# Numerical and Experimental Investigations of Composite Solar Walls Integrating Sensible or Latent Heat Thermal Storage

^{*}

## Abstract

**:**

## 1. Introduction

_{12}CaCl

_{2}O

_{6}) placed on a wooden frame behind a double-glazing. The results showed that for an equivalent effect, the latent heat storage wall can reduce 4 times the thickness of the concrete Trombe wall weighing a total of 6 times more than the PCM Trombe wall. Ghoneim et al. [18] performed the numerical simulation of a collector-storage wall incorporating various storage elements: sodium sulfate decahydrate (Na

_{2}·SO

_{4}·10H

_{2}O), medical paraffin, P116-wax, and classical concrete. Numerical results revealed that the Trombe wall containing PCM (Na

_{2}·SO

_{4}·10H

_{2}O) performed the thermal heat transfer with high efficiency compared to other storage elements (concrete, paraffin, P116-wax).

_{2}·6H

_{2}O), and paraffin-wax (N-eicosane); the imposed thermal boundary condition was based on Iraqi weather. Simulation results demonstrated that an 8-cm thick storage wall made of hydrated salt (CaCl

_{2}·6H

_{2}O) could maintain the temperature in the interior zone close to the comfort level (22–25 °C), while a 20-cm thick concrete storage wall and a 5-cm thick paraffin storage wall were both affected by the ambient temperature, causing a decrease in the inside temperature (18–22 °C).

_{2}·6H

_{2}O) is presented in [21]. The purpose of using this tool was to enhance heat transfer by convection; consequently, the results relative to airflow rate and room heating rate indicated that use of DWVG raised performance by 28.5% and 39.4%, respectively, compared to the case without DWVG.

^{2}, 600 W/m

^{2}and 700 W/m

^{2}; each experiment was run for 24 h. These experimental results showed that paraffin wax could efficiently store solar thermal energy during the day and release it several hours later; moreover, the duration of circulating air created from heat transfer exchanges could extend the period of released heat, especially at night, to around 14 h for all cases investigated.

_{2}O + CaCl

_{2}+ KCl + various additives), which can store much more heat than the same volume of concrete. The authors also proved that these bricks (thickness: 23 mm) allow recovering solar gains with a shorter time delay (approx. 2 h, 40 min), which had been the drawback in winter when a house wall required additional energy supply (i.e., heat gain) at the end of the day. Nevertheless, such a wall can be considered to be advantageous in winter when used for structures occupied during the day, e.g., offices, shopping centers, hospitals, universities, schools. Leang et al. [22] created a numerical model using the Dymola/Modelica software and its various libraries [50,51] in order to simulate two cases of a solar wall component. The first case sought to compare experimental and numerical results for a composite Trombe wall equipped with a concrete storage wall as a means of validating the model. The second case was intended to use the validated model to conduct other simulations of the composite Trombe wall, in which concrete was replaced by a wall integrating micro-encapsulated PCM.

- Present the specific features and experimental set-up of a composite Trombe wall containing PCM;
- Explain how the numerical method, with the help of the Dymola/Modelica software, performs in determining the thermal behavior of the composite solar walls;
- Validate this numerical model based on a comparison between simulation and measurement;
- Compare the efficiency of sensible vs. latent storage of composite solar walls.

## 2. Composite Solar Wall and Experimental Set-Up

^{3}.

_{ext}, T

_{ext}, $\varphi $

_{int}and T

_{int}) are placed on both sides of the storage wall in the central position (Figure 1). The fluxmeter ($\varphi $

_{ext}) measures the flux of heat entering or leaving the outer storage wall surface (solar radiation and exchanges between the storage wall and glazing). On the ventilated air layer side, the fluxmeter ($\varphi $

_{int}) simultaneously measures the convective exchanges between storage wall and air as well as the radiative exchanges between this same wall and the insulated wall located opposite. Two thermocouples measure air temperature at both the lower vent (T

_{lv}) and the air layer outlet at the upper vent (T

_{uv}).

## 3. Meteorological Data

^{2}); this is due to the presence of a horizontal light-colored roof under the windows of the floor where the experiments were carried out (Figure 4).

