In this study, we investigated the heat flux effect of thermal metamaterials, which can effectively suppress heat propagation, through the three-dimensional finite-difference time-domain techniques. When a concrete block was heated or cooled, different heat propagation characteristics were demonstrated according to the plate-shaped meta-structure embedded in the concrete block. Under the assumption that the overall thickness of the plate-shaped meta-structure is constant, separating the plate-shaped meta-structure into two or more layers has a better heat blocking effect than using a single plate-shaped meta-structure. In addition, the thermal blocking efficiency varies depending on the thermal metamaterial used as the plate-shaped meta-structure. The thermal blocking efficiency of the thermal metamaterials was better in the order of air, aerogel, Styrofoam, and paraffin. The result indicated that the heat transfer in a concrete block can be manipulated by controlling the material, number, and spacing of the plate-shaped meta-structures, and the proposed plate-shaped meta-structures can be applied to reduce the thickness of a concrete block containing an insulating layer used in buildings.

A metamaterial consists of a periodic array of meta atoms designed as a metal or dielectric material with a size much smaller than the wavelength of light in order to realize properties that do not exist in nature. Metamaterials are designed to interact with light and sound in ways that natural materials cannot and can be applied to new applications such as transparent cloak, high-performance lenses, efficient small antennas, and ultra-sensitive sensors.1–7 Metamaterials can block the propagation of ordinary waves, such as electromagnetic waves and sound waves, as well as light, and stealth functions are also possible.8–14 The type of metamaterial can be variously defined according to the operating wavelength and its function, and it can be broadly divided into electromagnetic wave, sound wave, and seismic metamaterial.

In recent years, the application range of metamaterials has been extended to studies on heat control.15–18 In particular, by applying a metamaterial to an electronic device that generates heat, it is possible to protect the circuit from heat by preventing the transmission of heat generated during circuit operation to neighboring circuits. Metamaterials can also be used in building structures that require high thermal insulation. Technological development is very important for the thermal diffusion of electronic devices in a situation where a nano-scale highly integrated circuit based on composite media, such as oxide-coated metallic grains, is required.19,20 Miton et al. proposed the invariance of diffusion equations for heat diffusion in metamaterials.21 Papers related to heat cloaks have been reported.22,23 From the thermal flux point of view, the control of heat flow by utilizing photonic materials and devices is becoming increasingly attractive because of its broad applications in energy conversion and modern computations, including thermoelectrics, thermal cloaks, thermal logic gates, and thermal diodes.24–28 As electronic devices are becoming smaller and the thickness of the concrete wall with a thermal insulator should be reduced, the development of a novel metamaterial-based structure that can exhibit a higher heat shielding effect in a smaller space is required.

In this study, we investigated the control of heat flux in a concrete block with a plate-shaped meta-structure as a thermal insulator. We aim to compare the heat flux effect for thermal blocking according to the plate-shaped meta-structures embedded in the concrete block through the finite-difference time-domain (FDTD) simulation. Thermal meta-structure models composed of the plate-shaped meta-structures were designed, and the heat transfer characteristics under the condition of heating and cooling were observed. The structural control of the proposed thin plate-shaped meta-structures based on thermal metamaterials could effectively suppress the heat transfer of the structure in the concrete block, and consequently reduce the thickness of the concrete block.

We propose a numerical simulation using FDTD to analyze the three-dimensional heat flux in a concrete block embedded with plate-shaped meta-structures, which is made of a conventional highly-thermal-insulating Styrofoam. Thermal conductivity was simulated by changing the plate-shaped meta-structures to air, aerogel, and paraffin instead of Styrofoam as the thermal metamaterial. The three-dimensional heat transfer can be described as follows:

Q+Qted=ρCPTt+ρCPuT+q
(1)
q=kT       
(2)

where ρ is the density, CP is the specific heat, T is the temperature, and k is the thermal conductivity. In the calculation, the heat transfer is significantly dependent on the thermal conductivity, density, and specific heat of the thermal metamaterials. For the Styrofoam used as a commercial insulator material, the thermal conductivity and density are relatively lower but the specific heat is higher than those of a concrete block. In static simulation, the calculation term of time is treated to be infinite, so that the thermal conductivity of the composite material is used as an important factor in the calculation. For the time-dependent model, however, the spatial distributions of material density and specific heat also play a significant role.24,29 Table I shows the calculation parameters for the concrete, Styrofoam, air, aerogel, and paraffin.

TABLE I.

Calculation parameters for the concrete, Styrofoam, air, aerogel, and paraffin.

