10

The design, properties, and performance of concrete masonry blocks with phase change materials

E.M. Alawadhi     Kuwait University, Kuwait

Abstract

Use of phase change material (PCM) in the building envelope has been studied extensively in literature as an effective technique for saving energy in buildings. PCMs are organic or inorganic substances with low melting temperature and high latent heat of fusion (e.g., paraffin), and they are classified as a capacitive type of insulation materials. The selection of the PCM for building is based on its melting temperature, cost, toxicity, flammability, and stability. There are several design proposals for masonry bricks containing PCM, such as bricks containing hollow cylinders filled with PCM and alveolar bricks with microencapsulated PCM, and PCM in the brick is represented by the porosity of the Sierpinski carpet. The thermal performance of bricks with PCM can be evaluated using either numerical analysis or directly using experimental measurements. The numerical method is commonly employed to perform optimization or paramedic studies to assess the effect of different design parameters, whereas the experimental method is typically employed to validate the numerical results.

Keywords

Brick with PCM; Masonry brick; PCM containers design for bricks

10.1. Introduction

Thermal insulation materials are chosen to reduce heat flow across a medium, and they can be made of a single or multiple materials. Thermal insulation materials save the U.S. industry more than $60 billion/year in energy costs (Cengel, 1998, pp. 158–159). Therefore, the significance of the insulation materials motivates energy engineers to enhance the thermal characteristics of the thermal insulation materials toward higher thermal resistance. Fibrous, cellular, and granular substances are commonly used insulation materials in buildings. The selection of thermal insulation material is based on its thermal conductivity, thermal mass, temperature of indoor and outdoor spaces, durability, cost, and other factors. The thermo-physical properties of the materials used in the building envelope strongly affect the heating or cooling energy consumptions. The thermal conductivity affects the heat flow at a steady-state condition. For a transient condition, the specific heat also affects the heat flow by absorbing and storing the heat in the form of sensible heat. The solar intensity and outdoor air temperature vary with time; hence, the thermal conductivity and the specific heat of the materials used in building envelopes affect the heat flow. The preferred thermal insulations are materials with high thermal capacity and low thermal conductivity. A comprehensive review of thermal insulation material design economics was accomplished by Turner & Malley, and Torgal, Mistretta, Kaklauskas, Granqvist, & Cabeza (2013) explained in their book how to tackle the challenges of building refurbishment toward nearly zero energy.
Incorporation of phase change material (PCM) into the building envelope has been investigated as a cost-effective technique for reducing the cooling loads. PCMs are organic or inorganic substances with low melting temperature and high latent heat of fusion, such as paraffin and salt. The PCMs are classified as a capacitive type of insulation materials because they slow down the heat flow by absorbing the heat. During high outdoor temperature times, the PCM melts and stores part of the heat as it transfers from outdoors to indoors, and at low outdoor temperature times, the PCM solidifies and releases the stored heat. During the melting process, the specific heat of the PCM increases to more than 100 times, which enables it to absorb a large amount of energy in a relatively small quantity of PCM. Using