Heat Reflective Thin-Film Polymer Insulation with Polymer Nanospheres—Determination of Thermal Conductivity Coefficient

Abstract

In this paper, a method to determine the thermal conductivity coefficient λ in a 200 μm thick heat reflective paint layer, filled with polymer nanospheres with a Total Solar Reflectance (TSR) of 86.95%, is proposed and presented. For this purpose, a “hot box”-type (cube-shaped) test rig was built to carry out experimental tests to measure the temperature distribution on the surface of a double-layer wall containing the material under investigation. Together with the experimental studies, a CFD numerical model was prepared to understand the nature of flow and heat transfer inside the cube—the test chamber. Based on the proposed measurement and analysis method, the thermal conductivity coefficient of the heat reflective coating layer was λ = 0.0007941 W/m∙K.

1. Introduction

In the European Community (EC) countries, energy consumption in buildings is estimated to be around 40%, which entails a share of around 36% in greenhouse gas emissions into the atmosphere. This makes it necessary to save energy in the building industry (as in other sectors of the economy). The civilization idea was formulated, i.e., the postulate of the so-called sustainable development, a process aiming at satisfying the needs of the present generation in a way that enables future generations to fulfil the same aspirations. The postulate of sustainable development has been reflected in European legislation [1], where the basic requirements to be met by buildings, in terms of sustainable use of natural resources, have been formulated. A consequence of the basic requirements is also an increase in the requirements for the thermal insulation of building partitions. EC legislation obliges member states to introduce regulations that require all buildings (except historical buildings) to reach standards close to so-called “zero energy”. This includes deep thermal modernization, resulting in a significant improvement in the energy efficiency of buildings, where a key role in the development of new insulation materials is attributed to scientific research aimed at achieving “zero energy” standards.

Given the needs of the near future for building partitions, new insulation materials and manufacturing technologies are being developed in many research centers around the world. These materials will successfully meet “zero energy” requirements thanks to their insulating properties. A building material with high insulation parameters is FC-SA composite [2], the thermal conductivity of which at room temperature (about 30 °C) reaches λ = 0.049 W/m∙K. According to the authors’ estimate [2], this represents a 48.4% decrease, compared to the commonly used foam concrete.

In order to improve the properties of hydrothermal and insulation liners, a nanostructured additive (in the form of an aerogel) for insulation materials was proposed in [3]. Aerogel reinforced insulation materials were analyzed and the porosity and hydrothermal properties were evaluated at different ambient temperatures. The results showed that an increase in the aerogel content of the liner (up to 64%) resulted in a decrease in density, and thus a favorable thermal conductivity value of λ = 0.0465 W/m∙K was obtained at 20 °C. On the other hand, work [4] explains the effect of hybrid microfibers of polypropylene, basalt, carbon and glass (at elevated temperature), on the effective thermal conductivity of cement-based composites. This phenomenon is closely related to changes in both porosity and moisture content of the insulation material through its thermal dehydration. It has been shown that in the temperature range 20–400 °C the thermal conductivity varies over a small range: λ = 1.9–1.5 W/m∙K. A newly developed multi-layer reflective insulation system called “Mirror Panel” [5] was tested. Mirror Panel samples were made from layers of aluminum foil and coated paper. These layers were separated by air spaces approximately 5 mm thick. The apparent thermal conductivity of the Mirror Panel (in the temperature range 0–35 °C) was λ = 0.024–0.035 W/m∙K.