ConcreteStyrofoamAirAerogelParaffin
Density (kg/m32300 35 1.18 @ 20 °C 25 777 
Specific heat (J/(kg·K)) 880 2300 1007 900 485 
Thermal conductivity (W/(m·K)) 1.8 0.035 0.024 0.03 0.35 
ConcreteStyrofoamAirAerogelParaffin
Density (kg/m32300 35 1.18 @ 20 °C 25 777 
Specific heat (J/(kg·K)) 880 2300 1007 900 485 
Thermal conductivity (W/(m·K)) 1.8 0.035 0.024 0.03 0.35 

All the aggregates were prepared in a saturated surface-dry state and dry-mixed with cement in a mixer pan of capacity 0.35 m3 for 1 min. Irregular gravel possessing a maximum size of 25 mm and natural sand were used as the coarse and fine aggregates, respectively, of the concrete mixture. For the targeted compressive strength of concrete, the water-to-cement ratio was determined to be 0.45. With control cylinders of diameter 100 mm and height 200 mm, the compressive strength and dry density of the concrete block measured at an age of 28 days were 32 MPa and 2200 kg/m3, respectively. The thermal conductivity of concrete was evaluated to be 1.6 W/m·K. The size of the fabricated concrete block was 150 × 150 mm2, and the size of the plate-shaped meta-structures inserted into the concrete block was 120 × 120 mm2. Styrofoam, aerogel, and air were used as the base materials of the plate-shaped meta-structure. Thermal infrared (IR) images were captured by using an IR thermography camera (T-420, FLIR) to monitor the temperature distribution of the fabricated concrete block without and with the plate-shaped meta-structures.

A rectangular parallelepiped structure is used as the base simulation model of the concrete block with the area of 150 × 150 mm2 in the thermally injected xy plane and the thickness of 50 mm in the thermal propagated z direction. (Fig. 1(a)) The initial temperature of the concrete block was set at 20 °C. To make the simulation condition similar to the experimental condition, the side of the concrete block in the xy plane was heated to 50 °C or 20 °C, and the four sides of the concrete block were set at 20 °C. Figure 1(b) shows the rectangular parallelepiped structures without the plate-shaped meta-structure and with four different plate-shaped meta-structures (one, two, five, and ten layers) as the concrete blocks. The area and thickness of each plate-shaped meta-structure were 120 × 120 mm2 and 10/5/2/1 mm (one/two/five/ten layers, respectively), respectively. Note that the plate-shaped meta-structure is based on the Styrofoam layer. The gap between the adjusted plate-shaped meta-structures was 6, 3, and 2 mm for two, five, and ten layers, respectively. The total thickness of the plate-shaped meta-structures without considering the gap between them was equal to 10 mm in all cases.

FIG. 1.

(a) Rectangular parallelepiped structure as the base simulation model of a concrete block. One side of the concrete block in the xy plane was set at 50 °C or 20 °C. Four sides of the concrete were set at 20 °C. (b) Rectangular parallelepiped structures without the plate-shaped meta-structure and with four different plate-shaped meta-structures (one, two, five, and ten layers).

FIG. 1.

(a) Rectangular parallelepiped structure as the base simulation model of a concrete block. One side of the concrete block in the xy plane was set at 50 °C or 20 °C. Four sides of the concrete were set at 20 °C. (b) Rectangular parallelepiped structures without the plate-shaped meta-structure and with four different plate-shaped meta-structures (one, two, five, and ten layers).

Close modal

To understand the effects of the thermal flow according to the number of plate-shaped meta-structures, the temperature changes for the concrete block without the plate-shaped meta-structures and with four different plate-shaped meta-structures during 300 min were observed. Figure 2(a) shows the distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of heating at 50 °C. As shown in the figure, the heat is transmitted to the center of the concrete block. After embedding plate-shaped meta-structures in the concrete block, the heat transfer is effectively blocked by the plate-shaped meta-structures, and the heat flow transmitted to the opposite plane is reduced. It was easily observed that the amount of heat propagated to the opposite plane of the concrete block is reduced with the increase in the number of plate-shaped meta-structures. To compare the results of exact temperature changes of the opposite plane, we simulated the temperature changes over 0–300 min for the concrete block without and with plate-shaped meta-structures. Figure 2(c) shows the temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of heating at 50 °C. For the condition of heating, the saturation temperature can be obtained by

T=22.372+16.568/[1+n0.110.87],

where n is the number of insulator layers. According to this calculation, the saturation temperature decreases with the increase in the number of insulator layers. For the only concrete block without the plate-shaped meta-structure, the temperature on the opposite plane becomes saturated at 38.9 °C after 100 min from the start of heating. As the plate-shaped meta-structures are added, the time required for saturation increases and the saturation temperature drops from 24.5 °C for a single layer to 22.67 °C for ten layers.

