Apparent heat capacity method to investigate heat transfer in a composite phase change material

Journal of Energy Storage 28 (2020) 101239

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Apparent heat capacity method to investigate heat transfer in a composite phase change material

T

⁎

Y. Khattaria, , T. El Rhafikib, N. Choabc, T. Kousksouc, M. Alaphilippec, Y. Zeraoulic a

Department of Physics, Faculty of Sciences, Moulay-Ismaïl University, Meknes, Morocco Engineering Sciences Laboratory, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University Fez Morocco, Morocco c Universite de Pau et des Pays de l'Adour, E2S UPPA, SIAME, Pau, France b

A R T I C LE I N FO

A B S T R A C T

Keywords: PCM Thermal analysis Building material Fluxmeter Micro-encapsulation

In this research, heat transfer in a construction material integrating microencapsulated phase change material (PCM) has been studied and analyzed using a physical model based on the apparent heat capacity approach. The PCM considered includes impurities and behaves like a binary solution. The physical model was validated with the experimental and numerical data from literature. The numerical and experimental results revealed that the fusion and freezing operations were asymmetrical. The impact of the scan rate, the melting temperature, the volume fraction of the PCM and the thickness of the composite material on the phase transition process has been examined and outlined.

1. Introduction

capacity, size and working area of a composite PCM. In addition, an accurate measurement of the heat capacity and enthalpy functions of these materials through the phase transition process is crucial for a correct mathematical modelling of heat transfers in the composite material. Independently of the physical model, if such functions are used, they could be a potential source of imprecision [17,18]. In general, the specific enthalpy and specific calorific capacity of a PCM in relation to temperature are commonly measured using the DSC device. However, the precision of this device relies on the accuracy of the protocol employed to describe the phase change characteristic of the PCM. When performing DSC experiments, particular consideration must be paid to the choice of the scan rates, as various heating rates provide various outputs for heat flux and phase transition temperatures [19,20]. This problem can be addressed by employing the T-history technique, a simplest and inexpensive technique to determine both latent heat and the fusion point of PCMs [21,22]. Using this method, the sample size is considerably larger and the effect of the non-homogeneity of the material can be considered when carrying out the thermal characterization of the sample. However, even with the merits of the T-history technique, it is not suitable to use this method to determine the enthalpy of large-scale of composite phase change material. Another possibility for a dynamic measuring of composite materials integrating PCM is the fluxmeter [23-26]. The principal benefit of this device is the possibility of testing building material samples in cement blocks or in panel form, which eliminates the problems related to the small mass of the sample [27,28]. In addition, for the same reason, this apparatus has been

In the European continent, approximately 40% of energy use and CO2 emissions are generated by the technical installations systems in the building sector [1,2]. Consequently, it became imperative to introduce passive and active technologies to enhance energy efficiency in buildings [3,4]. This issue is extremely urgent that the European Commission has introduced a goal of a 20% mitigation in energy use by 2020 and a 30% by 2030 [5,6]. To accomplish such a goal, the introduction of phase change materials (PCMs) into the building envelopes can be an operative alternative [7–10]. PCMs showed an ability of decreasing the temperature fluctuations and storing high amount of energy [11-13]. In spite of the fact that the incorporation of the PCMs in the building materials affects their mechanical and thermal behaviour, it has been ascertained that the resulting composite material is in all cases eligible as a construction material [14,15]. Leakage detected during the melting process is the main current concern regarding the integration of PCM into the mortar. However, this problem can be remedied by an adequate integration method of the PCM into the mortar. In this regard, the PCM packaging strategy in organic polymer microcapsules, which are generally between 1μm to 1000 μm in size, has been developed to include the PCM into building materials [16]. It is essential to recognize that characterization of phase transition is a central point influencing both the thermal performance and the conception of a composite PCMs. The storage density and the fusion temperatures are among the key design criteria as they determine the ⁎

Corresponding author. E-mail address: [email protected] (T. Kousksou).

https://doi.org/10.1016/j.est.2020.101239 Received 11 August 2019; Received in revised form 17 January 2020; Accepted 22 January 2020 2352-152X/ © 2020 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 28 (2020) 101239