PCM in building material was suggested by Barkmann & Wessling (1975). Morikama, Suzuki, Okagawa, and Kanki (1985) introduced the concept of the encapsulation of PCM in an unsaturated polyester matrix for building material. A recent review of the PCM for building envelopes can be found in references (Osterman, Tyagi, Butala, Rahim, & Stritih, 2012; Pomianowski, Heiselberg, & Zhang, 2013; Soares, Costa, Gaspar, & Santos, 2013; Waqas & Din, 2013). Depending on the envelope's component, research for PCM can be classified into three groups: bricks, roofs, and windows. For bricks, Alawadhi (2008) presented a thermal analysis of bricks with cylindrical hollows filled with PCM, and the results indicate that the heat gain can be reduced by 17.55% for certain design and weather conditions. Zhang, Chen, Wu, & Shi (2011) reported the thermal characteristics of brick with PCM under real fluctuating outdoor temperature. The thermal response represented by the inside wall surface temperature of brick wall filled with PCM is evaluated and compared with that of solid brick wall. Chwieduk (2013) published a paper about the possibility of substituting the thick and heavy thermal mass external bricks used in high-latitude countries by thin and light thermal mass bricks. The effect of orientation, position of the PCM layer, phase change temperature, and weather conditions was studied by Izquierdo-Barrientos et al. (2012), and they found that the PCM helps to reduce the maximum and amplitude of the instantaneous heat flux.
For roofs, Alawadhi & Alqallaf (2011) investigated a concrete roof with vertical cone frustum holes filled with PCM. The objective of the PCM roof is to reduce the heat flow from the outdoor to indoor space by increasing the thermal mass of the roof. The shape for the PCM containers maintains the physical strength of the roof, can be replaced easily if needed, and allows the PCM to expand during the melting process in the upward direction. The heat flux at the indoor surface of the roof can be reduced by 39%, as reported. Numerical analysis of heat transfer across the roof structure with PCM is by Ravikumar & Sirinivasan (2011), and approximately 56% reduction in heat gain into the room is obtained with a PCM roof structure when compared with a conventional roof. On the other hand, the concept of double layers of PCM in a building roof was proposed by Pasupathy & Velraj (2008) for a year-round thermal management. The double layer of PCM in the roof is recommended to reduce the heat flow through the roof.
Research for PCM in windows was also accomplished as a technique for reducing the heat gain through windows. Windows account for a large percentage of heat gain during the daytime, and energy penetrates the windows through solar radiation and convection. Therefore, reducing heat gain through windows is the key factor for saving energy in buildings, and to reduce the heat gain, external shutters are installed to eliminate the effect of the solar radiation. A window shutter filled with PCM was proposed and analyzed by Alawadhi (2012), and a parametric study is conducted to assess the effect of different design parameters, such as PCM type and quantity in the shutter. It was reported that the melting temperature of PCM should be close to the maximum outdoor temperature during the daytime, and the quantity of PCM should be sufficient to absorb large quantities of heat gain. Goia et al. (2012) described the thermo-physical behavior of PCM glazing system configurations. PCM-filled glass windows for reducing the solar radiation entering the indoor space through the windows was also investigated (Ismail, Salinas, & Henriquez, 2008), and the effectiveness of the system is compared with windows filled with reflective gases.