FIG. 2.

(a) Distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of heating at 50 °C. (b) Distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of cooling at 20 °C. (c) Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of heating at 50 °C. (d) Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of cooling at 20 °C.

FIG. 2.

(a) Distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of heating at 50 °C. (b) Distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of cooling at 20 °C. (c) Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of heating at 50 °C. (d) Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of cooling at 20 °C.

Close modal

Figure 2(b) presents the distribution of heat flow in the concrete block without and with plate-shaped meta-structures under the condition of cooling at −20 °C. It can be observed that the phenomenon of heat flow is similar to that of the heating condition. Figure 2(d) shows the temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of cooling at 20 °C. The initial cooling condition was set at 20 °C on one side in the xy plane of the concrete block and at 20 °C on four sides of the concrete block. The saturation temperature for the cooling condition can be expressed as follows:

T=16.8422.10/[1+n0.110.87].

The effect of heat transfer blocking under heating and cooling conditions is enhanced by the number of insulator layers. In case of the concrete block without plate-shaped meta-structures, the temperature is significantly lowered from 20 to 5.25 °C with time. The saturation time is close to 110 min. In case of applying the single plate-shaped meta-structures, the temperature on the opposite plane of the concrete block is 20 °C at 0 min and 14.02 °C at 140 min. The saturation temperatures are 15.22 and 15.99 °C for the two and five layers, respectively. The ten layers of the plate-shaped meta-structure showed a slightly reduced temperature from 20 to 16.44 °C with time. These results indicate that the increase in the number of plate-shaped meta-structures is a significantly effective method for suppressing the thermal flux. The plate-shaped meta-structure arranged into a multi-layer stack has low thermal conductivity, which makes the heat transfer slower, and can suppress heat transfer in the concrete block more efficiently.

To understand the thermal blocking effect according to the changes in the thickness of the concrete block, the temperature propagated to the opposite side of the concrete block embedded with four different plate-shaped meta-structures from the applied side of the concrete block was simulated with the decrease in the thickness of the concrete block from 50 to 40 mm at steps of 1 mm without changing the embedded plate-shaped meta-structures. Figure 3 shows the temperature changes according to the thickness of the concrete block. For the heating modes, as shown in Fig. 3(a), all cases of concrete blocks embedded with four different plate-shaped meta-structures showed that, as the thickness of the concrete block decreased, the temperature blocking effect was reduced, and accordingly the propagated temperature increased. It is also observed that, as the number of plate-shaped meta-structures decreased, the temperature propagated to the opposite side of the concrete block increased. When a single plate-shaped meta-structure was embedded in the 50-mm-thick concrete block, the temperature on the opposite side of the concrete block was increased to 24.51 °C. When two plate-shaped meta-structures were used, the thickness of the concrete block could be reduced to less than 45 cm to maintain the temperature of 24.50 °C. To maintain a similar temperature when using one layer of the plate-shaped meta-structure, the thickness of the concrete block can be reduced to 41 mm when five layers are used, and the thickness can be reduced to 40 mm or less when ten layers are used. Therefore, the thermal blocking is more efficient when ten plate-shaped meta-structures are embedded in the concrete block, which has the advantage of reducing the thickness of the concrete block, resulting in an increase in the living area ratio when constructing the building. Figure 3(b) presents the temperature changes for the cooling modes according to the thickness of the concrete block. Similar to the heating modes, temperature changes are consistent in that the saturation temperature decreases as the thickness of the concrete block decreases. When one side of the 50-mm-thick concrete block embedded with a single plate-shaped meta-structure was cooled to 20 °C, the temperature on the opposite side of the surface decreased to 14 °C. When using two plate-shaped meta-structures, the thickness of the concrete block could be reduced to 45 mm to maintain the temperature of 14 °C as with one layer of the plate-shaped meta-structure. The thickness of the concrete block was reduced to 42.5 mm for five layers and to 40 mm for ten layers.

FIG. 3.

Temperature propagated into concrete blocks embedded with four different plate-shaped meta-structures (one, two, five, and ten layers) by changing the thickness of the concrete block. The initial temperature applied to one side of the concrete block was set at 50 °C (a) and 20 °C (b).

FIG. 3.

Temperature propagated into concrete blocks embedded with four different plate-shaped meta-structures (one, two, five, and ten layers) by changing the thickness of the concrete block. The initial temperature applied to one side of the concrete block was set at 50 °C (a) and 20 °C (b).