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cp h k K Lf q t T x

density (kg.m−3) volume fraction of the PCM

ρ ε

Nomenclature specific heat (J.kg−1.K−1) enthalpy (J/kg) thermal conductivity (W.m−1.K−1) convective heat transfer coefficient (W.m−2.K−1) latent heat (J/kg) heat flux (W.m−2) time (s) temperature ( °C) position along the direction of the composite material (m)

Subscripts App in l m out PCM s

apparent inlet liquid melting outlet phase change material solid

Greek letters β

heating/cooling rate ( °C/s)

transition process inside composite phase change material and to avoid any possible errors during the use of the Fluxmeter apparatus.

previously used to validate physical models describing the thermal behaviour of composites incorporating PCMs [29,30]. The implementation of a realistic simulation of the heat transfer within a composite material incorporating PCM is also an important issue. Due to the non-linear heat transfer in the PCM [31], a limited number of analytical solutions can be obtained while the numerical solutions are the most part more easily accessible. They can be obtained from leading publications on heat transfer, such as those by Crank [32], Hill [33] and Alexiades and Solomon [34]. It is also noteworthy that the analytical solution of an ideal case of isothermal phase transition may not be able to produce a complete picture of the composite material containing the PCM. In composite materials, PCMs are commonly altered by a certain amount of additives that enhance their longevity or ameliorate their thermal conductivity. In addition, PCMs in building materials contain impurities and behave like binary mixtures [35]. These specific characteristics signify that phase change processes in such materials are not isothermal and usually operate over a range of temperature [36-37]. In this context, some of the analytical solutions described earlier may give some useful insights, but may be not suitable for composite materials including PCMs [38,39]. Thermal gradients within a construction material incorporating a PCM can be examined using the apparent heat capacity method or by the enthalpy approach [40,41]. These methods can solve the problem of the phase transition process without explicit monitoring of the solidliquid interface [42,43]. In the enthalpy approach, the enthalpy function is used as the primary variable and temperature is calculated from enthalpy by the correlation between them [42,44]. In comparison with the enthalpy method, the apparent heat capacity approach contains only one unknown variable (i.e. temperature) which makes its solution easier and computationally straightforward. The form of energy equation in the apparent heat capacity method is also suitable for implicit discretization in time, which can benefit in the unconditional numerical stability. The keystone of this approach resides in the approximation of the heat capacity. Many numerical approximations of the heat capacity during melting and freezing of PCMs have been proposed in literature [46-49]. In this work, the apparent heat capacity method is chosen to describe the non-linear heat transfer properties within a composite material including PCM. The apparent heat capacity function used in this work is determined from an enthalpy function, which is deduced from an inverse method presented in detail in Ref. [50]. The thermal performance of composite materials incorporating PCM have been studied by many researchers [51,52]. However, most investigations reported in the literature suppose that the phase change process occurs at a constant temperature and have not analyzed the thermal gradients these materials [53,54]. The objective of this study is to numerically evaluate the thermal gradients inside a composite material during non-isothermal phase change process. Finally, we present some guidelines to understand some phenomenon during the phase

2. Apparent heat capacity method To simplify the physical model, the following hypotheses have been formulated: - The composite material includes two phases: mortar and PCM. - Thermophysical properties are different for the solid and liquid phases while being independent of temperature and constant with time. - The PCM contains impurities and behaves as a binary mixture. - The thermal conduction is unidirectional in the x-axis. When the numerical model is based on the apparent heat capacity approach, the heat transfer within the composite material integrating micro-encapsulated PCM can be characterized by a single energy equation [51], i. e.

ρc capp (T )

∂T (x , t ) ∂2T (x , t ) = kc ∂t ∂x 2

(1) 3

where ρc and kc are the density [kg/m ] and the thermal conductivity [W/(m.K] of the composite material including PCM respectively. T and t represent temperature ( °C) and time (s) and capp (T ) denotes the apparent heat capacity [kJ/(kg.K)]. We suppose that each face of the composite material is subject to a linear plate temperature which is dependent on time:

Tp = β . t + To

(2)

where β is the heating/cooling rate and To the temperature of the composite material at t = 0 . The capp (T ) function in Eq. (1) can be defined as [45,55]:

capp (T ) =

dh (T ) dt

(3)

where h is the enthalpy of the construction material and may be obtained by considering the formula below:

h (T ) = ε . hpcm + (1 − ε ). hmortar

(4)

where ɛ is the volume fraction of the PCM in the composite material. Eq. (3) can be expressed as:

capp (T ) = ε .