## 4. Mathematical Model

_{glass1}, $\varphi $

_{glass2}, $\varphi $

_{wall}, glass1, glass2, storage wall with/without PCM, insulating panel, ventilated air layer. The most interesting point here is implementation of the model focused on the latent storage wall and based on the enthalpy method. The typical procedure for running Dymola/Modelica is to graphically build a model by selecting, drawing, connecting and configuring the individual components extracted from a library. The meteorological data are stored in tables, while the codes (formulas and equations) representing the physical behavior of the various model parts (convection, radiation, conduction) are embedded in the components:

- $\varphi $
_{glass}: evaluate the solar heat flux absorbed by glazing and the direct flux transmitted to the outer storage wall surface M+PCM Equation (14); - $\varphi $
_{wall}: evaluate the total energy absorbed by the wall in considering the heat flux transmitted from the glazing and multi-reflections in the non-ventilated air gap Equation (15); - Conv_ext: evaluate the total heat transfers by convection between the composite Trombe wall and the outside. This step depends on the outdoor air temperature as well as the wind velocity and direction Equation (6);
- Rad_int: evaluate the inside longwave radiative heat transfer between the inner wall facade and the indoor environment Equation (35);

#### 4.1. Thermal Balance on the External Glazing Surface

_{glob,vert}is the vertical global solar flux on the outer surface of the double glazing; this flux is the sum of the various components of the incident solar radiation that reaches the surface of the double glazing (direct, diffuse and reflected radiation).

_{r}is the balance of longwave radiation exchanges between the surface of the double glazing and its external environment (ground environment and celestial vault); this total flux is given by the following equation:

_{r,sky}and h

_{r,gro}are the radiative heat transfer coefficients on the outer surface of the double glazing. h

_{r,sky}and h

_{r,gro}are calculated based on the fluctuation between the sky temperature, the outside air temperature (T

_{sky}, T

_{gro}) and the glass temperature (T

_{g,ext}).

_{conv}is the convective heat transfer at the outer surface of the double glazing with the outside air; it is calculated by the following equation:

#### 4.2. Thermal Balance on the Inner Surface of the Glazing (Non-Ventilated Air Gap)

_{g}) and the outer storage wall surface (x = e

_{g}+ $\delta $

_{1}), the average temperature of fluid ${T}_{f1}$ is set equal to the average glazing and storage wall surface temperatures: ${T}_{f1}=({T}_{g}+{T}_{w})/2$. The thermal balance of the two walls (glazing and storage wall) is calculated by the following equations:

#### 4.3. Thermal Transfer by Conduction on the Storage Wall

_{mesh}). After a parametric study, a discretization of 30 meshes was selected. The thermophysical and dimensional properties introduced are those of the apparent composite material, which means that the composite material resulting from the mixture of cement mortar and PCM is considered to be a homogeneous isotropic material:

_{M}), the melting temperature associated with the pure substance (T

_{A}) of the PCM, the specific heats of the composite material when the PCM is in the solid state (c

_{solid}) and in the liquid state (c

_{liquid}), as well as the latent heat of phase change (L

_{A}) contained in the composite material.

_{m_pcm}represents the derivative of enthalpy with respect to temperature T [63,66] and is presented in Figure 9b. The following equations are used to determine the value of c

_{m_pcm}once the material temperature is known.

#### 4.4. Thermal Balance in the Ventilated-Air Layer

^{9}). Therefore, the correlation considered for all calculations is the first one during the measurement period.

#### 4.5. Thermal Balance towards the Interior Atmosphere

#### 4.6. Material Properties

^{®}PCM DS 5001 X) at a proportion of mixed cement mortar in 17 % of the total mass of dry materials (sand, cement, PCM). The mix proportions are listed in Table 1.