10.2. Phase change material (PCM) candidates for buildings

The selection of the PCM for a building envelope is mainly based on its melting temperature. To have an effective PCM, the melting temperature of the PCM should be within outdoor minima and maxima temperatures to allow the PCM to melt and solidify. Having low cost and being nontoxic, nonflammable, and chemically stable are preferred characteristics of PCMs. PCMs are classified as organic or inorganic substances with a high latent heat of fusion and a relatively low melting temperature (e.g., paraffin, and salt). There are hundreds of potential PCM candidates that are reviewed and listed with their properties in the literature (Cabezaa et al., 2011). However, few PCMs have actually been tested and used for buildings. Several PCM candidates are substantially reduced to only a few because many PCMs have a high latent heat of fusion and a convenient melting temperature, but they are hazardous or highly corrosive. The organic or inorganic PCMs are known to melt with a high heat of fusion in a wide range of melting temperatures. However, the PCM melting temperature and latent heat of fusion are not the only criteria to select the PCM. The PCM must exhibit certain desirable thermodynamic and chemical properties. In addition, economic considerations of the cost and availability in large scales must also be considered.

10.2.1. PCM selection criteria

The PCM selection criteria for building envelopes are listed below. Many researchers highlighted the desirable and undesirable features of the PCM, such as Kenisarin & Mahkamov (2007). The most important properties for selecting the PCM for buildings are PCM melting temperature and latent heat of fusion. To be a successful PCM in a building envelope, the following thermodynamic, chemical, and economic criteria should be considered:
1. Thermodynamic criteria
a. The thermo-physical properties should be available and accurate.
b. The PCM melting temperature should be close to outdoor temperature.
c. The latent heat of fusion and specific heat must be high.
d. A high thermal conductivity to prevent potential PCM overheating and fast thermal response.
e. The PCM solid and liquid phase properties are preferred to be close to each other. Large variations in densities between the solid and liquid could cause segregation, resulting in changes in the chemical composition of the material.
f. The volumetric thermal expansion of PCM during melting should be low.
2. Chemical criteria
a. Chemically stable, so that the PCM can be in service for a long time.
b. No chemical decomposition.
c. Noncorrosive.
d. The PCM must be nonpoisonous to ensure the safety of the residents.
e. Nonflammable.
f. Insulator to electricity to avoid a short circuit if leakage occurs.
3. Economic criteria
a. Commercially available in large quantities in the market.
b. PCM pureness should be high to guarantee high performance of the PCM.
c. Inexpensive, so that the price is comparable to traditional insulation materials.
Unfortunately, a single PCM that possesses all of the above criteria is not available, and there is simply no perfect PCM. However, some of the undesirable PCM characteristics can be corrected. For example, high conductive metals can be incorporated into the PCM to increase its low thermal conductivity if fast thermal response is required. The negative effect of high thermal expansion of the PCM can be corrected by leaving a measured air pocket in the housing to allow the PCM to expand.

10.2.2. PCM types

PCMs are grouped into the families of organic and inorganic. Subfamilies of the organic materials include paraffin and nonparaffin. Salt hydrates may be regarded as alloys of inorganic PCM. Abhat (1983) classified the PCM used for thermal energy systems, and a detailed classification was suggested by Mehling and Cabeza (1997).
1. Paraffin organics
    Paraffin organics are an oil product, and they are a family of saturated hydrocarbons with similar properties. They are characterized by CnH2n+2, and all series below n = 5 are gases at 25 °C. Those between n = 5 and n = 15 are liquid, and the rest are waxy solids. The thermal conductivity of paraffin is very low and it is comparable to the best insulators. In addition, paraffin is serviced as a PCM for building envelopes because it possesses most of the PCM selection criteria for buildings. Paraffin organics are inexpensive, have high sensible and latent heat storage capacities, and are available in a wide range of melting temperatures, which facilitates the design and optimization of PCM for buildings. However, paraffin should not be exposed to high temperature because it is flammable. The general characteristics of the paraffin are as follows:
a. High latent heat of fusion, around 240,000 J/kg
b. Wide range of melting point selection, from 6 to 66 °C
c. Flammable
d. Nontoxic
e. Noncorrosive
f. Chemically stable
g. High volumetric thermal expansion
h. High density, around 750 kg/m3
i. Low thermal conductivity, around 0.3 W/m-K
j. High wetting ability
k. Low vapor pressure in the melt
    Table 10.1 provides a list of paraffin organics previously used in building components (Hale, Hoover, & O’Neill, 1971; Izquierdo-Barrientos, Belmonte, Rodríguez-Sánchez, Molina, & Almendros-Ibáñez, 2012; Koschenz & Lehmann, 2004). A comprehensive list and other PCMs can be found in Cabeza et al. (2011) and Osterman et al. (2012).

Table 10.1

Previously examined paraffin organics and their properties

Paraffin organicsFormulaMelting point (°C)Latent heat (kJ/kg)Density (kg/m3)Conductivity (W/m-K)
n-TetradecaneC14H305.5228.07710.15
n-HexadecaneC16H3416.7237.07740.25
n-OctadenceC18H3828.0244.07740.35
EicosaneC20H4236.8241.07780.27