dhpcm dT

+ (1 − ε ).

dhmortar = ε . cpcm (T ) + (1 − ε ). cmortar dT (5)

In Eq. (5), the mortar enthalpy is an usual sensible enthalpy, while the enthalpy of the PCM should be defined during both sensible and latent storage. 2

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As shown in Eqs (10) and (11), the apparent heat capacity of the composite material is calculated at the previous time (n) by using Eq. (6.) In this paper, Eqs. (8) were solved iteratively by using a Tridiagonal Matrix Algorithm (TDMA) method. The computation procedure was carried out using Fortan 90. The space grid size of the composite phase change material is 0.2 mm and the time step is 1 min. Further refinement of either space grids or time steps has no impact on the numerical results. The specified iteration in each time interval was considered convergent when the maximum relative residual of T was less than 10−4.

It can be noted that according to Eqs. (1) and (5), the physical model can provide a clear description of the phase transition inside the composite material as long as the specific thermal capacity of the PCM is adequately defined. In this work, the correlation developed by Erwin et al. [28] is selected to determine the value of the heat capacity of PCM behaving as a binary mixture:

cpcm (T ) =

⎧ cs, pcm + (cL, pcm − cS, pcm) × ⎨c ⎩ L, pcm

(

TA − Tm TA − T

)+L

f

×

TA − Tm (TA − T )2

if

if

T ≺Tm

T ≥ Tm 4. Results and discussion

(6) where Tm represents the end of the non-isothermal melting of the PCM, TA is the melting temperature of the pure PCM and is Lf the latent heat of fusion. The first two terms in Eq. (6) reflect the sensible part and the last one describes the variation of the latent fusion throughout the phase transition of the PCM. By using Eq. (6), one can analyze and explain the non-isothermal phase change in PCMs behaving as a binary solutions. An analogous expression can be deduced for the specific enthalpy of the composite material containing microencapsulated PCM [28]:

As mentioned previously, one of the principal motivations for the development of microcapsules with PCMs is their potential application in the building sector, which allows energy savings and comfort to be preserved in the building's interior. To use composite phase change materials in the building, it is required to have a good understanding of the thermophysical properties of the phase transition of the PCM in order to suggest an appropriate design/optimization strategy. Currently, the fluxmeter is among the most widely used instruments for determining the thermophysical properties of composite materials containing microencapsulated PCM [23,26]. The fluxmeter (see Fig. 2) provides only temperature (Tp) and heat flux (∅) measurements on the extremities of the material and does not measure the temperature variation within the composite material. In this paper, the numerical model presented in Section 2 is checked and validated based on the experimental heat fluxes provided by the fluxmeter device [28]. Our physical model is also validated using numerical results provided by Zhou et al. [57].

h (T )

(

⎧ cS (T − Tm) + cL (Tm − TA) − εLf 1 − ⎪ ⎪ T −T if T ≺Tm (TA − Tm)ln T A− T = A m ⎨ ⎪ cL (T − TA) ⎪ if T ≥ Tm ⎩

(

TA − Tm TA − T

) + (c

S

− cL)

)

(7) 4.1. Thermal analysis of a composite material integrating microencapsulated PCM under linear variation of outside temperature

where ci = ε . ci, pcm (T ) + (1 − ε ). cmortar (i being either Solid or Liquid). Fig. 1 illustrates the variation of the specific enthalpy versus temperature for two cases: Tm < TA and Tm = TA. During the heating process, the state of the composite material displaces from left to right across the curve, with increasing enthalpy and temperature. In a first step, the temperature of the PCM increases with the additional energy that is stored as sensible heat in the solid PCM. The latent heat of fusion is absorbed as the PCM passes from solid phase to liquid phase. When the melting process is concluded, additional energy input again results in a temperature increase (sensible heat in liquid phase). We note that in the case of Tm < TA, the PCM behaves like a binary mixture and the melting process is carried out over a range of temperatures. However, in the case of Tm = TA the PCM acts as a pure substance and the phase transition process is done at constant temperature.