## 5. Model Validation, Results and Discussion

^{2}(Figure 5), the storage wall can absorb a large quantity of incoming solar flux (400–450 W/m

^{2}of heat flux at the external surface of the storage wall), corresponding to about 50% of the incident solar radiation during sunshine hours. This percentage confirms the transmission rate measurements conducted in our laboratory with two pyranometers placed on both sides of the double glazing. The heat flux becomes negative (−50 W/m

^{2}) at the outer surface of the storage wall by the end of the day due to heat losses into the external environment. It should be noted here that the semi-transparent cover is a conventional double glazing; a glass with reinforced insulation would certainly have made it possible to limit these heat losses. The time lag between the incident solar radiation and the heat flux release in the ventilated air layer (${\varphi}_{\mathrm{int}}$), for this 4-cm thick experimental storage wall, is estimated by calculating the cross-correlation function [24] at 184 min (i.e., approximately 3 h). During sunny periods, the storage wall temperature can reach 65 °C on the outer surface and 45 °C on the inner surface.

_{ext}and T

_{int}) is on the order of 1 °C. The difference of 8.6% between the calculated and measured flows on the inner side of the storage wall is due to the less accurate estimation of temperature on this surface, which is especially true at maximum temperatures. This difference is most probably due to the unidirectional (1D) calculation of heat transfers in the wall; consequently, heat losses towards the edges of the storage wall are not being taken into account. Moreover, the difference between numerical calculation and thermocouple measurement of the air temperature at the upper vent level of the ventilated air layer T

_{uv}is on average 0.4 °C. In Figure 11, the released latent heat can be observed every day around 8:00 pm by the inflection of temperature curves at 26 °C, corresponding to the solidification point.

_{lv}) and outlet (T

_{uv}) of the ventilated air layer, as well as the ambient temperature of the room (T

_{room}). When the average temperature of air inside the ventilated air layer is higher or warmer than the room air temperature, a natural thermocirculation is thus activated, with air entering through the lower vent (T

_{lv}) and being released from the upper vent (T

_{uv}). This phenomenon is due to the thermal contributions of the storage wall in the ventilated air layer (convection and radiation), which in turn cause the air to be heated and then set into motion (i.e., a thermosiphon or “chimney effect”). During its movement towards the upper vent, the air is warmed up in contact with the storage wall before being introduced into the room; a very small portion of the energy supplied by the solar wall is transmitted to the room by means of conductive heat transfer through the insulating wall. On the other hand, during non-sunny periods or at the end of the night, when heat flux at the external surface of the storage wall is negative, the storage wall discharges its thermal energy towards the outside and becomes colder than the air in the room. As a consequence, the air circulating in the ventilated air layer during the inverse thermocirculation is affected by this convective heat transfer, in turn decreasing the air temperature. When the storage wall is cooler than the indoor environment, air enters through the upper vent, cools in contact with the walls, becomes heavier and returns to the room through the lower vent of the ventilated air layer. In this case therefore, a reverse thermocirculation effect is at work.

_{lv}and T

_{uv}is closest to the room air temperature (T

_{room}). A negative heat flux sign on the inner surface of the storage wall (${\varphi}_{\mathrm{int}}$) makes it possible to identify this phenomenon. For our model, the following conditions must be input in order to define the air flow direction: if T

_{air layer}> T

_{room}, air enters at the lower vent of the composite solar wall and heats the room; if T

_{air layer}< T

_{room}, air enters at the upper vent and exits at a colder temperature through the lower vent (Figure 13). T

_{air layer}is the mean of the temperature of the walls inside the ventilated air layer (T

_{int}) and the temperature of the insulated panel. It should be noted that air can exit very hot (nearly 35 °C) from the air layer, and this air temperature (T

_{uv}) was correctly estimated. The temperature difference between measured and calculated air temperatures at the upper vent equals 0.4 °C on average for this period.

_{uv_cal}, T

_{uv_exp}) show very strong similarities between experimental measurements and numerical results. The comparison of heat fluxes exchanged and temperatures within the ventilated air layer serves to confirm the good level of agreement between behavioral modeling of a composite Trombe wall integrating PCM and experimentation. It is possible therefore to calculate the energy recovered through the energy balance of the solar wall over a given period (19–26 April 2014). This balance was calculated in the ventilated air layer using two methods validated in previous studies [22,24]. The first method is the energy balance due to the total head loss coefficient of air between the inlet and outlet of the ventilated air layer (Equation 32), while the second method is based on a direct heat flux measurement (Equation 33).

