A system to monitor and model the thermal isolation of coating compounds applied to closed spaces

Abstract

Smart control systems and new technologies are necessary to reduce the energy consumption in buildings while achieving thermal comfort. In this work, we monitor the thermal evolution inside a scale reduced closed space whose exterior and/ or interior wall faces have been painted with a coating solution. Based on the experimental data obtained under different environmental conditions, a simulator was developed and tuned to reproduce the thermodynamic behavior inside the spaces, with a relative error of less than 3.5%. This simulator lets us also estimate energy savings, temperature, and flux behavior under other conditions.

Full text

A system to monitor and model the thermal isolation of coating
compounds applied to closed spaces
Frank Florez Montesa, Pedro Fernández de Córdobab, José Luis Higón Calvetc,
J. Alberto Conejerob, José-Luis Poza-Lujánb.
aFaculty of Engineering and Architecture, Universidad Nacional de Colombia, Campus la Nubia, 170003
Manizales, Colombia, email: frflorezmo@unal.edu.co
bInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valéncia,
Spain, email: pfernandez@mat.upv.es, aconejero@mat.upv.es
cDepartment of Architectural Graphic Expression, Universitat Politècnica de València, 46022 Valéncia,
Spain, email: jhigonc@ega.upv.es
dInstituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022
Valencia, Spain, email: jopolu@upv.es
corresponding author: José-Luis Poza-Luján
Smart control systems and new technologies are necessary to reduce the en-
ergy consumption in buildings while achieving thermal comfort. In this work, we
monitor the thermal evolution inside a scale reduced closed space whose exterior
and/or interior wall faces have been painted with a coating solution. Based on the
experimental data obtained under different environmental conditions, a simula-
tor was developed and tuned to reproduce the thermodynamic behavior inside the
spaces, with a relative error of less than 3.5%. This simulator lets us also estimate
energy savings, temperature, and flux behavior under other conditions.
Keywords: Coating, Thermal isolation; Building modeling; Energy savings.
1 Introduction1
The reduction of energy consumption is a critical factor for urban sustainability. The main efforts are asso-2
ciated with achieving thermal comfort in residential and commercial buildings [1, 2]. Different technologies3
and strategies are alternatives to the use of Heating, Ventilating, and Air Conditioning (HVAC) systems,4
which have been historically criticized for their high energy consumptions.5
Passive strategies search to mitigate the heat transfer between the thermal zones and the environment,6
using new materials and alloys for construction or retrofitting in order to give buildings a better resistance7
against the environmental conditions [3]. However, these solutions are still in development and its deploy-8
ment is subject to the economic cost, durability, climatic factors, and facilities of installation.9
Passive techniques for thermal isolation can be classified according to different aspects, such as the heat10
exchange properties, composition, and form [4]. Additionally, depending on its use of shading or isolation,11
it can incorporate ambient benefits. For example, the installation of photo-voltaic panels on the rooftop of12
a building permits to generate electric energy in situ and to approximate the building to a zero consume13
[5, 6]. Another important initiative is the use the green roofs that changes the surfaces albedo and reduces14
1

