A 3D Model of a Photovoltaic Thermal Panel with the Heat Transfer Fluid Tube Embedded in a Layer of Phase Change Material and Metal Foam

Currently, photovoltaic modules can only convert 5 to 25% of incoming solar radiation into electricity, with the rest of the solar energy being converted into heat within the modules, which is often wasted. In contrast, a hybrid PV/T system can capture this excess heat and convert it into usable thermal energy while also generating electricity from solar radiation using PV panels [1]. Mousavi et al. [2] showed that electrical and exergy efficiencies could be optimized by integrating phase change materials and metal foam into the PV-T panel. In their study, they observed that thermal efficiency was lower in configurations lacking the optimized combination of PCM and MF. In the climate of Benha, Egypt, Sharaf et al. [3] investigated the yearly energy and exergy performance of a PV panel in conjunction with aluminium metal foam embedded into pure PCM. They discovered that combining PCM with PV panels improved the efficiency and output of electricity. In order to attain peak performance, careful consideration should go into choosing PCM [4-6]. Moreover, Dayer et al. [7] investigated a 3D model of a PV-T panel incorporating copper metal foam and phase change material (PCM), resulting in reduced PV surface temperature and increased electrical efficiency. In experiments conducted under 1000 W/m² irradiance and 20℃ ambient temperature, the collector exhibited thermal and electrical efficiencies of 65% and 13%, respectively. Sharaf et al. [8] showed that PCM is quite effective at absorbing extra heat from PV panels that would otherwise be wasted. During peak heat periods, the latent heat of PCM is used to keep panel temperatures below 25℃, which improves the overall performance of PV-T system as well as its thermal and electrical efficiency. Alsaqoor et al. [9] investigated the impact of integrating phase change materials into PVT panels and developed a graphic user interface within MATLAB Simulink, using the weather conditions of Amman, Jordan. They found that the maximum electrical power achievable in a PVT system with PCM was 21 kW, compared to 18 kW in a PVT system without PCM. According to Bandaru et al. [10], PVT-PCM systems may store 50% more heat than conventional PVT-water systems, which increases power output and extends the time that thermal energy is available. Nevertheless, poor PCM selection might result in problems like poor heat conductivity and incorrect cycles of charging and discharging, requiring more experimental study to guarantee long-term system integrity and stop leaks. Hossain et al. [11] demonstrated that PCM was used in the development of a hybrid solar PVT system, and its performance was compared with meteorological data from Malaysia. The results show that the use of PCMs improved PV performance (both electrical and thermal). PVT and PVT-PCM collectors were found to have maximum electrical and thermal efficiencies of 14.57% and 15.32%, and 75.29% and 86.19%, respectively. Noxpanco et al. [12] highlighted the necessity of conducting an economic assessment of PV/T systems, stressing the difficulty in acquiring pricing data and arguing in favour of the timely availability of such data to support engineering and design decisions. Furthermore, they recommended that in order to increase acceptance and efficiency, greater attention should be paid to enhancing the aesthetics of PV/T systems. The purpose of this article is to create a photovoltaic thermal panel 3D module, consisting of a heat transfer tube embedded in a layer of phase change material and metal foam, in order to provide the panel itself with a heat storage capacity that allows it to operate for a greater number of hours compared to a typical photovoltaic thermal panel. Specifically, the layer that acts as insulation in conventional PVT panels has been replaced with a layer of PCM+MF. The analysis was conducted assuming a temperature of the heat transfer fluid at 20℃, and examining the performance of the panel module under environmental conditions of temperature and irradiance typical of January, June, July, and December in Aversa (IT), with an inclination of 30°.

In this study, several assumptions and simplifications have been incorporated:

-The PV panel components are assumed to exhibit isotropic and homogeneous properties.

-The first layer of the PV unit (EVA) generates incident solar radiation, which is uniform, and it is considered that the transmissivity of the EVA layer is 100%

-There is negligible contact resistance between the various solid components of PVT/PCM systems.

-The analysis does not consider the possible impact of rain on the density of accumulated dust.

-Equations governing the system are expressed in terms of velocity and pressure variables.

-Enthalpy-porosity modeling, following method of Voller and Prakash, is employed for the PCM.

-The influence of gravity is included in this investigation.

-Flow of the heat transfer fluid (HTF), water, through the channel is presumed to be two-dimensional, unsteady, laminar, and incompressible.

-Natural convection within the molten PCM container is considered as two-dimensional, unsteady, laminar, and incompressible.

