweiger, G.; Pichler, M.; Brandl, D.; Mach, T.; Heimrath, R.; Schranzhofer, H.; Hochenauer, C. Validation of dynamic
building energy simulation tools based on a real test-box with thermally activated building systems (TABS). Energy Build. 2018,
168, 42–55. [CrossRef]
19.
ISO 11855-4:2021; Building Environment Design—Desig Installation and Control of Embedded Cooling Systems: Part 4: Dimen-
sioning and Calculation of the Dynamic Heating and Cooling Capacity of Thermo Active Building Systems (TABS). International
Organization for Standardization: Geneva, Switzerland, 2021.
20.
Behrendt, B. General Rights Possibilities and Limitations of Thermally Activated Building Systems Simply TABS and a Climate
Classification for TABS. Ph.D. Thesis, Technical University of Denmark, Kongens Lyngby, Denmark, 2016.
21.
Lu, F.; Yu, Z.; Zou, Y.; Yang, X. Cooling system energy flexibility of a nearly zero-energy office building using building thermal
mass: Potential evaluation and parametric analysis. Energy Build. 2021,236, 110763. [CrossRef]
22.
Saelens, D.; Parys, W.; Baetens, R. Energy and comfort performance of thermally activated building systems including occupant
behavior. Build. Environ. 2011,46, 835–848. [CrossRef]
23.
Rijksen, D.O.; Wisse, C.J.; Schijndel, A.W.M.V. Reducing peak requirements for cooling by using thermally activated building
systems. Energy Build. 2010,42, 298–304. [CrossRef]
24.
Samuel, D.L.; Nagendra, S.S.; Maiya, M.P. Parametric analysis on the thermal comfort of a cooling tower based thermally
activated building system in tropical climate-An experimental study. Appl. Therm. Eng. 2018,138, 325–335. [CrossRef]
25.
Ning, B.; Schiavon, S.; Bauman, F.S. A novel classification scheme for design and control of radiant system based on thermal
response time. Energy Build. 2017,137, 38–45. [CrossRef]
26.
Samuel, D.L.; Nagendra, S.S.; Maiya, M. A sensitivity analysis of the design parameters for thermal comfort of thermally activated
building system. Sadhana 2019,44, 48. [CrossRef]
27.
Chandrashekar, R.; Kumar, B. Experimental investigation of thermally activated building system under the two different floor
covering materials to maximize the underfloor cooling efficiency. Int. J. Therm. Sci. 2023,188, 108223. [CrossRef]
28.
Rakesh, C.; Vivek, T.; Balaji, K. Experimental investigation on cooling surface heat transfer behavior of a thermally activated
building system in warm and humid zones. Case Stud. Therm. Eng. 2023,49, 103254. [CrossRef]
29.
Szpytma, M.; Rybka, A. Ecological ideas in Polish architecture—Environmental impact. J. Civ. Eng. Environ. Arch. 2016,
XXXIII, 321–328. [CrossRef]
30. pyDOE3 1.0.1. Available online: https://pypi.org/project/pyDOE3/1.0.1/ (accessed on 10 January 2024).
31.
ISO 10456:2007; Building Materials and Products. Hygrothermal Properties. Tabulated Design Values and Procedures for
Determining Declared and Design Thermal Values. International Organization for Standardization: Geneva, Switzerland, 2007.
32.
ISO 10077-1:2017; Thermal Performance of Windows, Doors and Shutters. Calculation of Thermal Transmittance. Part 1: General.
International Organization for Standardization: Geneva, Switzerland, 2017.
33.
ISO 6946:2017; Building Components and Building Elements. Thermal Resistance and Thermal Transmittance. Calculation
Methods. International Organization for Standardization: Geneva, Switzerland, 2017.
34.
2021 ASHRAE® Handbook—Fundamentals (SI Edition); American Society of Heating, Refrigerating and Air-Conditioning Engineers,
Inc. (ASHRAE): Atlanta, GA, USA, 2021.
35.
Heat Flux Plate, Heat Flux Sensor HFP01 & HFP03. User Manual. Hukseflux Manual v1721. Available online: https://www.
fiedler.company/sites/default/files/dokumenty/hfp01_hfp03_manual_v1721.pdf (accessed on 10 January 2024).
36.
LPPYRA03.. . Series—Spectrally Flat Class C Pyranometers. Available online: https://pvl.co.uk/products/lppyra03-series-
spectrally-flat-class-c-pyranometers (accessed on 10 January 2024).
37.
Walikewitz, N.; Jänicke, B.; Langner, M.; Meier, F.; Endlicher, W. The difference between the mean radiant temperature and the air
temperature within indoor environments: A case study during summer conditions. Build. Environ. 2015,84, 151–161. [CrossRef]
38. Kazkaz, M.; Pavelek, M. Operative temperature and globe temperature. Eng. Mech. 2013,20, 319–325.
39.
d’Ambrosio Alfano, F.R.; Ficco, G.; Frattolillo, A.; Palella, B.I.; Riccio, G. Mean Radiant Temperature Measurements through
Small Black Globes under Forced Convection Conditions. Atmosphere 2021,12, 621. [CrossRef]
40.
d’Ambrosio Alfano, F.R.; Pepe, D.; Riccio, G.; Vio, M.; Palella, B.I. On the effects of the mean radiant temperature evaluation in
the assessment of thermal comfort by dynamic energy simulation tools. Build. Environ. 2023,236, 110254. [CrossRef]
41.
2638A Hydra Series III Data Acquisition System/Digital Multimeter. Available online: https://www.fluke.com/en-ca/product/
precision-measurement/data-acquisition/fluke-2638a (accessed on 10 January 2024).
42.
IEC 60751:2022; Industrial Platinum Resistance Thermometers and Platinum Temperature Sensors. International Electrotechnical
Commission: Geneva, Switzerland, 2022.
43.
BIPM. Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement (GUM 1995 with Minor Correction);
JCGM 100: 2008; BIPM: Geneva, Switzerland, 2008.
44.
Directive 2014/32/EU of the European Parliament and of the Council of 26 February 2014 on the harmonisation of the laws of
the Member States relating to the making available on the market of measuring instruments (recast). Off. J. Eur. Union 2014,
L96, 149–250.
45.
ISO 11855-2:2021; Building Environment Design—Embedded Radiant Heating and Cooling Systems Part 2: Determination of the
Design Heating and Cooling Capacity. International Organization for Standardization: Geneva, Switzerland, 2021.
Energies 2024,17, 1951 22 of 22
46.
PN EN 12831-1:2017; Energy Performance of Buildings—Method for Calculation of the Design Heat Load. Polish Committee of
Standardisation: Warsaw, Poland, 2017.
47.
Awbi, H.B. Calculation of convective heat transfer coefficients of room surfaces for natural convection. Energy Build. 1998,
1998, 219–227. [CrossRef]
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