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Numerical study of heat and mass transfer of a wall containing micro-encapsulated phase change concrete (PCC)


 The aim of this work is to study the one-dimensional heat and mass transfer through a ceiling wall containing micro-encapsulated PCC (phase change concrete) under realistic climatic conditions based on meteorological data in Tunisia based on software EnergyPlus. This work deals with a numerical study based on the nodal method to predict the effect of integration of a layer of PCC on the thermal, mass behavior and on the thermal sensation of the occupant as well as on the reduction of the energy consumption for the summer and winter period associated with the composite envelope building.


Introduction
To improve the thermal inertia of a building envelope, we have studied another technique which is the integration of phase change concrete (PCC) thanks to the high latent heat that it exchanges during heat transfers. We note that several studies have been carried out with the aim of improving the energy performance of buildings.
Laurie et al [1] used Comsol Multiphysics software to study the model of hollow core slabs serving as a floor or ceiling filled with MCP in order to increase the thermal inertia of a building. To avoid the possibility of PCM (phase change material) leaks when it is in the liquid state, a polymer / MCP composite is made and then incorporated inside the existing cylindrical cavities in the slabs of floors or ceilings. They used commercial paraffin as a PCM with a melting temperature close to 27 ° C, its apparent latent heat is around 110 KJ / kg. Then, they carried out several dynamic tests, a periodic temperature variation (between 22 and 35 ° C) was imposed on the inside face of a slab and the temperature on the upper face was measured and compared to that observed for a reference panel without MCP. They showed that the variations of this temperature have a lower amplitude when the slab contains an MCP and moreover the phase shift between the imposed variations and those measured on the other face is about 1.5 times greater for the slabs with MCP. which clearly shows the increase in thermal inertia. Sharma et al [2] have shown that the MCP microencapsulation method is best suited to the building envelope because PCMs are easy to handle and integrate into all building materials. Alexander M. Thiele et al [3] studied the addition of microencapsulated MCP to the exterior concrete walls of a mid-size family residence in San Francisco and Los Angeles.
They used numerical simulations to process this study. The results showed that adding PCM can lead to significant annual energy savings. In fact, the annual reduction in cooling load varies from 85% to 100% and from 53% to 82% in San Francisco and Los Angeles, respectively, thus the decrease in power consumption. Jiawei Lei et al [4] numerically studied the energy performance of buildings integrating MCP in order to reduce the cooling load in Singapore. They incorporated a 10mm thick MCP layer with a melting temperature of 28 ° C in all vertical walls either on the exterior surfaces or on the interior surfaces of the building envelope. They have shown that the optimum phase change temperature is affected by the location of the MCP and that the integration of MCP into the exterior surfaces of the walls improves the thermal performance of a building more than that of the interior surfaces.
. K. Saafi and N. Daoues [5] have shown that MCP applied to the exterior face of a brick wall provides better energy efficiency, with the highest energy savings of up to 13.4% achieved for south orientation. The integration of the 3cm thick MCP improved the thermal inertia of the wall with a 2 hour increase in the jet lag for the east orientation. A 30 year life cycle cost analysis has shown that integrating MCP into a brick wall is not cost effective. The interaction between MCP and thermal insulation in a brick wall showed improved efficiency of MCP in the absence of insulation, providing the highest rate of reduction in energy consumption, estimated at 12. 21  in China and showed that PCM increased the temperature delay through the roof by 3 h. According to Saffari et al.
[12], the combination of cool roof and PCM technologies reduced roof cooling stress by 18% to 30% and resulted in energy savings of 1% to 6%.
Controlling indoor air humidity is a major factor in improving comfort in a building. N. Subramanyam et al [13] have shown that maintaining indoor relative humidity is important for improving indoor air quality, energy performance and the durability of the building envelope. [14,15] pointed out that a low humidity environment causes dryness of the skin and throat, mucous membranes, while a high humidity environment can lead to dryness, discomfort and respiratory allergies affecting the visibility of air quality, causing fungal growth, affecting the durability of the building, etc. Shi et al. [16] concluded that PCM models are thermally efficient and that by reducing relative humidity 8% to 16%, they provide a comfortable and healthy indoor environment. Additionally, they showed that the application of PCM in social housing in Hong Kong is economically visible with an 11-year payback period. Therefore, thermal and water performance are essential for a comfortable and healthy life. For the above reasons, this research also investigated the effect of microencapsulated concrete on changes in temperature and humidity based on physical models [17,18] to predict the coupling between the transfer of heat and mass of different types of envelopes in the building. Based on the nodal method as a numerical method, we cut the building into several elements so that we got 81 nodes in total and we solved the problem of heat transfer and mass using the method of the thermoelectric analogy ( Figure 1). The simplicity of the model used, based on the thermoelectricity method and validated with an analytical method [19,20], facilitated the prediction and evaluation of the energy benefits of walls and results in BC composite materials.