the solar radiation absorption. Besides, they also report ambient benefits such as the stormwater retention,15
the reduction of the urban heat island effect, and the increase of the roofs lifespan [7].16
Retrofitting of existing buildings and reducing the use of HVAC systems, is a trending line of research17
around the world [8, 9]. The effect of materials such as aerogels, cork lime and PIR over the thermal18
transmittance of the walls of a historic building in Dublin was analyzed in [10]. In India, the isolation given19
by a thermal paint on the facade and rooftop of a building provided reductions of 4.4◦C[11]. Similarly, in20
Shanghai, the reflectance of the walls after applying thermal paints increase from 32% until 61% [3].21
Most of these passive strategies are designed and tested in warm regions, since they present problems of22
holding back the heat contained in buildings on cold regions. Nevertheless, coating solutions can be adjusted23
for both climates. They consist on their application over the faces of the building to be thermally isolated.24
On the one hand, if they are applied on the interior surfaces, they can create a greenhouse effect reducing the25
warming needs of the people living there. On the other hand, their application on the external surfaces can26
increase the convection process to evacuate the internal heat or to reflect the solar radiation [12, 13, 14].27
To quantify thermal reductions and energy savings of thermal coating solutions , experimental results28
are needed. They can be obtained from existing buildings, from experiments on a lab, where environmental29
conditions are controlled [2, 15], or from a combination of both of them. In any case, the development of a30
mathematical model would permit to extrapolate the results to different conditions.31
In this article, we construct and validate such a model to quantify the thermal isolation and energy32
savings of s coating solution with low thermal conductivity. More information on the thermal conductivity33
properties of polymers at molecular level can be found in [16].34
We built three scale-reduced models. They were evaluated indoor, for minimizing the effect of envi-35
ronmental disturbances, and outdoor, for evaluating the influence of the weather conditions. We designed a36
control system to collect data from the experiments. Based on the experimental data recorded, we developed37
a simulator that can reproduce the obtained experimental results with high accuracy. It allows us to estimate38
the behavior of the models under different experimental conditions.39
In Section 2, we describe the experiment and the characteristics of the mathematical model chosen for40
the simulator. Later, we describe the indoor and outdoor tests carried out in València (Spain) and the results41
of the simulations in Sections 3 and 4. In Section 5, we calculate the thermal impact of the solution over the42
inner temperature of the models. Finally, we show the conclusions and lines of future work in Section 6.43
2 Design of the experiments and methodology44
We have considered a water-proof insulating coating with very low thermal conductivity and high resistance45
to weathering. It has a stable aqueous dispersion and is formed of a very heavy molecular styrenoacrylic46
polymer. The product presents a thermal conductivity λ= 0.0556 W
mK .47
To test the effect of this coating solution on heat transfer, we built 3 reduced scale thermal zones with48
wooden boxes (named U, I, O) of dimensions 0.4×0.545 ×0.7m3and thickness of 15.8mm. Each box is49
equipped with a 60Wincandescent internal lamp with infrared light to generate thermal gradients between50
the air contained in the box and the air outside. Box Uwas left in its original state (unpainted), with no51
coating applied on their surfaces. We apply a coating layer of 0.5mm on the inner faces of box I. Finally,52
a similar coating layer was applied on the outer surfaces of box O. In each one of the boxes, an electrical53
2

installation was implemented in order to supply energy to the internal lamp and to the temperature and54
humidity sensor Data Logger Whöler CDL. The final result is shown in Figure 1. To guarantee the correct55
development of the experiment, and to reduce sources of interruption, we initially carried out tests of ignition56
cycles with the models in a closed space, where abrupt changes in ambient temperature and solar radiation57
were minimized.58
To manage the experiments, we developed a distributed control system that allowed varying tempera-59
tures, validating conditions, and managing data collection. Each box has a control node, based on Arduino,60
that allows it to change temperature, to validate the conditions, and to manage the data collected. Control61
nodes are connected to a database server in order to get experiments configuration and to send the data col-62
lected. This system allows planning cycles of experiments for each box. With this, we can contrast the data63
collected by the sensors with the conditions in order to ensure the coherence of the results.64
Figure 1: Wooden boxes U,I, and Owith internal gains.
2.1 Mathematical model and tuning process65
We have considered a simulator based on the mathematical model, obtained with the technique of Lumped66
Parameters, which is described in [17]. This model lays on the analogy between thermal and electrical67
phenomena. More precisely, the temperature is represented by voltage, the heat flux by an electric current,68
thermal resistance is defined as the resistance to heat transfer through walls, and the wall’s capacity to69
accumulate energy is identified with capacitors. The following equations described the transfer processes in70
any one of the boxes, whose six faces are indexed with i= 1, . . . 6.71
dTi,ex
dt =Ti
Ri,exCi,ex
−Ti,ex 1
Ri,exCi,ex
+1
Ri,midCi,ex +Ti,in
Ri,midCi,ex
(1)
72
dTi,in
dt =Ti,ex
Ri,midCi,in
−Ti,in 1
Ri,midCi,in
+1
Ri,inCi,in +T
Ri,inCi,in
(2)
73
dT
dt =T1,in −T
R1,inCr
+T2,in −T
R2,inCr
+T3,in −T
R3,inCr
+T4,in −T
R4,inCr
+T5,in −T
R5,inCr
+T6,in −T
R6,inCr
+uIL
Cr
(3)
The internal heat source is represented by uIL, where ILis the heat power source, and uis the source74
state. Ti,in and Ti,ex are superficial temperatures, and the internal temperature is presented by T. Capacitors75
Cr,Ci,in and Ci,ex, and resistors Ri,mid are calculated in terms of the physical parameters of the materials76
3