In Ref. [28], the mortar including 12.5% of microencapsulated PCM is disposed in a parallelepiped form with dimension of 25 × 25 × 4 cm3 [28]. Each face of the sample (i.e. rectangular composite material containing microencapsulated PCM) is subjected to a linear plate temperature Tp (see Eq. (2)) ranging from 7 to 39 °C over time by using different heating/cooling rates β. The thermophysical properties of the composite material are indicated in Tables 1a, b [28]. Fig. 3 displays the temperature variation versus time (see Fig. 3a) or versus TP (see Fig. 3b) at different points inside the building material for β = 5. 2∘C/h . One can observe that the temperature pattern at the center of the mortar exhibits an inflection point due to melting/

3. Numerical solution The energy Eq. (1) were discretized over each control volume by using the finite volume approach [56]. A fully implicit scheme was implemented in time. The uniform size of the control volumes and constant time steps have been applied. The resultant finite volume equations are represented by the following formulas:

ai Tin + 1 = ai + 1 Tin++11 + ai − 1 Tin−+11 + bi

(8)

where:

ai + 1 = ai − 1 =

kc Δx

ai = ai − 1 + ai + 1 +

bi =

ρc capp (Tin ) Δt

(9)

ρc capp (Tin )

× Tin

Δt

(10)

(11)

Fig. 1. Specific enthalpy versus temperature. 3

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Y. Khattari, et al.

Fig. 2. Fluxmeter device [28].

the freezing phenomena inside the sample are not symmetric. Fig. 4, which represents the specific enthalpy as a function of time (see Fig. 4a) or versus TP (see Fig. 4b) at different points inside the composite material, confirms the asymmetric character of the freezing and the melting processes at the center of the composite material. This result implies that the enthalpy-temperature relationship during the heating process is not the same as that during the cooling process. One can conclude that the enthalpy function of the PCM is not only dependent on its temperature, but also affected by the thermal gradients inside the composite material. We can also see from this figure, that the melting/freezing takes place over a range of temperature, compared to the case of the pure PCM, where an isothermal transition is observed. It is essential to point out that during the heating/cooling mode, the plate temperature TP at the extremities of the composite material increases/decreases continuously during the heating/cooling mode without being influenced by the melting/freezing process inside the composite material (see Fig. 3). We can also note that the shape of the specific enthalpy function calculated according to TP remains the same throughout the freezing and the melting processes (see Fig. 4). Many operators of the fluxmeter suppose that the temperature within the sample remains uniform during the heating (melting)/ cooling (freezing) process. This implies that the plate temperature TP is the only representative temperature of the composite material and the enthalpy function is only dependent on TP and not influenced by the

Table 1a Thermophysical properties of phase change material. ρ k cS cL Lf Tm TA

1412 kg.m−3 0.55 W.m−1. °C−1 1100 J.kg−1 °C−1 1070 J.kg−1 °C−1 12 J.g−1 25.5 °C 26.8 °C

Table 1b Thermophysical properties of the mortar. Density Thermal conductivity Specific heat capacity

1400 kg.m−3 0.65 W.m−1. °C−1 925 J.kg−1. °C−1

solidification process of the PCM inside the composite material. During the heating mode, the progressive melting (i.e. non-isothermal melting) inside the composite material is carried out over a range of temperatures and the end of the melting process coincides with the fusion temperature Tm. During the cooling mode, the freezing process begins at the melting temperature Tm. We can conclude that the melting and

Fig. 3. Temperature inside the composite material versus time (a) or TP (b). 4

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Fig. 4. Specific enthalpy versus time (a) or TP (b).

heating or cooling modes. In other words, the melting and freezing processes inside the composite material are symmetrical. Normally, when a composite material incorporating a

microencapsulated PCM is continuously heated/cooled, thermal gradients inside the composite material appear during the phase transition process (see Fig. 3). It is reasonable to note that during the phase

Fig. 5. Comparisons between numerical and experimental heat flux. 5

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Y. Khattari, et al.

enthalpy towards the left throughout the cooling process and the right throughout the heating process. These results can be explained by the heating/cooling rate effect on the thermal gradients inside the composite material (Figs. 6b and 7b). For slower heating/cooling rates, the thermal gradient inside the composite material decreases but the time duration of the phase transition increases (see Figs. 6a and 7a).