Advances in manufacturing technology have made it possible to produce ordered nanostructures as insulation materials for use in construction. This has made it possible to produce high-quality insulating materials with a λ = 0.01 W/m∙K [6]. Insulating materials with such properties are referred to as super insulators and include so-called empty packing structures of the nanosphere. This thermal conductivity coefficient is obtained for metal-organic structures (MOF) [7]. It has been found that the effective thermal conductivity can be reduced to about 0.01 W/m∙K by adjusting the packing style and size of the hollow packing structures of the nanosphere [6]. Hollow polymer structures (HGM microspheres) are used for so-called coarse modification of the insulation performance of common building materials, such as cement-based synthetic foams (CFS) [8]. For the thermal conductivity of polymer coatings with silica aerogel microspheres (depending on the volume fraction of microspheres), values between 0.01 and 0.04 W/m∙K are obtained [9]. The value of the thermal conductivity coefficient of HGM materials is significantly affected by the quality of the microspheres—especially those with a diameter of 10–100 μm. The reduction in quality is due to damage (cracking) of the microsphere surface. The thermal conductivity coefficient of insulation coverings, depending on the proportion of damaged (cracked) samples in the covering, is λ = 0.18–0.22 W/m∙K [10]. In [11], the authors proposed actual guidelines for the design and control of the preparation of composite materials with hollow polymer microspheres. They determined the relationship between thermal conductivity and actual density: for a density of 0.25–0.60 g/cm³ at T = 23 °C, the thermal conductivity coefficient can reach values λ = 0.05–0.09 W/m∙K. The obtained thermal conductivity values of polymeric materials, e.g., foam geopolymers with microspheres, are in the range of λ = 0.05223–0.0711 W/m∙K [12].

Producing lightweight thermal insulation materials with high strength and very low thermal conductivity is a major challenge and of growing interest worldwide. Interesting conclusions on the procedures for measuring thermal conductivity are presented in the paper [13]. The author discussed materials with very low thermal conductivity coefficients reaching values of λ = 0.001–0.003 W/m∙K. Such values of coefficients refer to thermally insulating thin-layer coatings (coating thickness 1–2 mm) with reflective properties achieved through ceramic microspheres. The binding material of the coating compounds with microspheres is a mixture of synthetic rubber and other polymers. The author, quoting divergent literature data and based on his own research experience, drew attention to the imperfection of the methodology used to perform measurements of heat conductivity coefficients in thin (1–2 mm) insulation layers.

In this paper, a method for determining the thermal conductivity λ in a 200-μm-thick heat reflective layer filled with polymer nanospheres is proposed and presented. When developing the method for determining the thermal conductivity coefficient, the experience presented in [13] was taken into account. Measurements were taken in a specially designed cube called a “hot box”, which was made from plasterboard. The method is recognized and widely used in in situ measurements of thermal properties of partitions of many insulation materials in steady and dynamic conditions—the described case relates to the steady state. The literature widely describes the measurement methodology related to building materials [14,15,16,17,18,19,20,21,22,23] and thin-film insulation materials with reflective properties [24,25,26,27]. The research results obtained by the cited authors justify the credibility of the method. This allows to successfully use the “hot-box” method to measure the temperature distribution on the partition surfaces with a thin-film reflective coating (tested in this paper) as the most reliable experimental method of testing. This is confirmed in [24,25]. It should be noted, however, that the thermal assessment of reflective insulation is a relatively rare study discussed in the literature (as indicated by the authors in [24,25]). Usually, thin films and mats are tested, while thin-layer coatings (coatings, paints) have practically not found a permanent, extensive place in the literature on the subject. The basis for determining the thermal conductivity coefficient λ were measurements of the temperature distribution on the inner and outer surfaces of the cube. The heat transfer coefficient was determined using the method of heat flow balance through the walls of the cube, in which the Fourier equation was the basis for describing the heat transport process under steady-state conditions. Then, in order to identify the nature of the flow and heat transfer inside the cube—the test chamber, the experimental results were confronted with the developed CFD numerical model.

2. Materials and Methods

2.1. Materials Characteristic

Tests to determine the thermal conductivity λ were carried out for a white paint (named “IZOPLUS”) with thermal insulation and heat reflective properties. The paint was manufactured in the research laboratory of the Adalio company. The manufacturing technology and composition are patent protected [28]. The emulsion paint is based on a selected resin polymer filled with a reflective material in the form of polymer microspheres with a diameter of 5–60 μm. Microspheres are essentially so-called “traps” with dimensions in the infra-red wavelength range (10–100 μm). A ray of light entering the microsphere (“trap”) is subjected to multiple reflections and is then directed towards the entrance. The idea behind the reflective paint layer is shown in Figure 1. The density of the wet emulsion was 0.5–0.60 g/cm³, dry 0.3360 g/cm³.