^{2}for the calculation and 4.7 kWh/m

^{2}for the estimation derived from fluxmeter measurements; the difference between the two methods is on the order of 6.3%.

^{2}(per m

^{2}of solar wall). Most recently, 35.8% of the total energy, i.e., 7.7 kWh/m

^{2}, was absorbed by the storage wall at its external surface. The stored energy, which was released within a 3h 04 min time delay (calculation with cross-correlation function between ${\varphi}_{\mathrm{ext}}$ and ${\varphi}_{\mathrm{int}}$) to the ventilated air layer is estimated at 4.7 kWh/m

^{2}, which equals to 60.8% of the absorbed energy and 21.8% of the energy generated from the total incident solar flux on the vertical facade of the solar wall (as measured by the pyranometer).

## 6. Comparing Performance of Composite Solar Walls with Sensible vs. Latent Heat Storage

^{®}PCM DS 5001 X, i.e., the same as that incorporated into the experimental solar wall studied herein. Previous works highlighted that the micro-encapsulated PCM incorporated into mortar allows for 41% more energy to be stored compared to cement mortar. The thermophysical parameters of these materials are reported in Table 4 below. These same materials were introduced into the composite Trombe wall model to run the simulations.

_{ext,m+pcm}and T

_{int,m+pcm}curves can be detected. For the cement mortar + PCM storage wall, PCM solidifies and releases latent heat, in which case the storage wall remains warmer longer. As such, the cement mortar + PCM storage wall can release energy later, which helps avoid reverse thermocirculation (as highlighted in Figure 16 by negative powers for the cement mortar storage).

^{2}for the solar wall equipped with cement mortar storage and 3.9 kW/m

^{2}for the solar wall equipped with mortar + PCM storage. Surprisingly, the solar wall capable of storing more energy is not the more efficient. The possible reason for this finding is either a lower transfer rate or a different energy storage than initially thought. The first reason pertains to the fact that thermal conductivity is almost 1.75 times lower for cement mortar with PCM. Furthermore, if the solar wall operating temperature range were to be examined, it would differ from that of the study cited [69]. In that previous study, the temperature range spanned 28 °C (between 11.4 °C and 39.4 °C), while the thermal capacity was 41% greater for the mortar integrating PCM. In this present case, the temperature range spans 45 °C (from 15 °C to 60 °C, in considering the average maximum temperatures); consequently, the difference is slightly higher, by 13%, in favor of the mortar + PCM. Hence, the higher thermal conductivity and lower total thermal capacity of storage without PCM produce a faster and greater energy release from the solar wall equipped with cement mortar storage and, therefore over the study period, improved energy efficiency.

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols: | |

A | area, m^{2} |

A_{exch} | exchange surface, m^{2} |

C | heat capacity, J/K |

c | specific heat capacity, J/kg K |

c_{f} | specific heat capacity of fluid, J/kg K |

c_{solid} | specific heat capacity when PCM is in the solid state, J/kg K |

c_{liquid} | specific heat capacity when PCM is in the liquid state, J/kg K |

E | thermal energy, J |

e | thickness, m |

Gr | Grashof number |

H | height, m |

h | specific enthalpy, J/kg |

h_{c} | convective heat transfer coefficient, W/m^{2} K |

h_{c1} | convective heat transfer coefficient in non-ventilated air layer, W/m^{2} K |

h_{c2} | convective heat transfer coefficient in ventilated air layer, W/m^{2} K |

h_{r} | radiative heat transfer coefficient, W/m^{2} K |

h_{r1} | radiant heat transfer coefficient between glazing and wall, W/m^{2} K |

h_{r2} | radiant heat transfer coefficient between wall and insulating panel, W/m^{2} K |

