Table 1.

Mathematical model of the PV/T-LHP system [50,51].

Description	Equations
PV/T module	${\rho }_c{C}_c{l}_c\frac{\partial T_c}{\partial t}=\frac{T_p-T_c}{R_{p,c}}-\frac{20A_{bi}}{A_c}\frac{T_c-T_{p,e}}{R_{c,b}}-\frac{T_c-T_a}{R_{c,a}}$ $M_{p,e}{c}_{p,e}{l}_c\frac{\partial T_{p,e}}{\partial t}=20\cdot A_{bi}(\frac{T_c-T_{p,e}}{R_{c,b}}-\frac{T_{p,e}-T_{p,c}}{R_{c,a}})$
The overall thermal resistance	$R_{e,c}=R_{e,p}+R_{e,\mathrm{wick}}+R_{c,i}+R_{c,p}$ $R_{e,p}=\frac{\ln \left(\frac{D_{e,o}}{D_{e,i}}\right)}{2\pi N_{hp}{L}_{p,e}{k}_{p,e}}$ $R_{e,\mathrm{wick}}=\frac{\ln \left(\frac{D_{\mathrm{wick},o}}{D_{\mathrm{wick},i}}\right)}{2\pi N_{ap}{L}_{p,e}{k}_{wick}}$ $R_{c,i}=\frac{1}{\pi D_{c,i}{L}_{p,c}{h}_{c,i}}$ $R_{c,p}=\frac{\ln \left(\frac{D_{c,o}}{D_{c,i}}\right)}{2\pi L_{p,c}{k}_{p,c}}$
Immersed coil condenser	$M_{p,c}{c}_{p,c}\frac{\partial T_{p,c}}{\partial t}=\frac{T_{p,e}-T_{p,c}}{R_{e,c}}-\frac{T_{p,c}-T_w}{R_{c,w}}$
Thermal efficiency	${\eta }_c\left(j\right)=\frac{Q_c\left(j\right)}{A_{c}I\left(j\right)}$
Overall photo-thermal efficiency	${\eta }_o\left(j\right)={\eta }_c\left(j\right)+\xi \cdot {\eta }_p\left(j\right)$
Heat pump COP	${\mathrm{COP}}_{\mathrm{SASHP}}\left(j\right)={10}^{-3}\cdot [72.3\cdot [T_a\left(j\right)-273.15)-29.5\cdot [T_{w,\mathrm{in}}\left(j\right)-273.15+1.64\cdot I\left(j\right)]+2.6$ ${\mathrm{COP}}_{\mathrm{ASHP}}\left(j\right)={10}^{-2}\cdot [72.3\cdot [T_a\left(j\right)-273.15)-2.95\cdot [T_{w,\mathrm{in}}\left(j\right)-273.15]+2.6$
Environmental benefits	$C{R}_{PV-LHP/SAHP}=(E_{nc,ASHP}-E_{nc,PV-LHP/SAHP})f_{\mathrm{el},{\mathrm{CO}}_2}$ $C{R}_{\mathrm{SA}-\mathrm{AS}HP}=(E_{nc,ASHP}-E_{nc,\mathrm{SA}-ASHP})f_{\mathrm{el},{\mathrm{CO}}_2}$
Life cycle cost	$P=A\left[\frac{{(1+i)}^n-1}{i{(1+i)}^n}\right]$