The company’s own research [15] has shown that the thermal conductivity coefficient of “IZOPLUS” paint, unlike that of other insulating materials (e.g., mineral wool, corkboard), does not depend on temperature. This indicates that the heat conduction mechanism of the reflective paint layer is not solely based on thermal conduction phenomena. This mechanism is further characterized by the reflection of heat radiation. In order to determine the value of the total solar reflectance index (TSR), using the Jasco V-670 two-beam UV/VIS/NIR spectrometer with a 150 mm integrating ball, tests were carried out for the coating—“IZOPLUS” white paint. Total Solar Reflectance—TSR measurement was made for solar radiation in the wavelength range from 250 nm to 2500 nm. The material tested (white reflective paint) is characterized by a high solar reflectance of 86.95%, in the radiation range 250–2500 nm [29]. The value of the total solar reflectance index in an accredited laboratory was calculated according to ASTM Standard Test Method for Solar Absorptance, Reflectance and Transmittance of Materials Using Integrating Spheres, based on the radiation energy values for individual wavelengths, taken from tables containing the spectral distributions of hemispheric solar radiation (direct and diffused radiation), found in ASTM G173–03 Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 370 Tilted Surface. The results of measurements of the total solar reflectance TSR for the coating with the “IZOPLUS” white heat reflective paint are shown in Figure 2.

The exceptional properties of microspheres, in terms of reflecting infra-red (thermal) radiation, result from their size in relation to the length of a wave of infra-red radiation. The wavelength of this radiation is in the range 10–100 μm.

2.2. Experimental Section

An experimental study was carried out to identify the thermal conductivity λ for paints with thermally insulating and heat reflective properties, using the “IZOPLUS” paint as an example. The thermal conductivity coefficient λ₁ for the test paint with reflective properties was determined under laboratory conditions, using a specially constructed test stand called “hot box”, shown in Figure 3.

The test rig was constructed as a closed cube (0.75 m side length) of 12.5 mm (0.00125 m) thick plasterboard. Hence the dimensions of the cube were 0.75 × 0.75 × 0.75 m. The gypsum boards used were weighed. The mass of each was the same at 4.4 kg. The base of the cube and the top wall parallel to the base were additionally insulated with a 0.3m layer of polystyrene with thermal conductivity coefficient λ = 0.036 W/(m∙K). All walls were coated internally with the test “IZOPLUS” white heat reflective paint. The thickness of the paint layer was 240 μm. The “hot box” measuring cube was placed on a levelled measuring table. The heat source was an infra-red light bulb, which was placed exactly at the geometric center of the cube. It was connected to an AC supply, with an ammeter and resistor connected in series. The ammeter and resistor allowed to determine the power of the bulb at 100 W. During the experiment, the measuring walls were the four side walls that were not insulated. On both sides of the measuring walls (inside the cube and outside) temperature sensors of PT-100 type were placed. Sensors indicated the magnitude of the temperatures on the wall surfaces. An additional thermometer measuring the ambient temperature was installed outside the “hot box”.

A schematic of the test chamber along with the location of the heat source and the placement of the sensors is shown in Figure 3.

Temperature measurements were made 4 days after switching on the heat source, i.e., only after obtaining stable values of temperature distribution on the inner and outer surface of the wall (partition consisting of two layers—gypsum board and covering its inner surface with white heat reflective paint). The stability of the temperature distribution was checked using a thermal imaging camera FLIR T620. A total of 10 measurement trials were performed at an ambient temperature of 19.3 °C. The ambient room temperature was maintained at the same level for each measurement. With a stable distribution of the temperature field on the inner and outer surfaces, all the heat passing through the side partitions (side walls of the cube) to the outside was equal to the heat output of the heat source of 100 W.