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2. Nonparaffin organics
    Nonparaffin organic components are characterized by CH3(CH2)2nCOOH, their latent heat of fusions are comparable to that of organic paraffin, and their densities are larger than paraffin organics. However, they are rarely used in building envelopes because of their many unacceptable characteristics. Their cost is twice greater than that of paraffins. In addition, almost all nonparaffin organic materials are flammable and should not be exposed to high temperature media, flame, or storage oxidizer agents. Also, exposure to high heat can cause decomposition and caution is needed in handling nonparaffin organic materials of any type. Another disadvantage of the nonparaffin organics is their thermal conductivity, which is 5–10 times higher than paraffin; therefore, they are considered good thermal conductors.
3. Salt hydrates
    Several paraffin and nonparaffin organics have a melting point within the desired range, but they are flammable and a special housing design is required, adding an additional manufacturing cost. Salts hydrates are successful substitutes for organic PCM, and they were previously used as a PCM for bricks (Principi & Fioretti, 2012). They are nonflammable, have a high heat of fusion, and have a wide range of melting temperature from 18.5 to 116.0 °C. However, the major disadvantage of the salt hydrates as PCM is that they are highly corrosive. Another disadvantage is the significant difference between liquid and solid densities. Therefore, the PCM housing structure must be perfectly designed to overcome the thermal expansion of the salt. Table 10.2 shows the salt hydrates that were previously used as PCMs for building (Waqas & Din, 2013). The general characteristics of salt hydrates are as follows:
a. High heat of fusion
b. Relatively low thermal conductivity
c. Highly corrosive
d. Relatively more expensive than paraffin and nonparaffin PCMs

10.3. Masonry brick designs for PCM

One of the early designs of masonry bricks with PCM was proposed by Lai & Chiang (2006) and followed by Alawadhi (2008). Basically, the design was bricks containing hollow cylinders filled with PCM. Figure 10.1 shows the geometry configuration of a brick containing three hollow cylinders filled with PCM, and the thermal analysis of the design was accomplished using experimental (Lai & Chiang, 2006) and theoretical methods (Mandelbrot, 1983).
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Figure 10.1 Brick containing three hollow cylinders filled with phase change material (PCM).

Table 10.2

Previously used salt hydrates and their properties

MaterialMelting point (°C)Heat of fusion (kJ/kg)Density (kg/m3)Specific heat (kJ/kg)Conductivity (W/m-K)
CaCl2 6H2O29.717113331.450.23
Na2SO4 10H2O32.425414851.930.544
Zn(NO3)2 6H2O36.414720651.80.31