change process of the PCM, the representative temperature of the sample cannot be assigned to TP. However, during the sensible heat storage (i.e. outside the phase change transition process), thermal gradients within the composite material can be neglected (see Fig. 3) and in that case TP can be chosen as the representative temperature of the sample. The comparison between the experimental and the numerical (solid lines) heat fluxes [28] are reported in Fig. 5a–d. These plots illustrate the variation of the heat flux at the extremities of the composite material versus time for different heating/cooling rates. The plate temperature Tp is also presented on these curves (see Fig. 5) to indicate the variation of the recorded heat flux during the heating and cooling processes. We can observe that the numerical results showed a good agreement with the experimental measurements. Regardless of the heating/cooling rate, the physical model reproduces easily the thermal behavior of the composite material during the phase transition process. It has been noticed that the solidification and melting processes are not symmetrical (see Fig. 5). In fact, during melting related to the heating rate of 7.8 °C/h (after 2 h), the heat flux exhibits a gradual increase versus time, while during the freezing process (around 9 h) there is a sharp variation in the heat flux. We can conclude that the physical model presented in Section 2 can describe the phase transition within the composite material considering the asymmetric nature between the melting and the freezing processes for PCM containing impurities (see Fig. 5). We now suggest examining two parameters (heating/cooling rate and melting temperature) affecting the thermal gradients inside the composite material, to identify the most appropriate experimental approaches to analyze the heat fluxes produced by the fluxmeter.

4.1.2. Effect of the melting temperature tm To use composite materials incorporating microencapsulated PCM in the building, it is required to check the purity of the PCM in order to optimize the latent energy stored or removed during the melting and crystallization phases. In this work, the impact of impurities (contained in the PCM) on the thermal performance of the composite material is investigated by modifying the value of the melting temperature Tm. Fig. 8a and b display the variation of the temperature and the specific enthalpy at the center of the composite material versus TP for various melting temperatures Tm. We note that when the melting temperature Tm is became near to the pure PCM melting temperature TA value (i.e. when the PCM's purity increases), the phase change process occurs approximately at constant temperature and the specific enthalpy curve becomes more abrupt. The impact of the melting temperature Tm value on the heat flux is presented on Fig. 9a and b. We can see that the heat flux released or absorbed during the phase change transition is highly dependent on the melting temperature Tm (i.e. the quantity of impurities contained in the PCM). When we move towards the behavior of the pure PCM, the asymmetric character between melting and crystallization disappears progressively. We can conclude that the presence of impurities in a PCM changes completely the process of phase transition in a composite material.

4.1.1. Effect of the heating/cooling rate As mentioned above, the sample is analyzed at various heating/ cooling rates β varying between 5.2 °C/h and 10.4 °C/h. The corresponding heat fluxes are indicated in Fig. 6 using either the plate temperature TP or the time for the abscissa coordinate. We note that the numerical heat flux produced by the fluxmeter is highly dependent on the heating/cooling rate. The phase transition time is reduced for higher heating/cooling rates due to the stronger heat flux (Fig. 6a). A significant temperature gradient occurs within the sample as the temperature difference between the plate and the sample's center increases with increasing β value (see Fig. 7). It has been also noticed that the usual shifting of the heat flux and the specific

4.1.3. Effect of the volume fraction of the PCM We have presented numerical heat flux versus the plat temperature Tp for different values of ɛ (see Fig. 10a). We note that the phase change process inside the composite material depends on ɛ. We remark that the rise in the volume fraction of the PCM inside the composite material increases the time required for the melting and freezing processes. We can also observe that the increase in the volume fraction of the PCM in the composite material shifts the heat flux to the left during the cooling process and to the right during the heating process.

Fig. 6. Numerical heat fluxes for various heating/cooling rates. (a) Heat fluxes versus time (b) Heat fluxes versus TP. 6

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Fig. 7. Temperature (a) and specific enthalpy (b) at the center of the sample versus TP.