The obtained temperature courses allowed the estimation of heat movement through the tested wall partition made of plasterboard covered with heat reflective paint, for which the thermal conductivity coefficient λ₁ (W/m∙K) was to be determined.

2.3. Methodology for Determining the Thermal Conductivity

In order to determine the thermal conductivity coefficient of the heat reflective material tested, an analytical procedure was used in which the Fourier heat transfer equation was the starting point. The equivalent heat transfer coefficient for the tested paint λ₁ was calculated using the model presented below (Figure 4), according to relations (1)–(6).

The transport process of heat transfer through the partition is fixed, so the following relationships occur:

$$\dot{q}={\alpha }_1\left(T_1-T_2\right)=\frac{{\lambda }_1}{{\delta }_1}\left(T_2-T_3\right)=\frac{{\lambda }_2}{{\delta }_2}\left(T_3-T_4\right)={\alpha }_2\left(T_4-T_5\right),$$

(1)

the heat flux density is:

$$\dot{q}=\frac{\dot{Q}}{F } ,$$

(2)

thus:

$$\frac{{\lambda }_1}{{\delta }_1}\left(T_2-T_3\right)=\dot{q}\to T_3=T_2-\frac{\dot{q}·{\delta }_1}{{\lambda }_1},$$

(3)

and:

$$\frac{{\lambda }_2}{{\delta }_2}\left(T_3-T_4\right)=\dot{q}\to T_3=\frac{\dot{q}·{\delta }_2}{{\lambda }_2}+T_4,$$

(4)

From relations (3) and (4) the condition (5) of equality of temperature T₃ on the contact surface of the heat reflective covering and the plasterboard was obtained equal:

$$T_2-\frac{\dot{q}·{\delta }_1}{{\lambda }_1}=\frac{\dot{q}·{\delta }_2}{{\lambda }_2}+T_4,$$

(5)

After transforming relation (5) in an analytical manner, the heat transfer coefficient ${\lambda }_1$ for the inner layer of the heat reflective coating of the tested material was determined in an analytical manner and is equal to (6):

$${\lambda }_1=\frac{\dot{q}·{\delta }_1}{\left(T_2-T_4-\frac{\dot{q}·{\delta }_2}{{\lambda }_2}\right)}=\frac{\dot{q}·{\delta }_1·{\lambda }_2}{{\lambda }_2\left(T_2-T_4\right)-\dot{q}·{\delta }_2},$$

(6)

where

• $\dot{Q}$—heat flux generated inside the measuring system (cube) (W),
• $\dot{q}$—heat flux density (W/m²),
• $F$—heat exchange surface area (m²),
• $T_2$, $T_3$, $T_4$—temperature distribution on heat transfer surfaces (K),
• $T_1$—temperature inside the measuring box (K),
• $T_5$—temperature outside the measuring box (ambient temperature) (K),
• ${\delta }_1$—thickness of plasterboard partition (m),
• ${\delta }_2$—thickness of heat reflective covering layer (m),
• λ₁—thermal conductivity coefficient of heat reflective covering layer(W/m∙K),
• λ₂—thermal conductivity coefficient of gypsum board (W/m∙K).

The necessary data for the calculation of the thermal conductivity coefficient λ₁ for the tested heat reflective covering, i.e., the temperature distributions T₂, T₄, were obtained based on measurements carried out with temperature sensors PT-100. The thickness of the heat reflective paint coating was calculated from the volume of paint used to paint the inner surface of the walls of the measuring cube. The thickness of the plasterboard was measured with a caliper.

Table 1. Data for the calculation of the equivalent thermal conductivity λ₁ of the heat reflective material tested.

Item	Parameter	Value
Heat flux generated inside the measuring system	$\dot{Q}$ [W]	100
Total heat transfer surface area	$F$ [m2]	2.25
Heat flux density	$\dot{q}$ [W/m2]	44.44
Thickness of heat reflective coating	${\delta }_1$ [m]	0.00024
Plasterboard wall thickness	${\delta }_2$ [m]	0.0125
Thermal conductivity coefficient of a plasterboard wall	λ2 [W/m∙K]	0.23

shows the data used to calculate the equivalent thermal conductivity λ₁ (W/m∙K) of the tested material.