Close modal

To expand the plate-shaped meta-structures, four different thermal metamaterials, viz., Styrofoam, paraffin, aerogel, and air, were used. Figures 4(a) and 4(b) show the temperature changes of Styrofoam, paraffin, aerogel, and air on the opposite plane of the concrete block under the condition of heating at 50 °C. First, the thermal blocking effect for air- and aerogel-based plate-shaped meta-structures is more efficient than that of Styrofoam- and paraffin-based plate-shaped meta-structures. The saturation temperatures are 22.65 °C and 22.41 °C for the aerogel- and air-based plate-shaped meta-structures, respectively. The temperature of the aerogel-based plate-shaped meta-structures can be maintained close to 0.6 °C lower than that of the plate-shaped meta-structures based on Styrofoam, which is a conventional thermal insulating material in the concrete block. In the case of paraffin, the heat flow blocking effect is worse than that in the case of Styrofoam. Figures 4(c) and 4(d) present the temperature changes of various insulator materials on the opposite plane under the condition of cooling at −20 °C. It can be observed that the thermal blocking effect of air- and aerogel-based plate-shaped meta-structures is more efficient than that of the Styrofoam-based plate-shaped meta-structures. The aerogel-based plate-shaped meta-structures showed a slightly reduced temperature from 20 to 16.47 °C. For the air-based plate-shaped meta-structures, the saturation temperature is 16.96 °C, which is approximately 1.0 °C higher than that of Styrofoam-based plate-shaped meta-structures. These results indicated that air- and aerogel-based plate-shaped meta-structures are significantly more efficient than Styrofoam-based plate-shaped meta-structures in suppressing heat transfer because the densities and the thermal conductivities of air and aerogels are lower than that of Styrofoam. The heat transfer was affected by thermal conductivity, density, and specific heat of the metamaterial. Among three factors influencing the heat transfer, thermal conductivity had the greatest influence, followed by density and specific heat in order.

FIG. 4.

Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of (a) heating at 50 °C and (b) cooling at 20 °C by using four different materials (Styrofoam, paraffin, aerogel, and air) for the plate-shaped meta-structures.

FIG. 4.

Temperature changes on the opposite plane of the concrete block over 0–300 min under the condition of (a) heating at 50 °C and (b) cooling at 20 °C by using four different materials (Styrofoam, paraffin, aerogel, and air) for the plate-shaped meta-structures.

Close modal

Figure 5(a) shows the temperature change characteristics according to the heat flow of the concrete blocks without and with the plate-shaped meta-structures. The different plate-shaped meta-structures consisted of one Styrofoam layer, five Styrofoam layers, five aerogel layers, and five air layers. For a meta-structure with one layer, the total thickness of the layer was 10 mm. In the case of a meta-structure with five layers, each layer was 2 mm thick, resulting in a total thickness of 10 mm and the gap between layers was maintained at 2 mm. One side of the concrete block was heated to 50 °C and the temperature change on the opposite side of the concrete block was measured over 0–120 min. The average temperature of 9 points (the point size of 70 × 70 mm2) was measured based on the concrete block. The ambient temperature was maintained at 22 °C and the humidity was maintained at 70% RH. After 120 min, the temperatures of the concrete blocks were 38.1 ± 0.2 °C (concrete block without the plate-shaped meta-structure), 26.7 ± 0.5 °C (one Styrofoam layer), 25.9 ± 0.3 °C (five Styrofoam layers), 25.5 ± 0.2 °C (five aerogel layers), and 23.9 ± 0.4 °C (five air layers). The temperatures in all samples were measured to have a slight variation within ∼2 °C compared to the simulation results because the heat transfer was disturbed by non-ideal factors, such as impurities, cracks, and air present inside the concrete block. Nevertheless, similar to the previous simulation results, the heat transfer was lower in the order of five air layers, five aerogel layers, five Styrofoam layers, one Styrofoam layer, and no layer.

FIG. 5.

(a) Temperature changes over 0–120 min and (b) relevant infrared thermal images on the opposite plane of the fabricated concrete block embedded with four different plate-shaped meta-structures (one Styrofoam layer, five Styrofoam layers, five aerogel layers, and five air layers) under the condition of heating at 50 °C.

FIG. 5.

(a) Temperature changes over 0–120 min and (b) relevant infrared thermal images on the opposite plane of the fabricated concrete block embedded with four different plate-shaped meta-structures (one Styrofoam layer, five Styrofoam layers, five aerogel layers, and five air layers) under the condition of heating at 50 °C.