Fig. 8. Temperature (a) and specific enthalpy (b) at the center of the sample versus TP.

possible cause of the real hysteresis is when the latent heat is released too slowly during the freezing process [58]. The presence of impurities in the PCM can also render the processes of melting and crystallization asymmetric inside the composite material. To verify if the hysteresis phenomenon is present or not in the case of pure PCM, specific enthalpy functions at the center of the composite material during heating and cooling modes for Tm = TA and for different scan rates β are presented on Fig. 11. We notice that the specific enthalpy function of the composite material integrating pure PCM is shifted towards the right (heating mode) and the left (cooling mode) respectively. As a result, the hysteresis phenomenon is present despite the fact that the phase change is carried out under constant temperature. We can also note that the hysteresis phenomenon is amplified by increasing the rate of heating and cooling modes. This phenomenon is most probably due to the thermal gradients inside the composite material. It is important to remind that when the specific enthalpy of the

4.1.4. Effect of the thickness of the composite material Fig. 10b presents heat flux versus the plate temperature Tp for different thickness of the composite phase change material. The increase in the sample thickness leads to an additional amount of PCM in the composite material. As a result, the flux released or absorbed during crystallization or melting becomes more important by increasing the thickness of the sample. 4.1.5. Hysteresis phenomenon The hysteresis phenomenon is generally characterized by a total shifting of the specific enthalpy function during the freezing process of the PCM with respect to the same function during the melting process [58]. There are a various phenomena associated with the thermophysical properties of the material under study which can generate the hysteresis phenomenon. The most common one is supercooling. In our work the effect of the supercooling phenomenon is neglected. Another 7

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Fig. 9. Numerical heat fluxes for various melting temperature Tm. (a) Heat fluxes versus time (b) Heat fluxes versus TP.

Fig. 10. Numerical heat fluxes for various volume fraction of the PCM (a) and various thickness (b).

Fig. 12. Heat transfer condition of the SSPCM wallboard.

Fig. 11. Specific enthalpy at the center of the sample versus TP for various β.

8

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Table 2 Thermophysical properties and convective heat transfer coefficient for the SSPCM wallboard [57]. ρ (kg.m−3) k (W.m−1. °C − 1) cS (J.kg−1 °C−1) cL (J.kg−1 °C−1) Lf (J.g−1) Tm( °C) ɛ Kin(W.m−2. °C−1) L(m)

850 0.2 2000 2000 120, 150, 200 18, 20, 22 1 8.7 0.02

Fig. 15. Inner heat flux versus time for different latent heat fusion.

temperature is maintained constant at 20 °C (see Eq. (13)). The PCM investigated in the context of this problem is supposed pure.

qout = −kc

∂T ∂x

(12)

x=0

Kin (20 − T (x = L, t )) = −kc

∂T ∂x

x=L

(13)

where Kin is the inner convective heat transfer coefficient, respectively. Zhou et al. [57] have already investigated the same problem by using the implicit enthalpy method. The thermophysical properties of the SSPCM wallboard used by Zhou et al. [57] are shown in Table 2. Fig. 13 presents a comparison between the hourly inner heat flux calculated by our method and that obtained by Zhou et al. [57] for Tm = 20 °C. As shown in Fig. 13, there is a good agreement between our results and those obtained by Zhou et al. [57]. Fig. 14 illustrates the effect of the melting temperature on the inner heat flux. It is interesting to see that for Tm = 20 °C, the inner heat flux keeps almost flat near the zero point during the phase change process. For Tm = 18 °C and 22 °C, the heat flux is not flat during the phase transition period. This is due to the fact that the indoor temperature is assumed to be constant at 20 °C, so there is temperature difference between the inner surface of the wallboard and indoor air and then heat flux keeps around some value during the phase transition period for Tm = 18 °C and 22° Fig. 15 presents the influence of the latent heat on the melting/freezing process inside the SSPCM wallboard. Fig. 15 indicates that there exist fluctuations of inner surface heat flux between the two-phase transition times for cases of 120 and 150 kJ/kg. While for the case of 200 kJ/kg the inner surface heat flux remains near zero all times which means that the outside heat flux wave is completely stopped by the phase transition process due to the high latent heat of fusion. This implies that, for some external heat flux waves, there exists a critical value of the latent heat of fusion for SSPCM beyond which the inner surface heat flux keeps constant at or near zero. Zhou et al. [57] obtain the similar results concerning the effect of the melting temperature and the latent heat of fusion on the inner heat flux.

Fig. 13. Inner heat flux versus time for Tm = 20 °C.