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For the Lai & Chiang (2006) design, the size of the brick is 172 × 70 × 305 mm, and the brick has three cylindrical holes with a diameter of 45 mm. An acrylic tube, k = 0.19 W/m-K, with diameter slightly less than 45 mm, was completely filled with n-octadecane, an organic paraffin. The ends of the acrylic tubes were completely sealed by silicone, and they were repeatedly tested at high and low temperatures to ensure there were no leaks. They evaluated the thermal performance of the bricks with PCM by comparing the temperature variations of the top surface, the center of the holes, and the bottom surface with a brick without PCM or just a hollow cylinder. They indicated that when the temperature of the PCM tube exceeded the PCM melting temperature, a liquid zone at the upper region was observed, and the zone grew under the influence of the natural convection flow of liquid PCM. In addition, the experimental results indicated that the temperature at the top surface of the brick with PCM was lower than brick without PCM during the daytime. On the other hand, the brick with PCM became a heat source, resulting in a higher temperature at the top surface at nighttime. In general, the brick with PCM design was capable of reducing the maximum bottom surface temperature by 4.9 °C when the maximum outdoor temperature was 35.5 °C.
A brick with dimensions of 0.25 × 0.15 × 0.15 m with cylindrical holes was evaluated numerically by Alawadhi (2012). The diameter of the holes is 0.03 m, and the effect of the number of PCM cylinders in the brick was investigated. The number of cylinders reflects the PCM quantity in the brick. A brick with one, two, and three PCM cylinders as well as a brick without PCM were considered as case studies, as shown in Figure 10.2. A brick with a minimum quantity of the PCM is desirable to maintain the physical strength of the brick and to reduce the production cost.
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Figure 10.2 A brick with one, two, and three phase change material (PCM) cylinders.
In these designs, the PCM cylinders are located at the middle of the brick. The outdoor surface of the wall is subjected to a time-dependent solar radiation and forced convection boundary conditions, whereas the indoor surface is subjected to a time-independent free convection boundary condition. Three types of organic paraffin were selected for the numerical study, and they are n-octadecane, n-eicosane, and P116. P116 has a melting temperature of 47°C. These PCMs were selected because their melting temperatures are within the temperature variations of the outdoor space. Real weather data for the month of June for the state of Kuwait were used for the outer boundary condition. The weather data are for the month of June when the temperature and solar radiation are the highest. The thermal performance of the brick with PCM is compared with brick without PCM, and heat flux at the indoor surface of the brick is calculated. The results indicated that the P116 and n-octadence are ineffective in reducing the heat flux at the indoor space. The n-octadence was in the liquid phase all of the time because of its low melting temperature whereas n-eicosane was in the solid phase all of the time because of its high melting temperature. With P117, the rate of change of the heat flux is dramatically decreased during the daytime compared with the brick without PCM, with a maximum heat flux reduction of 24.2%. A brick with one, two and three cylinders, with P116 PCM, was evaluated. For a brick with a one-cylinder design, the maximum heat flux reduced at the indoor space was 11.5%; this value was 17.9% with two cylinders and 24.2% with three cylinders.
Castell, Martorell, Medrano, Perez, & Cabrza (2010) added microencapsulated PCM in conventional and alveolar bricks that were typically used in Mediterranean regions. The experimental wall consisted of convectional bricks with a dimension of 0.29 × 0.14 × 0.75 m, and there were three rows of hollow cylinders each containing seven holes, as shown in Figure 10.3. A panel containing PCM is attached at the outdoor surface of the brick, followed by a spray foam polyurethane, k = 0.028 W/m-K and ρ = 35 kg/m3. The PCM is paraffin with a melting temperature of 28°C. Wall temperatures were obtained, as well as heat flux entering the wall, and the results were compared to wall without PCM. The report results indicated that the brick with PCM can smooth out the daily temperature fluctuations. In addition, the energy consumption of the brick with PCM can be reduced by 15% compared with bricks without PCM. The Sierpinski carpet (Mandelbrot, 1983) is used to characterize the geometric structure of a brick filled with PCM. Figure 10.4 shows the schematic of the Sierpinski carpet. The Sierpinski carpet is commonly used to characterize porous objects, and because a brick with hollows is physically considered a porous object, the Sierpinski carpet can be applied to study brick with PCM. The filling amount of PCM in the brick is represented by the porosity of the Sierpinski carpet.
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Figure 10.3 Brick with three rows of hollow cylinders each containing seven holes.
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Figure 10.4 A schematic of the Sierpinski carpet.
In addition, the effects of the PCM amount and spatial distribution of the PCM on the thermal characteristics of the brick wall can be easily determined by comparing it with that of the brick without PCM. The Sierpinski carpet is a typical self-similar porous fractal object. A square is the general algorithm, and the carpet is constructed by dividing the square into nine congruent smaller squares and removing the central one then repeating the same procedure recursively to the remains. The fractal dimension of the carpet is D = ln(8)/ln(3). For the ith recirculation, the porosity (εi), and pore scale (Li) of the Sierpinski carpet can be calculated as, respectively,