2.4. Numerical Model

A numerical model of a “hot box” test rig including steady-state flow and heat transfer was developed according to Figure 5. The numerical grid (Figure 5) was built of 540.000 polyhedral cells. In the central part of the air-filled chamber, a model of a light bulb was placed, the upper part of which constituted the heat source (heat flux) corresponding to the power of a 100 W bulb. The convective motion of the air inside the “hot box” was modelled using classical equations with the implementation of the Realizable k-ε turbulence model enables the Reynolds turbulent equations to be closed. The Energy equation [30] and the DO radiation model [30] were used for heat-transfer modelling. The bulb was a source of heat. Based on the bulb’s data, the heat flux = 13,116 W/m² condition was defined. No heat flow was assumed on the upper and lower walls of the cube—heat flux = 0 W/m². The side walls were modelled by means of a shell conduction condition [30], i.e., two layers corresponding to a physical layer of gypsum [Thickness δ₂ = 0.01 m, Thermal conductivity λ₂ = 0.23 W/(m∙K)] and an insulation coating [Density ς = 300 kg/m³, Specific Heat Cp = 1300 J/(kg∙K), Thickness δ₁ = 0.0002 m, Thermal conductivity λ₁ = 0.00079 W/(m∙K)].

3. Result and Discussion

The determination of the thermal conductivity coefficient of the tested heat reflective layer, 240 μm thick, was based on the measurement of temperatures on the internal and external surface of a wall partition made of plasterboard covered with heat reflective paint. The measurement results are shown in Figure 6.

Figure 7 shows the temperature profile on the side walls of the measuring cube on the inner plane covered with a heat reflective layer and on the outer plane not covered with a heat reflective layer. The mean square error (standard deviation) was calculated, expressed by the deviation of the measured values from the mean value. The mean square error for the temperature T₂ is 0.1917, and for the temperature T₄ it is 0.1487.

The values shown in Figure 7 refer to the averages of the measurements at the inner wall plane and the averages of the temperature distribution at the lateral planes of the outer walls. The temperature waveforms clearly show a stable distribution of the measured temperatures on the inner side walls. The resulting average temperature difference between the environment and the interior of the measuring cube was 13.12 °C. The above measured data, taking into account the average values of temperatures T₂ and T₄ and the data from Table 1, were substituted into Formula (6), according to which the thermal conductivity coefficient of the heat reflective coating layer was calculated. This factor is:

$${\lambda }_1=\frac{44.44·0.0002·0.23}{0.23·\left(37.55-24.43\right)-44.44·0.01}=0.00079431 \mathrm{W}/\mathrm{m}·\mathrm{K}.$$

The results obtained with the numerical model are shown in Figure 8, Figure 9, Figure 10 and Figure 11.

The temperature distribution on the outer surface of the side walls (Figure 8) coincides with analogous temperature distributions obtained with a thermal imaging camera (Figure 6). The mean values of the temperatures on the outside of the walls were also compared (

Table 2. Summary of temperature measurement results on the inner and outer walls of the “hot box” measuring cube.

Side Walls of the Measuring Cube	“Hot Box” Wall Temperature [°C]
	$\mathbf{Inner} {\mathit{T}}_2$	$\mathbf{Outer} {\mathit{T}}_4$
Area 1	37.9	24.6
Area 2	37.4	24.1
Area 3	37.3	24.6
Area 4	37.6	24.4
Average temperature values	37.55	24.43
Numerical verification of mean values	36.59	24.44

). In the upper part of the walls, characteristic (“oval”) zones of increased temperature are visible (Figure 9 and Figure 10), which corresponds to the temperature distribution inside the “hot-box”. The warm air movement is central over the bulb towards the top wall. Then, the air is directed downwards along the walls (Figure 11). Considering the trajectory of the air particles inside the “hot-box” cube, as well as the low velocities below 0.05 m/s (Figure 11), it can be successfully assumed that convection is not the dominant mechanism—it does not play a significant role in the heat transfer process inside the cube. The recalculated measurement results are given in Table 2.

