## 3 Steady-State Thermal Modeling
Therefore, the heat transfer coefficients \(h_{\text{c,APb}}\) and \(h_{\text{c,APu}}\) correspond to the heat transfer process \(q_{\text{t,AP}}\). Assuming that some of the parameters from Figure 1 are unknown, it is necessary to estimate the parameters of the air at the outlet of the solar chimney (\(T_{\text{o}}\) and \(v_{\text{o}}\)), as well as energy losses in the considered system. The iteration procedure for calculating \(T_{\text{o}}\), \(v_{\text{o}}\), \(h_{\text{c,PV}}\), \(h_{\text{r,PV}}\), \(h_{\text{c,APb}}\), and \(h_{\text{c,APu}}\) requires knowledge of the temperatures \(T_{\text{PV}}\), \(T_{\text{AP}}\), and \(T_{\text{sky}}\), which are also unknown. The initial values for all unknown heat transfer coefficients should be specified so that they correspond to turbulent free convection in air (for instance, 10 W/(m\({}^{2}\cdot\)K)), while any positive number (for instance, 1 m/s) can be specified for the initial value of the air velocity at the outlet of the solar chimney. The initial value for \(T_{\text{o}}\) can be estimated using the energy balance equation  
\[(\alpha_{\text{PV}}S_{\text{PV}}+\alpha_{\text{A}}T_{\text{AP}}S_{\text{AP} })q_{\text{E,S}}=Q_{\text{air}}+q_{\text{t,AP}}S_{\text{AP}}+(q_{\text{c,PV}}+ q_{\text{r,PV}})S_{\text{PV}}+Q_{\text{el}}, \tag{1}\]  
in the following manner  
\[T_{\text{o}}=T_{\text{a}}+\frac{2[\alpha_{\text{PV}}S_{\text{PV}}(1-\eta_{ \text{el}})+\alpha_{\text{A}}T_{\text{AP}}S_{\text{AP}}]q_{\text{E,S}}}{2v_{ \text{o}}\rho_{\text{o}}S_{\text{D}}c_{\text{D}}c_{\text{D}}i+(h_{\text{c,PV}}+ h_{\text{r,PV}})S_{\text{PV}}+U_{\text{AP}}S_{\text{AP}}}, \tag{2}\]  
where [36; 39]:  
\[q_{\text{c,PV}}=h_{\text{c,PV}}(T_{\text{PV}}-T_{\text{a}}), \tag{3}\]  
\[q_{\text{r,PV}}=h_{\text{r,PV}}(T_{\text{PV}}-T_{\text{a}}), \tag{4}\]\[h_{\rm r,PV}=\epsilon_{\rm PV}\sigma_{\rm SB}(T_{\rm PV}+T_{\rm sky})(T_{\rm PV}^{2 }+T_{\rm sky}^{2})\frac{\left(T_{\rm PV}-T_{\rm sky}\right)}{(T_{\rm PV}-T_{\rm a })}, \tag{5}\]  
\[Q_{\rm el}=\eta_{\rm el}a_{\rm PV}q_{\rm E,S}S_{\rm PV}, \tag{6}\]  
\[q_{\rm t,AP}=U_{\rm AP}(T_{\rm AP}-T_{\rm a}), \tag{7}\]  
Figure 1:0  
Figure 1:1  
Figure 1:2  
Figure 1:3  
\(S_{\rm AP}\) is the area of one side of the acrylic plate in \(\rm m^{2}\); \(S_{\rm PV}\) is the area of one side of the PV section in \(\rm m^{2}\); \(\eta_{\rm el}\) is the efficiency of conversion of solar energy into electricity; \(\rho_{\rm o}\) is the density of air at temperature \(T_{\rm o}\) in kg/\(\rm m^{3}\); \(c_{\rm t,i}\) is the specific heat of air at temperature \(T_{\rm a}\) in J/(kg\(\cdot\)K); \(S_{\rm D}\) is the cross-sectional area of the ventilation channel (or air flow in that channel) in \(\rm m^{2}\); \(U_{\rm AP}\) is the overall heat transfer coefficient for the acrylic plate in W/(\(\rm m^{2}\cdot\)K); \(\epsilon_{\rm PV}\) is the thermal emissivity for the upper surface of the PV section; \(\sigma_{\rm SB}=5.67\times 10^{-8}\) W/(\(\rm m^{2}\cdot\)K\({}^{4}\)) is the Stefan-Boltzmann constant; \(h_{\rm c,APb}\) is the forced convection heat transfer coefficient between the air in the ventilation channel and the bottom surface of the acrylic plate in W/(\(\rm m^{2}\cdot\)K); \(\Delta_{\rm AP}=0.003\) m is the thickness of the acrylic plate; \(k_{\rm t,AP}=0.19\) W/(\(\rm m\cdot\)K) is the thermal conductivity of the acrylic plate; and \(h_{\rm c,APu}\) is the free convection heat transfer coefficient between the upper surface of the acrylic plate and the ambient air in W/(\(\rm m^{2}\cdot\)K). Values of density \(\rho\) in kg/\(\rm m^{3}\), specific heat \(c_{\rm t}\) in J/(kg\(\cdot\)K), dynamic viscosity \(\mu\) in kg/(m\(\cdot\)s), thermal conductivity \(k_{\rm t}\) in W/(m\(\cdot\)K), and Prandtl number Pr for air at the film temperature \(T_{\rm f}=(T_{\rm a,av}+T_{\rm a})/2\) in K were read from corresponding input data files and interpolated using a cubic spline.