L_{A} | latent heat, J/kg |

$\dot{m}$ | air mass flow rate, kg/s |

Nu | Nusselt number |

P | power supplied by air layer, W |

Pr | Prandtl number |

Q_{sol} | solar radiation intensity, W/m^{2} |

Ra | Rayleigh number |

Re | Reynolds number |

T | temperature, °C |

t | time, s |

V | velocity of wind, m/s |

W | width, m |

Greek symbols | |

$\alpha $ | absorptivity |

$\beta $ | dilatation coefficient at constant pressure, K^{−1} |

${\delta}_{1}$ | non ventilated air gap width, m |

${\delta}_{2}$ | ventilated air gap width, m |

$\epsilon $ | emissivity |

$\lambda $ | thermal conductivity, W/m K |

$\mu $ | dynamic viscosity of air, kg/m s |

$\upsilon $ | kinematic viscosity of air, m^{2}/s |

$\xi $_{g} | absorptivity of multi-reflection radiation intensity to glazing |

$\xi $_{w} | global absorptivity of wall (including multi-reflection) |

$\rho $ | density, kg/m^{3} |

$\sigma $ | Stefan-Boltzmann constant, 5.67 × 10${}^{-8}$ W/m^{2} K^{4} |

$\tau $ | transmissivity |

$\varphi $ | heat flux, W |

Subscripts | |

A | pure substance |

amb | ambient |

cal | calculation |

env | environment |

exp | experimentation |

ext | exterior surface |

f | fluid |

f_{1} | fluid circulating in non-ventilated |

f_{2} | fluid circulating in ventilated air layer |

g | glazing |

gro | ground |

i | initial |

ins | insulating |

int | interior surface |

lv | lower vent |

M | melting |

uv | upper vent |

w | wall (storage wall) |

Abbreviations | |

CM | cement mortar |

M_PCM | composite material: mortar + PCM |

PCM | phase change material |

Q_cm | internal capacity of CM |

Q_pcm | internal capacity of M_PCM |

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**Figure 4.**Sensors used to measure outside temperature (

**a**) and anemometer/wind vane used to measure wind speed and direction (

**b**).

**Figure 5.**Meteorological data: $\varphi $

_{glob_vert}denotes global solar radiation on the vertical facade of the wall, and T

_{ext}denotes outside air temperature.

**Figure 10.**Comparison of heat fluxes on both sides of the storage wall (model results and experimentation). $\varphi $

_{ext,(m+pcm)_cal}and $\varphi $

_{ext,(m+pcm)_exp}denote respectively the evolution in numerical and experimental heat fluxes on the exterior surface of the storage wall containing PCM; $\varphi $

_{int,(m+pcm)_cal}and $\varphi $

_{int,(m+pcm)_exp}denote respectively the evolution in numerical and experimental heat fluxes on the interior surface of the storage wall containing PCM.

**Figure 11.**Comparison of temperatures on both sides of the storage wall (model results and experimentation). T

_{ext,(m+pcm)_cal}and T

_{ext,(m+pcm)_exp}denote respectively the evolution in numerical and experimental temperatures on the exterior surface of the storage wall containing PCM; T

_{int,(m+pcm)_cal}and T

_{int,(m+pcm)_exp}denote respectively the evolution in numerical and experimental temperatures on the interior surface of the storage wall containing PCM.

**Figure 12.**Comparison of air temperatures at the upper vent of the ventilated air layer (model results and experimentation). T

_{lv}is the experimental air temperature at the lower vent of the ventilated air layer; T

_{uv_cal}and T

_{uv_exp}denote respectively the evolution in numerical and experimental air temperatures at the upper vent of the ventilated air layer; T

_{room}is the room-temperature fluctuation.

**Figure 13.**Evolution in the average air temperature inside the ventilated air layer (T

_{air layer}) compared to the room-temperature fluctuation (T

_{room}).

**Figure 14.**Comparison of the power released by the solar wall. Power

_{cal}denotes the power released according to calculation results, while Power

_{fluxm}is the power released according to fluxmeter measurements.

**Figure 15.**Comparison of temperature on both sides of the storage wall (cement mortar and mortar containing PCM). T

_{ext,m+pcm}and T

_{ext,cm}denote respectively the evolution in numerical temperatures on the exterior surface of the storage wall made from mortar containing PCM and that made from cement mortar; T

_{int,m+pcm}and T

_{int,cm}denote respectively the evolution in numerical temperatures on the interior surface of the storage wall made from mortar containing PCM and that made from cement mortar.

**Figure 16.**Comparison of the power released by the solar wall. Power

_{m+pcm}and Power

_{cm}denote respectively the evolution in the numerical results of power released from the solar wall integrating a storage wall containing PCM and that integrating a storage wall made from cement mortar.