The measured temperature on the surface of the side wall of the “hot box” measuring station on the inside was 37.3–37.9 °C (average 37.55 °C), while on the outside 24.1–25.1 °C. The numerical verification resulted in an average temperature of 36.59 °C on the inner wall and 24.44 °C on the outer wall.

The tested material, with its very good thermal conductivity λ = 0.0007941 W/m∙K and high solar reflectance TSR = 86.95%, can be successfully used in construction. It can be used as insulation material in historic buildings under preservationist protection, where traditional methods of insulating the building envelope from the outside using insulating materials are not applicable. In this case, the use of thermal insulation coatings (paints) will improve its insulation performance as well as the technical condition of the façade.

Another application is the combination of the tested material with standard insulation (polystyrene foam or mineral wool), which will allow the use of a smaller thickness of traditional insulation which will make it possible to meet the requirements of WT2021 and even achieve lower values of heat transfer coefficients than those currently required [31]. This is very important in low and nearly zero energy buildings where insulation requirements are very high. A layer of test material with a thickness of 240 μm (0.00024 m) and λ = 0.0007941 W/m∙K corresponds to a thickness of 1 cm of insulating material, e.g., polystyrene or mineral wool, with a heat conductivity coefficient of λ = 0.04 W/m∙K.

Table 3. Comparison of the tested thin-film material thickness and the corresponding thickness of traditional insulation material (polystyrene or wool with λ = 0.04 W/m∙K).

Tested Material λ = 0.0007941 W/m∙K	Traditional Insulation Material λ = 0.04 W/m∙K
thickness [m]	thickness [m]
0.0002	0.010
0.0003	0.015
0.0004	0.020
0.0005	0.025
0.0006	0.030
0.0007	0.035
0.0008	0.040
0.0009	0.045
0.0010	0.050
0.004	0.200

presents a comparison of selected thicknesses of the tested material and the thickness of its equivalent, assuming that the thermal conductivity coefficient of the traditional insulation material is λ = 0.04 W/m∙K.

Table 3 shows that a mere 0.004 m of the test material can replace 20 cm of a traditional material, such as polystyrene or mineral wool with λ = 0.04 W/m∙K.

The material can also be used to paint surfaces that heat up very quickly and used as an insulator, e.g., to paint roofs, to insulate overheated attics in summer and as an additional insulating layer in winter.

According to the authors, the development of a research methodology for determining the thermal conductivity coefficient of thin-film materials, characterized by high heat reflectivity, is very important from the point of view of development and implementation of innovative insulation materials by companies involved in their production. Since the thermal conductivity coefficient value of insulating materials is an indicator of their quality, as shown in Table 3.

4. Conclusions

The measurement and analytical method proposed and presented for determining the heat conductivity coefficient of thin-layer materials (characterized by high thermal reflectivity) allowed to determine this coefficient for the layer (240 μm thick) of the white paint tested—in the form of an emulsion produced on the basis of a resin polymer filled with a polymer microsphere. The Total Solar Reflectance TSR value of paint is 86.95%. Based on the measurements, the thermal conductivity coefficient of the heat reflective coating layer—white paint—was λ = 0.00079431 W/m∙K.

The temperature distribution results obtained from the measurements showed good agreement with the temperature distribution results obtained from the numerical calculations. The average temperature measured on the inner wall was 37.55 °C, the average temperature calculated numerically was 36.59 °C. The temperature value on the outer walls according to the numerical algorithm was 24.44 °C, while the actual measurement indicated a temperature value of 24.43 °C.

On the basis of the analysis carried out, it can be concluded that the proposed test stand (“hot box” type) together with the presented measurement and analytical method can be successfully used to determine the thermal conductivity coefficient of thin-layer coatings characterized by high heat reflectivity.