(wood and internal air) summarized in Table 1. Resistances Ri,in and Ri,ex are calculated with the convection77
and radiation coefficients that are tuned to the specific conditions of the test. For convection with natural78
ventilation we initially took 60 kJ
hm2kand the emissivity coefficient of white painted wood was set to 0.9, see79
[17, 18]. With these values, we run a fitting algorithm to look for the values of the parameters that provide a80
best fitting of the solutions respect to the data obtained from the indoor experiments. Later, these values let81
us calculate the resistances and capacitors in equations (1),(2) and (3). Results are presented in Table 2.82
Material Parameter Value
Wood Conductivity 0.645 KJ
hmK
Density 700 kg
m3
Specific heat 1.6KJ
kgK
Air Density 1.2kg
m3
Specific heat 1.007 KJ
kgK
Coating solution Density 1250 kg
m3
Conductivity 0.2002 KJ
hmK
Table 1: Coating solution and material parameters
3 Indoor simulation and experimental results83
A first indoor test was required to tune the convection and radiation coefficients of the internal and external84
surfaces of the boxes. That experiment was conducted on March 15th, 2018, and it lasted 24 hours. The first85
6 hours the lamp was turned on, producing a period of charge and heat transfer from the air contained in the86
boxes to the environment, which remained in the range of 14.6◦Cto 17.3◦C, with an average temperature87
of 16◦C. For the rest of the test, the lamp was off. With these experimental data, we determined the best88
values for tuning the heat transfer coefficients for each box and lamp state, see Table 2, by using the Pattern89
Search optimization algorithm of Matlab OptimTool. Here, hiand hoare the internal and external convection90
coefficients, and eiand eoare the internal and external emissivity of the surfaces.91
Box Lamp state hi[K J
hm2K]ho[KJ
hm2K]eieo
U (unpainted) Active 44.6875 11.1250 0.9430 0.9
Inactive 0 9.7324 0.0211 0.8805
O (outer) Active 44.6875 19.0938 0.9430 0.9
Inactive 0 10.4910 0.0211 0.8
I (Inner) Active 20.4805 11.1250 0.99 0.9
Inactive 0.2578 9.7324 0.0190 0.8805
Table 2: Heat transfer coefficients
Comparing the real temperatures with the ones provided by the simulations, see Figure 2, we obtain92
an error of around 3% (2.7% in box U, 2.8% in box I, and 3.5% in box O). It is possible that replacing93
derivatives by fractional derivatives would improve the predictions, see [19].94
4

Figure 2: Temperatures during the indoor experiment at boxes U(left), I(middle), and O(right).
4 Simulation and experimental results outdoors95
On July 12th, 2018, we conducted an outdoor experiment in a protected space. As in the indoor experiment,96
the tests were carried out with the same data logger. Additionally, contact sensors (DS18b20) were used97
to measure the surface temperatures of the upper and lower faces in each box. The central data acquisition98
was done with an ESP32 LOLIN32 Lite card. Initially, continuous loading and unloading tests were carried99
out, beginning at 12:00 pm. The loading phases lasted 8 hours, while discharge phases lasted only 4 hours.100
Figure 3 shows the evolution of the internal temperature in all the boxes along three days of sampling.101
Figure 3: Experimental results in all the boxes during outdoor experiments.
As mentioned above, internal and external surface temperatures were also measured. Figure 4 shows102
the evolution of these temperatures at each box. With these data, it is possible to calculate the thermal103
transmittance Tdefined by equation (4), where Land kdefine the thickness and conductivity of the walls104
[20].105
T=1
1
hi+1
ho+L
kKJ
hm2K(4)
During the active periods of the day, the transmittance values at the boxes were: 6.1124 K J
hm2Kat box106
U,7.2939 KJ
hm2Kat box I, and 1.004 KJ
hm2Kat box O. With these results, we conclude that for high external107
temperatures, it is counterproductive to paint the internal faces of the boxes.108
5