-The porous medium is treated as saturated, homogeneous, and isotropic.

-Flow within the porous medium is analyzed using the Brinkman–Forchheimer-extended Darcy model.

-Thermo-physical properties are assumed temperature-independent, except for density which varies linearly with temperature (Boussinesq approximation), evaluated at ambient temperature.

-The porous medium analysis is conducted under local thermal equilibrium (LTE) conditions.

3.1 Energy equation for PV-layer

The energy equation for PV-layer is:

${{\left( \rho {{C}_{p}} \right)}_{PV-layer}}\frac{\partial T}{\partial \tau }={{\lambda }_{PV-layer}}\left( \frac{{{\partial }^{2}}T}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{z}^{2}}} \right)+Q$     (1)

Q is the internal heat source, ρ is the density, C is the heat capacity (J/(kg·K)) and λ is the thermal conductivity.

It has been assumed that heat will be released as a result of the residual solar energy that is absorbed and not transformed into electricity. As a result, this internal heat source causes the temperature of the PV panel to rise. To evaluate Q the Eq. (2) is used:

$Q=\frac{(1-{{\eta }_{el}}){{G}_{i}}A}{{{V}_{PV}}}$     (2)

Gi is the absorbed solar radiation, A is the surface of the PV panel and V_pv is the volume of the PV cells in the panel.

3.2 PCM and metal foam layer

Continuity equation, momentum and energy equations in local thermal equilibrium, were used for PCM and MF.

Continuity equation:

$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$     (3)

Momentum equations:

(momentum x)

$\frac{{{\rho }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{\partial u}{\partial \tau }+\frac{u}{{{\varepsilon }_{P}}}\frac{\partial u}{\partial x}+\frac{v}{{{\varepsilon }_{P}}}\frac{\partial u}{\partial y}+\frac{w}{{{\varepsilon }_{P}}}\frac{\partial u}{\partial z} \right)=$$-\frac{\partial p}{\partial x}+\frac{{{\mu }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{{{\partial }^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}u}{\partial {{z}^{2}}} \right)-$

$\frac{{{\left( 1-{{\beta }_{l}} \right)}^{2}}}{{{\left( {{\beta }_{l}}^{3}-0.001 \right)}^{3}}}{{A}_{mush}}u-\left( \frac{{{\mu }_{pcm}}}{K}+\frac{{{C}_{F}}{{\rho }_{pcm}}}{\sqrt{K}}\left| V \right| \right)u$$+{{\rho }_{pcm}}\gamma \left( T-{{T}_{melt}} \right)g\cos \left( \alpha  \right)$     (4)

(momentum y)

$\frac{{{\rho }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{\partial v}{\partial \tau }+\frac{u}{{{\varepsilon }_{P}}}\frac{\partial v}{\partial x}+\frac{v}{{{\varepsilon }_{P}}}\frac{\partial v}{\partial y}+\frac{w}{{{\varepsilon }_{P}}}\frac{\partial v}{\partial z} \right)=$$-\frac{\partial p}{\partial y}+\frac{{{\mu }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{{{\partial }^{2}}v}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}v}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}v}{\partial {{z}^{2}}} \right)-$

$\frac{{{\left( 1-{{\beta }_{l}} \right)}^{2}}}{{{\left( {{\beta }_{l}}^{3}-0.001 \right)}^{3}}}{{A}_{mush}}v-\left( \frac{{{\mu }_{pcm}}}{K}+\frac{{{C}_{F}}{{\rho }_{pcm}}}{\sqrt{K}}\left| V \right| \right)v$$+{{\rho }_{pcm}}\gamma \left( T-{{T}_{melt}} \right)g\sin \left( \alpha  \right)$     (5)

(momentum z)

$\frac{{{\rho }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{\partial w}{\partial \tau }+\frac{u}{{{\varepsilon }_{P}}}\frac{\partial w}{\partial x}+\frac{v}{{{\varepsilon }_{P}}}\frac{\partial w}{\partial y}+\frac{w}{{{\varepsilon }_{P}}}\frac{\partial w}{\partial z} \right)=$$-\frac{\partial p}{\partial z}+\frac{{{\mu }_{pcm}}}{{{\varepsilon }_{P}}}\left( \frac{{{\partial }^{2}}w}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}w}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}w}{\partial {{z}^{2}}} \right)-$