Fig. 14. Inner heat flux versus time for various melting temperatures.

sample is calculated as a function of the plate temperature Tp and not according to the real temperature of the composite material, the hysteresis phenomenon disappears. 4.2. Thermal analysis of a PCM wallboard under sinusoidal outside heat flux

5. Conclusion

To verify the robustness of our numerical model, we have applied the apparent capacity method to investigate the problem of heat transfer inside a shape-stabilized PCM (SSPCM) wallboard as illustrated in Fig. 12. The outer surface of the wallboard is subjected to a sinusoidal heat flux qout (see Eq. (12)). While at the inner face of the wallboard, convection boundary condition is satisfied and the air

This paper investigated the heat transfer within a building material including microencapsulated PCM using a physical model based on the apparent calorific capacity method. The PCM studied contains impurities and acts as a binary solution. The physical model used in this study was validated with the experimental and numerical data reported in previous studies in the literature. The impact of the heating/cooling 9

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rate and the melting temperature value on the thermal behavior of the composite material is also presented. The conclusions of this numerical investigation can be synthesized below:

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• During the phase change process of the PCM, thermal gradients have • •

been observed, which is responsible for the form of the heat flux. Decreasing the heating/cooling rate β could reduce these thermal gradients. It is very important to determine carefully the percentage of impurities present in a PCM to correctly describe the heat transfers throughout the phase change process. The presence of impurities in the PCM renders the processes of melting and crystallization asymmetric inside the composite material.

Work in progress will regard the numerical model validated in this paper as an optimization tool for the design of building materials incorporating PCM with impurities. It will be particularly important to study this kind of composite materials under realistic boundary conditions. Author statements T. Kousksou(c), M. Alaphilippe(c), Y. Zeraouli(c) are professors at the Université de Pau et des Pays de l'Adour in France T. El Rhafiki is professor at Université de Fès in Morocco Y. Khattari(a) and N. Choab(c) are Phd sutdents at Université de Pau et des Pays de l'Adour in France. CRediT authorship contribution statement Y. Khattari: Software. T. El Rhafiki: Validation. N. Choab: Visualization. T. Kousksou: Supervision, Writing - original draft. M. Alaphilippe: Methodology. Y. Zeraouli: Writing - review & editing. Declaration of Competing Interest Authors have no conflicts of interest regarding the work done and presented in our article. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.est.2020.101239. References [1] A. Allouhi, Y. El Fouih, T. Kousksou, A. Jamil, Y. Zeraouli, Y. Mourad, Energy consumption and efficiency in buildings: current status and future trends, J. Clean. Prod. 16 (2015) 118–130. [2] L. Brady, M. Abdellatif, Assessment of energy consumption in existing buildings, Energy Build. 149 (2017) 142–150. [3] S.D. Rezaei, S. Shannigrahi, S. Ramakrishna, A review of conventional, advanced, and mart glazing technologies and materials for improving indoor environment, Sol. Energy Mater. Sol. Cells 159 (2017) 26–51. [4] D. Sánchez-García, C. Rubio-Bellido, J. Jesús Martín del Río, A. Pérez-Fargallo, Towards the quantification of energy demand and consumption through the adaptive comfort approach in mixed mode office buildings considering climate change, Energy Build. 187 (2019) 173–185. [5] A. G.Gaglia, E. N.Dialynas, A.A. Argiriou, E. Kostopoulou, D. Tsiamitros, D. Stimoniaris, K.M. Laskos, Energy performance of European residential buildings: energy use, technical and environmental characteristics of the Greek residential sector – energy conservation and CO₂ reduction, Energy Build. 183 (2019) 86–104. [6] C. Deba, F. Zhang, J. Yang, S.E. Lee, K.W. Shah, A review on time series forecasting techniques for building energy consumption, Renew. Sustain. Energy Rev. 74 (2017) 902–924. [7] S. Hamdaoui, M. Mahdaoui, T. Kousksou, Y. El Afou, A.A. Msaad, A.Arid, A. Ahachad, Thermal behaviour of wallboard incorporating a binary mixture as a phase change material, J. Build. Eng. 25 (2019) 120–135. [8] L. Navarro, A. Solé, M. Martin, C. Barreneche, L. Olivieri, J.A. Tenorio, L.F. Cabeza, Benchmarking of useful phase change materials for a building application, Energy

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