Figure 4: Internal and superficial temperature of box U (left), I (middle), and O (right).
The next test was performed on July 19th, 2018. This time the lamp was turned off during the entire test;109
the average environmental temperature was 35◦C. Figure 5 shows the temperature registered inside boxes U110
and O, since it lacks of sense to study box Iin this case.111
Figure 5: Internal temperature of boxes Uand Oduring outdoor experiments.
In order to properly reproduce the outdoor data, it was also necessary to adjust the model to the new112
environmental conditions. One of the main differences between both situations is the ambient radiation: in113
the case of the indoor tests it was practically constant while in the open air it changes considerably throughout114
the day. The interaction of a body with the environment by radiation is defined by the Stefan-Boltzman law115
showed in equation (5). This allows to calculate the heat absorbed and issued from and to the environment by116
any surface. The radiation emission coefficient (ε) depends on the material, while the absorption coefficient117
(α) is related to the ambient radiation [21]. The surface and environmental temperatures are denoted by118
Tsurf and Tenv and Qstands for the heat transferred by radiation.119
˙
Q=εσT 4
surf −ασT 4
env (5)
Another important treatment of the simulation was the establishment of three periods of analysis. We120
show in Table 3 the coefficients for each period. Figure 6(a) shows the results obtained from the simulator121
for box U, with an error of 1.6% with respect to the experimental data, while Figure 6(b) shows the results122
for box O, with an error of 2.2%.123
6

Box Time hi[KJ
hm2K]ho[KJ
hm2K]ε α
Unpainted 8:00-12:00 0.1777 7.9688 0.9992 0.9323
12:00-20:00 0.0542 22.48 0.9992 0.9323
20:00-24:00 0.0542 22.48 0.9992 0.9870
External faces painted 8:00-12:00 68.4836 0.9332 0.9992 0.91
12:00-20:00 0.0107 0.0254 0.9992 0.8591
20:00-24:00 0.1 4.6666 0.9992 0.9705
Table 3: Parameters adjusted to outdoor environmental conditions.
Figure 6: Experimental and simulated results on boxes U (left) and O (right).
5 Energy savings124
Quantify energy savings is a hard task, since it depends on different factors such as electric sources, collection125
fees in each country, and seasonal factors [22]. However, temperature reductions are directly proportional to126
energy savings. We have determined the savings by comparison of the temperature in boxes with coating, I127
and O, respect to the unpainted one, U. With an average environmental temperature of 16◦C, the energy sav-128
ings obtained by taking box Iinstead of box Uare of around a 4.5%, and with an environmental temperature129
of 35◦C, the energy savings obtained when taking Oinstead of Uare around 7.4%.130
Finally, we have used our simulator for estimating energy savings on larger spaces and with different131
external temperatures. The original experiment had a volume of v1= 0.153m3and we used an internal132
lamp of 60W. For these new estimations, we have considered two different volumes: v2= 14.98m3and133
v3= 47.3m3; the last volume corresponds to a maritime container and the second one is an intermediate134
value. Setting the maritime container in a place with an external temperature of 35◦C(or the intermediate135
volume in a place with external temperature of 30◦C), the energy savings move up to 15%.136
6 Conclusions137
During the project development, reduced scale models were used to verify the impact of applying a coating138
solution to the internal and external faces of a building. The experiments were carried out using a distributed139
control system. That allows to configure a large number of possible experiments. Consequently, it is possible140
to collect data with adequate conditions to design the simulation. The indoor and outdoor tests allowed us141
to design an accurate simulator to analyze and reproduce the experimental results. This also let us predict142
7

energy savings with different models and under environmental conditions, and the determine the convenience143
of using a coating solution.144
First, we conclude that a greenhouse effect is generated when painting the internal faces of a closed145
space, since this prevents the heat flow from internal sources to the environment, which would be of interest146
for cold climates, where the efforts must be pointed to preserve the thermal energy in the interior of the147
thermal zones. Secondly, applying the solution on the outer faces contributes to significantly reduce the148
inner temperature, which would be interesting for warm climates.149
For future work we leave the evaluation of coatings on different models with materials such as con-150
crete and metal. Besides, it can be of interest to evaluate the effectiveness of the solution in locations with151
environmental temperatures under 0◦C.152
Acknowledgments153
This research was supported by the National Doctoral Program of the Colombian Administrative Department154
of Science Technology and Innovation (Colciencias).155
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