Cement-Sand Mass Ratio | Water to Cement Ratio | PCM/(Cement + Sand) Mass Ratio |
---|---|---|

1/2.6 | 1/1.1 | 1/4.1 |

Material | Symbol | Explanation | Unit | Value |
---|---|---|---|---|

Glazing | ${\rho}_{g}$ | density | kg/m${}^{3}$ | 2500 |

${c}_{g}$ | specific heat capacity | J/(kg.K) | 830 | |

${\lambda}_{g}$ | thermal conductivity | W/(m.K) | 1.47 | |

${\alpha}_{g}$ | absorptivity | - | 0.84 | |

${\tau}_{g}$ | transmissivity | - | 0.76 | |

${\epsilon}_{g}$ | emissivity | - | 0.84 | |

Mortar + PCM | ${\rho}_{m\_pcm}$ | density | kg/m${}^{3}$ | 1329 |

${c}_{solid}$ | specific heat at solid state | J/(kg.K) | 1178 | |

${c}_{liquid}$ | specific heat at liquid state | J/(kg.K) | 1150 | |

${L}_{A}$ | latent heat | J/kg | 17,100 | |

${T}_{A}$ | pure substance temperature | °C | 27.37 | |

${T}_{M}$ | melting temperature | °C | 25.83 | |

${\lambda}_{m\_pcm}$ | thermal conductivity | W/(m.K) | 0.62 | |

${\alpha}_{m\_pcm}$ | absorptivity | - | 0.9 | |

${\epsilon}_{m\_pcm}$ | emissivity | - | 0.9 | |

Insulating wall | ${\rho}_{ins}$ | density | kg/m${}^{3}$ | 30 |

${c}_{ins}$ | specific heat capacity | J/(kg.K) | 880 | |

${\lambda}_{ins}$ | thermal conductivity | W/(m.K) | 0.041 | |

${\alpha}_{ins}$ | absorptivity | - | 0.9 | |

${\epsilon}_{ins}$ | emissivity | - | 0.9 |

Symbol | Explanation | Unit | Value | |
---|---|---|---|---|

Solar energy | E_{sol} | energy | kWh/m^{2} | 21.4 |

Energy absorbed | E_{pcm,ext_cal} | energy | kWh/m^{2} | 7.8 |

E_{pcm,ext_exp} | energy | kWh/m^{2} | 7.7 | |

- | variance | % | 1.3 | |

Solar release | E_{pcm,int_cal} | energy | kWh/m^{2} | 5.1 |

E_{pcm,int_exp} | energy | kWh/m^{2} | 4.7 | |

- | variance | % | 7.8 |

Material | Mortar | PCM-M |
---|---|---|

Solid State | Liquid State | ||

Thermal Conductivity (W.m^{−1}.K^{−1}) | 0.65 | 0.37 |

Heat Capacity (J.kg^{−1}.K^{−1}) | 925 | 1255; 1238 |

Latent Heat (J.kg^{−1}) | — | 19,520 |

Density (kg.m^{−3}) | 2001 | 1248 |

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**MDPI and ACS Style**

Leang, E.; Tittelein, P.; Zalewski, L.; Lassue, S.
Numerical and Experimental Investigations of Composite Solar Walls Integrating Sensible or Latent Heat Thermal Storage. *Appl. Sci.* **2020**, *10*, 1854.
https://doi.org/10.3390/app10051854

**AMA Style**

Leang E, Tittelein P, Zalewski L, Lassue S.
Numerical and Experimental Investigations of Composite Solar Walls Integrating Sensible or Latent Heat Thermal Storage. *Applied Sciences*. 2020; 10(5):1854.
https://doi.org/10.3390/app10051854

**Chicago/Turabian Style**

Leang, Enghok, Pierre Tittelein, Laurent Zalewski, and Stéphane Lassue.
2020. "Numerical and Experimental Investigations of Composite Solar Walls Integrating Sensible or Latent Heat Thermal Storage" *Applied Sciences* 10, no. 5: 1854.
https://doi.org/10.3390/app10051854