## 3 Important Parameters  
### Parabolic Trough Collector  
The thermal efficiency of the PTC is measured considering a normal incidence angle. However, its efficiency is affected when \(\theta>0\). According to [PERSON]. [41] for the PTC, the thermodynamics first-law efficiency, can be expressed as:  
\[\eta_{1}=F_{R}\left(\eta_{0}K_{\theta}-\frac{U_{L}}{C}\cdot\frac{(T_{i}-T_{a})}{ G_{B}}\right) \tag{2}\]  
where \(K_{\theta}\) is the incidence angle modifier that includes the spilling of radiation over the end of a finite PTC. Equation (3) shows the regression curve of \(K_{\theta}\) based on experimental data:  
\[K_{\theta}=1.0041+0.0003\theta-0.0002\theta^{2}+9\times 10^{-19}\theta^{3} \tag{3}\]  
Performance data for a single collector cannot be applied directly to a series of interconnected collectors. But, it is necessary to consider the thermal losses in the pipelines that interconnect the collectors and the heat exchanger that is used during the system's operation. [PERSON] et al. [42] describe a methodology to calculate the useful heat for an array composed by identical collectors. This methodology was conveniently adopted in the present work and it is described, as follows:  
The useful energy output from an array of \(N\) identical solar collectors operated in series can be calculated using  
\[Q_{u,N}=F_{R\varepsilon}\left[\frac{1-(1-K)^{N}}{K}\right]\left[\eta_{0}^{ \prime}K_{\theta}A_{a}G_{B}-U_{L}^{\prime}A_{r}(T_{s}-T_{a})\right]^{+} \tag{4}\]  
where \(F_{R\varepsilon}\) is the modified heat removal factor and it is calculated as:  
\[F_{R\varepsilon}=\frac{F_{R}}{1+K\left[\frac{\left(\dot{m}C_{p}\right)_{ \varepsilon}}{\varepsilon_{c}\left(\dot{m}C_{p}\right)_{min}}-1\right]} \tag{5}\]  
In Equation (5) \(\varepsilon_{c}\) is the effectiveness of the heat exchanger, \(\left(\dot{m}C_{p}\right)_{c}\) is the collector side capacitance, \(\left(\dot{m}C_{p}\right)_{min}\) is the lowest value for all the thermal capacitance rates of the working fluid in the heat exchanger on the collector side, and \(K\) is defined by [PERSON] et al. [42], as:  
\[K=\frac{A_{r}F_{R}U_{L}^{\prime}}{\left(\dot{m}C_{p}\right)_{\varepsilon}} \tag{6}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Input Parameter** & **Value** \\ \hline Condensation/absorption water temperature & 20–28 \({}^{\circ}\)C \\ Generation water temperature & 85–105 \({}^{\circ}\)C \\ Evaporation water temperature & 20 \({}^{\circ}\)C \\ Mass flow rate of condensation/absorption water & 12 kg/min \\ The mass flow rate of generation water & 16 kg/min \\ The mass flow rate of evaporation water & 10 kg/min \\ Expansion valve’s aperture & 10 turns \\ Strong solution mass flow rate & 0.8 kg/min \\ The initial concentration of the mixture & 54\% (refrigerant mass ratio) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input parameters values during the assessment of the system. The modified optical efficiency and global thermal losses coefficient are given by Equations (7) and (8), respectively:  
\[\eta_{0}^{\prime}=\frac{\eta_{0}}{1+\frac{\left(UA\right)_{ipz}}{\left(mC_{p} \right)_{c}}} \tag{7}\]  
\[U_{L}^{\prime}=\left(\frac{1-\frac{\left(UA\right)_{ipz}}{\left(mC_{p}\right) _{c}}+\frac{2\left(UA\right)_{ipc}}{A_{r}U_{L}F_{R}}}{1+\frac{\left(UA\right) _{ipz}}{\left(mC_{p}\right)_{c}}}\right) \tag{8}\]  
Disregarding the heat loss from the pipeline between the heat exchanger and the storage tank, according to [PERSON] et al. [42] Equation (3) can be rewritten as indicated by Equation (9). \[Q_{u,N}=0.87496\left[\frac{1-\left(1-3.02\times 10^{-3}\right)^{N}}{3.02\times 10^ {-3}}\right]\left[1.79189K_{\theta}G_{B}-13.67(T_{s}-T_{a})\right]^{+} \tag{9}\]  
The thermal efficiency (\(\eta_{Ther}\)) for the PTC is defined as the ratio of the useful heat (\(Q_{u}\)) gained by the heat transfer fluid, to the solar energy intercepted by the collector aperture area (\(S_{a}\)).