$\frac{{{\left( 1-{{\beta }_{l}} \right)}^{2}}}{{{\left( {{\beta }_{l}}^{3}-0.001 \right)}^{3}}}{{A}_{mush}}w-\left( \frac{{{\mu }_{pcm}}}{K}+\frac{{{C}_{F}}{{\rho }_{pcm}}}{\sqrt{K}}\left| V \right| \right)w$$+{{\rho }_{pcm}}\gamma \left( T-{{T}_{melt}} \right)g$     (6)

Energy equation in local thermal equilibrium (LTE):

${{\left( \rho C \right)}_{eff}}\frac{\partial v}{\partial \tau }+{{\left( \rho C \right)}_{pcm}}\left( u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z} \right)=$${{\lambda }_{eff}}\left( \frac{{{\partial }^{2}}T}{\partial {{x}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{y}^{2}}}+\frac{{{\partial }^{2}}T}{\partial {{z}^{2}}} \right)-{{\varepsilon }_{P}}{{\rho }_{pcm}}{{H}_{L}}\frac{\partial \beta }{\partial \tau }$     (7)

In the Eq. (8) H_Lrepresents the latent heat of the PCM, and t is the time.

${{(\rho C)}_{eff}}=(1-{{\varepsilon }_{P}}){{\rho }_{mf}}{{C}_{mf}}+{{\varepsilon }_{P}}{{\rho }_{p}}{{C}_{pcm}}$     (8)

${{\lambda }_{eff}}=(1-{{\varepsilon }_{P}}){{\lambda }_{mf}}+{{\varepsilon }_{P}}{{\lambda }_{pcm}}$     (9)

The weighted average is obtained in Eq. (8), and the effective thermal conductivity is calculated in Eq. (9). The density and specific heat of MF and PCM are represented by ρ_mf, ρ_pcm, and C_mf, C_pcm. The metal foam and PCM thermal conductivities are denoted by λ_mf and λ_p. P stands for porosity, K for permeability [m²] (viscous drag or Darcy drag), and C_F for Forcheimer coefficient (inertial drag) in the case of the metal foam. Regarding the phase change material, H_L stands for specific heat latent [J/kg], A_mush is an empirical constant that fluctuates between 10⁵ and 10⁸, and is the liquid fraction.

The model was validated based on the 3D model by Kazemian et al. [18], which had previously been validated by them through comparison of the numerical results obtained with the numerical work of Su et al. [19] and the experimental work of Browne et al. [20]. The properties of the various components used in the simulation are listed in Table 4.

Table 4. Characteristics validation components

In the numerical simulation, the calculation time for the unsteady model is set at two hours, during which the average electrical and thermal efficiencies are computed. The same boundary conditions were recreated and used the same numerical methods. The PCM used has the characteristics listed in Table 5 [15].

Table 5. Properties of the PCM used in validation [15]

The temperature of the outdoor environment is set at 30℃ for 2 hours of simulation. In Figure 3 the temperature of the heat transfer fluid (water) is set at 30℃, and the fluid velocity in the single channel is 0.0281 m/s. It was compared the surface temperature of the photovoltaic panel in the base case with a T₀ = 30℃ and solar radiation of 800 W/m².

3.png

Figure 3. Comparison between PVT+PCM surface temperature of the Kazemian et al. [15] model and our model

4.png

Figure 4. Comperison, in terms of the melted PCM percentage vs solar radiation, between present model and Kazemian et al. [18] model

Then, Figure 4 shows the comparison of the melting rate of the phase change material as the solar radiation on the panel changes. The obtained results show good agreement between the model of Kazemian et al. [18] and our model.

Based on the simulations and analysis conducted for different months throughout the year, several conclusions can be concluded regarding the performance of the PV panel with and without a PCM and MF layer. The PV module with the PCM+MF layer demonstrates higher electrical efficiency compared to the module without the storage layer, especially noticeable during winter months. The presence of the PCM+MF layer contributes to a more consistent efficiency throughout the day, particularly in winter, by absorbing excess heat and extending the effective operating period of the PV panel. This enhancement is attributed to the PCM+MF layer enabling the PV panel to maintain a temperature closer to the optimal operating range. Additionally, there is a notable extension in the operating hours of the system due to the effective heat storage and release capabilities of PCM+MF, with the operating period extension being more pronounced during winter months. In summary, the incorporation of a PCM+MF layer into the PV module results in improved electrical efficiency, maintained performance under varying solar conditions, and significantly extended hours of operation. These results highlight the potential benefits of using phase change materials and metal foams to improve the performance and effectiveness of photovoltaic systems, especially to optimize energy production and utilization in different seasons.