εi=1(32132)i

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Li=Lo3i

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Zhang et al. (2011) present the effect of PCM amount in the brick with a Sierpinski carpet design on the indoor surface temperature. They indicated that with increasing the amount of the PCM, the temperature fluctuation amplitudes indoors was effectively reduced, and the temperature hysteresis was correspondingly enhanced. A simpler design was proposed and analyzed by Silva, Vicente, Soares, & Ferreira (2012). In their design, steel macrocapsules were filled with PCM and inserted into the middle brick voids, as shown in Figure 10.5. The bricks are made of clay with dimensions of 30 × 20 × 15 cm, and the steel macrocapsules have dimensions of 30 × 17 × 2.8 cm and 0.75-mm thickness. In this research, organic paraffin was chosen, designated as RT18 with a melting temperature of 18°C.
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Figure 10.5 Steel macrocapsules were filled with phase change material (PCM) and inserted into the middle brick voids.
The experimental results indicated that the brick PCM design contributed to the reduction in the indoor space temperature fluctuations from 10 to 5°C. In addition, the time delay was about 3 h for brick with PCM on the charging mode whereas it was only 1 h for brick without PCM. A flexible plastic container was used, proposed by Principi & Fioretti (2012), to house the PCM in the brick. Then, the container was placed in the cavity and filled with PCM. Finally, the container was sealed to avoid the leakage of liquid PCM. The holes in the brick chosen for the design have a thickness of 0.027 m, as shown in Figure 10.6. The PCM was inserted in only one row in the brick, and the selected row is the closest to the external side of the brick. This position was chosen to effectively store energy coming from outdoors and to allow the release of most of the stored thermal energy toward the outdoor space.
The PCM used in this experimental study was Glauber salt (Na2SO4-10H2O), which has a melting temperature of 32.5°C. The design brick with PCM led to not only a delay of about 6 h in the heat flux peak but also a reduction of the heat flux by 25%. A brick of size 30 × 20 × 15 cm with 12 square cavities of 4 × 3.667 cm filled with PCM was designed by Hichem, Noureddine, Nadia, & Djamila (2013), and they optimized the type of the PCM, the location of the PCM, and the amount of the PCM in the brick. There are three possible positions of PCM in brick: (a) in the middle, (b) in the middle and near the outer surface, and (c) in the middle and near the inner surface. Figure 10.7 shows bricks with different positions and quantities of PCM.
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Figure 10.6 Brick with phase change material (PCM) inserted in only one row in the brick.
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Figure 10.7 Bricks with different positions and quantities of phase change material (PCM): (a) middle; (b) middle and near outer surface; (c) middle and near inner surface.
The reduction of total heat flux for 1 day was 82.1% for the (a) PCM position, 90.02% for (b) PCM position, and 69.93% for the (c) PCM position. Hence, if the double quantities of PCM are employed, the (a) PCM position, the efficiency of brick was only enhanced by 7.92%.

10.4. Analysis methods

The thermal performance of bricks with PCM can be evaluated by comparing the heat flux and surface temperature at the indoor surface with a brick without PCM. The heat flux and surface temperature can be determined for a brick with PCM by either numerically solving the heat conduction equation along with the boundary conditions or directly using experimental measurements. The numerical method is commonly employed to perform optimization or paramedic studies to assess the effect of different design parameters, such as the PCM quantity, type, and location in the brick. The design parameters are optimized by minimizing heat flux or surface temperature at the indoor surface. The experimental method is typically employed to validate the numerical method and to ensure that the governing equations and applied boundary conditions are accurate enough for practical implementation.

10.4.1. Numerical method

All structure components in a building, including masonry bricks, are three-dimensional space. However, an approximation can be made to reasonably reduce the size of the computation domain from three- to two- or even one-dimensional space. Computation domain reduction should be considered in numerical simulations to reduce the model size, computational time, and required data storage capacity. If the geometry and thermal boundary condition of the bricks can be completely described in one- or two-dimensional space, then the space can be reduced. When the geometry and boundaries of the model are repeated in a particular direction, then the model has a repetitive symmetry. For example, the simulation of a long wall made of masonry bricks with three holes can be easily modeled using the repetitive symmetry, as shown in Figure 10.8. This wall is relatively long, and if the indoor and outdoor thermal boundary conditions are not varied along the wall direction, then the thermal characteristics do not vary significantly along the wall. Therefore, the line of symmetries should have a zero heat flux. Note that the repetitive symmetry is valid anywhere in the object except at the end of the wall. Additionally, the height of the wall is large compared to its thickness; therefore, the height effect has a negligible effect on the heat transfer. Hence, only a quarter of the masonry brick is considered. Figure 10.8 shows the computational domain.
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Figure 10.8 Bricks with repetitive symmetry and the computational domain.
The thermo-physical properties of the bricks are temperature independent, but it is dependent for the PCM to account for latent heat effect. For simplicity, the thermal expansion of PCM is not considered, and the effect of the natural convection flow of the liquid PCM is neglected in the computations. A significant variation between the solid and liquid densities induces the natural convection flow in the liquid portion of the PCM. The natural convection flow reduces the thermal resistance in the bricks, and hence increases the heat transfer. However, the natural convection effect is significant only if the temperature difference between the boundaries is high (Alawadhi, 2012). The two-dimensional heat conduction equations for the brick and the PCM are expressed in the following mathematical form:

Brick:(ρCp)bTbnt=kb(2Tbx2+2Tby2)

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PCM:(ρCp)PCMTPCMt=kPCM(2TPCMx2+2TPCMy2)

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where (ρCp) is specific heat per unit volume, and (k) is the thermal conductivity. The subscript (b) and (PCM) refer to the property of the brick and PCM, respectively. For modeling the phase change process, there are two main methods: moving mesh and fixed mesh methods. The mesh of the moving mesh method is continuously changing to track the solid/liquid interface. This method is seldom used in modeling phase change because it will highly complicate the computations. The fixed mesh method is commonly used for modeling phase change. In this method, the geometry of the grid is independent of time, and the latent heat effect of the PCM is simulated by making the specific heat function of the temperature. The definition of the specific heat is as follows:

(ρCp)PCM={(ρCp)PCMT<Tm(ρCp)PCM+ρPCM(λΔT)TmTTm+ΔT(ρCp)PCMT>Tm+ΔT}

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λ is the latent heat of fusion, Tm is the melting temperature of PCM, and ΔT is the phase change transition temperature. ΔT = 1 °C is extensively used in numerical simulations for the PCM and is recommended by many researchers (Alawadhi, 2004). If there are significant variations of the PCM properties between the solid and liquid, then the average should be used. The outdoor surface of the wall is subjected to a time-dependent solar radiation heat flux, Qs, and air convective boundary conditions, with temperature and heat transfer coefficients of To and ho, respectively. At the indoor surface of the wall, a free convective boundary condition is applied with temperature and heat transfer coefficients of Ti and hi, respectively. The heat flux at the outdoor wall surface is expressed as

Qos=ho(ToTos)+(1ρ)Qs

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where Tos is the outdoor surface temperature and ρ is the solar reflectivity. The heat flux at the indoor surface can be obtained from

Qis=hi(TiTis)

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where Tis is the indoor surface temperature. The average heat flux at the indoor roof surface is calculated to evaluate the performance of the PCM, and it can be expressed as

Qis¯=Ahi(TiTis)dAy

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The total heat flux can be integrated to obtain the total average heat flux over a specific period:

(Qis¯)ave=1ttot+toQis¯dt

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Figure 10.9 The masonry brick discretized with (a) course and (b) fine meshes.
The finite element method is extensively used for thermal analysis of brick with PCM. The computational domain should be first divided into elements, and this process is called “discretization.” The element distribution in the computational domain is called the “mesh,” and the elements are connected to each other at points called “nodes.” The masonry brick with three holes, as shown in Figure 10.9a, is discretized with 1263 elements. The result of the finite element method can be additionally enhanced by increasing the number of elements in the model. On the other hand, increasing the number of elements leads to a proportional increase in the computational time and storage memory. High temperature gradients are expected in the PCM region whereas they are low in the brick region. Therefore, elements must be concentrated at the PCM region to correctly simulate the latent heat effect. In Figure 10.9b, the PCM region has more elements than the first mesh, and the number of elements is increased to 3561. After the computational domain is discretized, the element equations for the thermal analysis must be established.
The element equations are assembled to obtain the global equation for the mesh, which describe the thermal behavior as whole. The first law of thermodynamics states that thermal energy is conserved:

ρC(Tt)+{L}T{Q}=0

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where {L} is the vector operator and {Q} is the heat flux vector. Fourier's law is used to relate the heat flux vector to thermal gradients:

{Q}=[K]{L}{T}

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where [K] is thermal conductivity matrix and {T} is the temperature vector. Therefore, the element equation can be expressed as