Close modal

Concrete is a porous structure with approximately 20% of pore sizes ranging from 20 Å to 1000 μm. The macroporous pores generated during the hydration reaction and drying shrinkage between cement and water are interconnected in the concrete.30 In general, the heat transfer characteristics in a porous structure vary depending on the pore size, connectivity, and volume fraction. In particular, the mean free path of a gas molecule that transfers thermal energy to structures with microscopic pores is shorter than that of the gas molecule that transfers thermal energy to structures with macroscopic pores, resulting in less gas diffusion and consequently low heat transfer efficiency by convection.31 Conventional concrete with macro-sized interconnected pores shows the largest temperature change because of its high thermal conductivity (Fig. 5), whereas materials with low thermal conductivity, materials that can block heat convection by micropores, and materials that can absorb heat owing to high specific heat can more effectively block heat transfer. As shown in Fig. 5, when Styrofoam (whose thermal conductivity is low i.e., 0.035 W/m·K) was used as a meta layer, the heat transfer of the concrete block embedded with one Styrofoam layer was lower than that of the conventional concrete block (thermal conductivity of 1.8 W/m·K). The heat transfer of five Styrofoam layers arranged periodically with five meta-layers was lower than that of one Styrofoam layer. When aerogel (thermal conductivity of 0.03 W/m·K) is used as a heat flux material, heat transfer is more effectively blocked owing to the micropores inside the aerogels, which constitute 90% air. The thermal meta-structure filled with air blocked the heat transfer more effectively owing to the low density and thermal conductivity of air (thermal conductivity of 0.024 W/m·K).

Figure 5(b) shows the thermal IR images, which show the thermal distribution of the concrete blocks without and with the plate-shaped meta-structures at 50 °C after 120 min obtained by using an IR thermography camera. The temperature range was set from the minimum indicated blue bar (20 °C) to the maximum indicated red bar (45 °C). As shown in the figure, different temperature characteristics were shown depending on the meta-structure and material used in the area of the plate-shaped meta-structure (120 × 120 mm2) inserted into the concrete block (150 × 150 mm2). For concrete blocks without the plate-shaped meta-structures, the temperature measured using the IR thermography camera was 38.5 °C. The temperature of the plate-shaped meta-structures with concrete blocks was 27.4 °C (one Styrofoam layer), 26.6 °C (five Styrofoam layers), 26.0 °C (five aerogel layers), and 23.4 °C (five air layers). Note that the different temperatures measured in Fig. 5(a) and Fig. 5(b) were due to the variation in the method used for the temperature measurement of the concrete block i.e., the direct contact method in Fig. 5(a) and the non-contact method in Fig. 5(b). The temperature of the IR image is shown in the range 20–45 °C in the temperature bar shown on the right side of each image in Fig. 5(b). The red color of the temperature bar indicates high temperature and the blue color indicates low temperature. The concrete block without the plate-shaped meta-structure is represented by the red color at high temperature, whereas the concrete block with the plate-shaped meta-structure is represented by the blue color at low temperature. In particular, the concrete block containing five air layers is represented by the darkest blue color, which shows the best insulation effect. These results are consistent with the heat flux effect simulation results described above. The plate-shaped meta-structures proposed in this study can effectively block the heat transfer and improve the heat transfer suppression ability according to the material and arrangement method. Consequently, it is possible to use an insulation structure with a smaller thickness than the existing insulation structure.

In summary, plate-shaped meta-structures and thermal metamaterials to control the heat flux of a concrete block were designed. It is computationally proven that the heat transfer in the concrete block can be effectively suppressed by applying plate-shaped meta-structures. For the same total thickness, the effect of blocking heat transfer under heating and cooling conditions is enhanced by increasing the array of periodic plate-shaped meta-structures, which makes the heat transfer slower. The thermal blocking is more efficient when ten layers of the plate-shaped meta-structures are embedded in the concrete block, which has the advantage of reducing the thickness of the concrete block, resulting in the increase in the living area ratio when constructing buildings. We also simulated the heat flux effect for four different thermal metamaterials, viz., Styrofoam, paraffin, aerogel, and air. In cases of the air- and aerogel-based plate-shaped meta-structures, it is possible to suppress heat transfer effectively compared to the cases of Styrofoam- and paraffin-based plate-shaped meta-structures. The heat flux effect for the plate-shaped meta-structures introduced in this study can be applied to products that require high thermal insulation in small spaces. Particularly, it has the advantage of expanding the space inside the house by lowering the thickness of the concrete block while showing the same insulation effect.

This work was supported by Technology Advancement Research Program funded by Ministry of Land, Infrastructure and Transport of Korean Government and the Korea Agency for Infrastructure Technology Advancement(KAIA) (17CTAP-C132555-01).

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