# Coupled Model of Heat and Power Flow in Unventilated PV/PCM Wall-Validation in a Component Scale
## 3 Results and Discussions
### Numerical Model  
The challenge of the numerical simulation of the system under investigation is the simultaneous consideration of mutually affected temperature dependence of PV and PCM, and its additional heat transfer due to power generation and phase transition, respectively. Moreover, the proper numerical model of such a system should include in the calculation procedure the influence of rapidly changing external environmental conditions affecting convective and radiation heat transfer coefficients. The selected PV model, among the three available in the ESP-r, was the WATSUN-PV model that allows the most advanced consideration of the influence of the temperature on the power generation. The PV cell temperature is involved in the calculation of the  
Figure 4: Scheme of the experimental setup. Figure 5: Measured power generated by PV and temperature on its backside. short-circuit current (Equation (1)) and open-circuit voltage (Equation (2)). Finally, the power generated by PV is calculated using these two calculated electrical characteristics (Equation (3)) [34]. \[I_{sc}=I_{sc,ref}\frac{E_{T,eff}}{E_{T,ref}}[1+\alpha\big{(}T_{cell}-T_{cell,ref} \big{)}] \tag{1}\]  
\[V_{oc}=V_{oc,ref}\Big{[}1-\gamma\Big{(}T_{cell}-T_{cell,ref}\big{)}\Big{]}\cdot max \Bigg{\{} \begin{matrix}0\\ 1+\beta\cdot ln\Big{(}\frac{E_{T,eff}}{E_{T,ref}}\Big{)}\end{matrix} \Bigg{\}} \tag{2}\]  
\[P_{mp}=I_{mp,ref}\cdot V_{mp,ref}\Bigg{(}\frac{I_{sc}\cdot V_{oc}}{I_{sc,ref} \cdot V_{oc,ref}}\Bigg{)} \tag{3}\]  
The most important electrical and thermal parameters of the tested PV panel that are also used in simulation are given in Tables 1 and 2, respectively. Due to the fact that PV panel temperature is strongly affected by external environmental conditions, heat exchange processes on its outer surface were defined including time-dependent convection, short- and long-wave radiation (Equation (4)) [35]. \[\varepsilon_{n}\sigma\Big{[}F_{s-g}\Big{(}T(x_{L},t)^{4}-T_{g}^{4}\Big{)}+F_{ s-sky}\Big{(}T(x_{L},t)^{4}-T_{sky}^{4}\Big{)}\Big{]}+h_{cc}[T(x_{L},t)-T_{e}]+q_{ sol}=-\lambda\frac{\partial T(x,t)}{\partial x}\Big{|}_{x=x_{L}} \tag{4}\]  
Furthermore, the influence of the additional heat accumulation in the PCM layer was investigated in two ways, by:  
1. apparent heat capacity (AHC) method using special material subroutine;
2. changeable heat capacity (CHC) method using non-linear thermal properties subroutine. The one-dimensional transient heat conduction using the AHC method is defined as (Equation (5)):  
\[\frac{\partial^{2}T}{\partial x^{2}}=\frac{1}{\alpha}\frac{\partial T}{ \partial t}+\frac{1}{\lambda}\rho\frac{\partial L}{\partial t} \tag{5}\]  
Here, latent heat is defined as an integral from effective heat capacity Equation (6)):  
\[L=\int\limits_{C_{s}}^{C_{l}}C_{eff}(T)dT. \tag{6}\]  
On the other hand, using the CHC method, heat conduction transfer in the PCM layer is described as (Equation (7)):  
\[\frac{\partial^{2}T}{\partial x^{2}}=\frac{1}{\alpha}\frac{\partial T}{ \partial t} \tag{7}\] \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Nominal power & [W] & 30 \\ Voltage at nominal power & [V] & 34 \\ Current at nominal power & [A] & 0.88 \\ Open circuit voltage & [V] & 46 \\ Short circuit current & [A] & 0.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main electrical parameters of the tested PV panel. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Temperature coefficient Voc & [\%/\({}^{\circ}\)C] & \(-\)0.3 \\ Temperature coefficient Isc & [\%/\({}^{\circ}\)C] & 0.01 \\ Temperature coefficient Pmpp & [\%/\({}^{\circ}\)C] & \(-\)0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermal characteristics of the PV panel.