ρC(Tt){L}T[K]{L}{T}=0

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The preconditional generalized minimum residual (PGMR) solver is the most effective solver for solving the temperature field. The PGMR method is an iterative method for the numerical solution of a system of nonsymmetric linear equations. At each time step, the temperature result is checked for convergence, and the following condition is used to declare the convergence at each time step:

|Tijm+1Tijm|Tijm106

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The convergence condition represents the sum of the temperature difference calculated from the current (m + 1)th iteration and the previous (m)th iteration and normalized by the sum of the current iteration. This ratio should be small enough for the convergence condition. For more information regarding the numerical method for PCM, Alawadhi (2010) illustrates in his book a melting process of PCM inside of a circular enclosure. The PCM is n-eicosane and paraffin wax, and details about theory, modeling, meshing, and analyses are explained.

10.4.2. Experimental method

The experimental technique is extensively utilized for studying the thermal performance of masonry bricks because the experimental results are reliable and reflect real, practical situations. To conduct an experiment, a section of brick with a PCM wall with a dimension of at least 1.0 m2 should be constructed and ready for experiments. The wall is installed at one of the vertical walls of a testing room whereas other walls are made of brick without PCM. The roof and floor are perfectly insulated. Figure 10.10 shows a typical testing room for evaluating the brick with PCM. The testing room can be freely rotated to study the effect of the facing direction on the thermal performance of the brick with the PCM wall, and direct north, south, east, and west directions are typically considered. To ensure that the testing room will not be shaded, it should be placed in an open field, and the indoor temperature is controlled by a thermostat and air-conditioning unit (Castell et al., 2010). On the other hand, the entire testing can be conducted indoors. In this method, the indoors is heated to simulate the outdoor space whereas the surrounding simulates the low-temperature indoor space (Mandelbrot, 1983). Powerful bulbs must be installed in the testing room to simulate solar radiation. In both methods, the experiment should be continuously running for at least 3 days to ensure that a thermal periodic condition is established in the entire testing room. K-type thermocouples are attached to the indoor and outdoor surfaces of the walls as well as inside of the PCM to monitor the melting process of the PCM in the bricks. Heat flux sensors are attached to the indoor and outdoor surfaces to measure the heat flux from the outdoor to indoor spaces and to estimate the heat transfer coefficients. Data acquisition is used to record the temperature and heat flux readings every fixed interval.
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Figure 10.10 A typical testing room for evaluating the brick with the phase change material (PCM).
The heat flux variations with time at the indoor surface of the testing room are obtained for all walls, and the performance of the brick with the PCM wall is compared to a wall that does not contain PCM. The heat fluxes for all walls are integrated for a specific period, or 1 day, to obtain the net heat gain. If the wall made of brick with PCM is capable of considerably reducing the heat gain, the objective of reducing the heat gain using brick with PCM is achieved. To determine the equivalent specific heat with the temperature of PCM-concrete brick, Cheng, Pomianowski, Wang, Heiselberg, & Zhang (2013) propose a technique in which complex experimental installations are not required. The required needed data are only the top heat flux and the temperature distributions in different layers. The dynamic change of specific heat can be presented by using the proposed method. The environmental impact of construction systems on alveolar bricks and PCMs can be evaluated using life cycle assessment as presented by Castell et al. (2013).

10.4.3. Future trends

Practically, a single PCM type is used with bricks. Future trends involve the bricks filled with PCMs with different melting temperatures (Yang, Zhang, & Xu, 2014). The bricks with different PCMs work more effectively as a thermal barrier at a wide range of outdoor ambient temperatures. Solid packages of PCM in bricks will be replaced by spheres of encapsulated paraffin (Arkar & Medved, 2007). The spheres of encapsulated paraffin have a larger surface area that provides bricks with better thermal response with the outdoor ambient air temperature (Cabeza et al., 2007). The microencapsulated housing design enables PCM to freeze and melt in day and night cycles, in which night cooling is important to achieve this full cycle every day.

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