Problem position
We have studied the evaluation of the hydrothermal response of micro-encapsulated PCC composite panels whose melting temperature is set to be equal to 26 ° C of a two-zone building ( fig. 1) in which the walls of two zones (zone 1, zone 2) are identical (surface S = 100 m 2 with a height of 3m) and the effect of adding PCC in an exposed wall in the ceiling as shown in figure (2,3).    Table 1 Thermo-physical properties of materials [16,17] The heat transfer by conduction through a wall, in the case without a heat source, is described by: where ρ, cp and k are the density, thermal conductivity and specific heat capacity of the material, respectively.
Modified PCM / concrete materials can be considered as two-phase materials consisting of reference concrete and PCM particles. In this case, the thermal conductivity of the composite material can be predicted from homogenization schemes as a function of the thermal conductivities of the two phases (concrete and PCM) and of their volume fractions. The expression of the effective thermal conductivity of the composite wall has been accurately predicted by Felske's model [18]: The effective volumetric heat capacity is given by [19]: It depends on the temperature, as it is written below

Hypothesis
In this work, we have assumed the following assumptions: -The heat and mass transfer is unidirectional.
-Air is considered a perfect transparent gas.
-The thermo-physical properties of each material are constants.
-The liquid vapor interface is permeable only to water vapor, -Relative humidity was chosen as the potential governing mass transfer, -The diffusion of water vapor in the air, assuming that humid air is an ideal gas, is described according to Fick's law, -The adsorbed water remains immobile because of the strong adhesion with the pore surface -Constant pressure -The transfer of water vapor diffusion in building materials is expressed by the experimental correlation of Milos J. and

Robert C [25]:
-Dv0 is the diffusion coefficient of water vapor in the air, Rd is the factor of resistance to vapor diffusion and D is the coefficient of water vapor diffusion in building materials.
• The participation energy of the occupant is taken into account. To give more precision in our calculation, we considered that the bi-zone building is occupied by two persons at rest and taking a standing position (one in the center of each zone), so breathing contributes only with 10% to the global exchange, conduction with only 1 % (given the very small contact surface of the feet with the ground [26]). These two contributions are neglected. The metabolism is assumed to be equal to 70 W.m -2 [27].

3-1 balance equation
The mathematical model based on the balance equation is written: Knowing that the mass balance is written [18]: ) (t P i are the specific heat capacity, the temperature in real time, the coefficient of conductivity or convection between nodes i and j, the solar flux absorbed at time t by node i, respectively. Ki, j is the radiative coupling coefficient between i and j.   One method is to count the percentage of people dissatisfied with the comfort conditions. This percentage is directly linked to the average vote of a given population.
There are thus two parameters making it possible to measure thermal comfort: PMV: Average Predicted Vote and is used to quantify the feeling of comfort using the standardized scale according to EN ISO 7730 [32].
The Fanger equation [32] is given below: PPD predicts the percentage of unsatisfied people in a thermal environment [32]:

Boundary and Initial Conditions
The values of the meteorological temperature and the relative humidity of the outside air are provided by the local meteorological station of Sousse as shown in figures 4.5 represent evolution of the temperature and relative humidity of the outside air according to time [19] for the months January and July and curve 6 shows the variation in the density of the incident solar flux on the exterior face of the ceiling for the months January (fig6.a) and July   [19]. Direct and diffuse solar density fluxes are calculated hourly on the 15th day, which is considered a typical day of the month. during the night time the energy consumption is lower than that for a room (glass wool), thanks to the importance of the heat capacity which this room has to store heat during the period of sunshine (room with high inertia). During the daytime consumption is slightly higher than that of the local with glass wool, this is due to the accumulation of latent heat which ensures a large amount of energy stored during the day and large energy consumption. We have observed that the energy consumption in the case of an air conditioning application (month of July) is high with a reduction rate of 35% than that in the case of an application of type of heating (month of January) with a rate of 15% ( fig 13) and that due to the influence of the solar flux (see figure 4).

-Influence of the nature of a multilayer wall on the thermal sensation of the occupant for the month of July
To quantify sensation of comfort using the standardized scale according to EN ISO 7730 [32]. Figure 14 shows relationship between the percentages of dissatisfied (PPD) and the average vote (PMV) for different configurations (wit and without PCC) . We notice the thermal sensation of the occupant is tepid in the case where the ceiling with PCC, on the other hand in the case where the ceiling without PCC the thermal sensation is almost hot. In Table 5, we plotted the comfort index for different configurations studied.  A thermo-economic analysis of the wall of the envelope incorporated with PCM by varying its thickness will allow us to analyze the optimization of the cost of heating or cooling during the winter and summer periods. According to [5] the total cost per unit area of the wall Ct, including the present value of energy cost (C enr ) and PCM cost (C PCM ) is given by:

Conclusion:
In this work we studied the effectiveness of the integration of PCC in the ceiling of a Tunisian building; especially in terms of energy savings where heating and cooling have become essential. The results obtained show in particular that: -The temperature of the inner surface of the PCC wall is slightly reduced compared to glass wool insulation.
-The percentage reduction in the relative humidity for the PCC wall is around 8% for the month of January and 12% for the month of July. In addition, this feature can be useful to reduce air conditioning cooling loads and therefore energy consumption.
-The thermal sensation of the occupant is tepid in the case where the ceiling with PCC -An economic analysis has shown that the use of PCC reduces the energy cost by 20%. [10] Aguilar JLC, Smith GB, Gentle AR, Chen D. Optimum integration of albedo, subroof R-value, and phase change material for cool roofs. In: 13th conference of international building performance simulation association, chambery-France; 2013.