## 3 Steady-State Thermal Modeling  
In this section, an analytical model is given for the steady-state heat transfer from a building PV facade cooled by a solar chimney. In particular, the heat transfer processes taking place along the surfaces of the PV section, the absorber section and the ventilation channel are in accordance with Figure 1. The model is based on the laws of conservation of energy and mass, correlations for sky temperature and heat transfer by radiation between a flat plate and the surroundings, the balance between the total pressure difference due to buoyancy, and the total pressure drop (across the whole ventilation channel), as well as correlations for free and forced convection. The temperature and velocity of the air at the outlet of the ventilation channel, as well as the heat transfer coefficients, are calculated using the proposed model. According to Figure 1, the sky is modeled by an infinite horizontal  
Figure 1: Heat transfer processes from surfaces of facade-integrated PV modules cooled by solar chimney. flat plate of temperature \(T_{\text{sky}}\
eq T_{\text{a}}\)[36]. In addition, all channel walls are assumed to be adiabatic, except for the PV section and the acrylic plate, which are assumed to be isothermal, and their average temperatures are \(T_{\text{PV}}\) and \(T_{\text{AP}}\), respectively. The parameters appearing in Figure 1 have the following meanings: \(L_{\text{TS}}\) is the height of the top section of the solar chimney in m; \(L_{\text{AP}}\) is the height of the absorber section (or acrylic plate) in m; \(L_{\text{PV}}\) is the height of the PV section in m; \(L_{\text{BS}}\) is the height of the bottom section of the ventilation channel in m; \(T_{\text{i}}=T_{\text{a}}\), \(T_{\text{o}}\), \(T_{\text{a}}\), and \(T_{\text{sky}}\) are the temperatures of the air at the inlet of the ventilation channel, the air at the outlet of the ventilation channel, the ambient air, and the sky in \({}^{\circ}\)C, respectively; \(T_{\text{PV}}\), \(T_{\text{AP}}\), and \(T_{\text{a,AV}}\) are the average temperatures of the PV section, the acrylic plate, and the air in the ventilation channel in \({}^{\circ}\)C, respectively; \(v_{\text{i}}\) and \(v_{\text{o}}\) are the air velocities at the inlet of the ventilation channel and at the outlet of the ventilation channel in m/s, respectively; \(q_{\text{E,S}}\) is the solar irradiance that can be received by a horizontal surface on Earth in W/m\({}^{2}\); \(\alpha_{\text{PV}}\) and \(\alpha_{\text{A}}\) are the solar absorption coefficients for the upper surface of the PV section and the absorption area of the absorber, respectively; \(\tau_{\text{AP}}\) is the solar transmittance for the acrylic plate; \(q_{\text{c,PV}}\) is the free convection heat transfer between the upper surface of the PV section and the ambient air in W/m\({}^{2}\); \(q_{\text{t,PV}}\) is the radiation heat exchange between the upper surface of the PV section and the surroundings in W/m\({}^{2}\); \(Q_{\text{el}}\) is the power related to the generation of electricity in the PV section in W; \(q_{\text{t,AP}}\) is the heat transfer through the acrylic plate between the air in the ventilation channel and the ambient air in W/m\({}^{2}\); and \(Q_{\text{air}}\) is the amount of heat absorbed by the mass of the air in the ventilation channel in W. No SI units are given for the dimensionless parameters in Figure 1.  
The free convection and radiation heat transfer coefficients corresponding to the heat transfer processes \(q_{\text{c,PV}}\) and \(q_{\text{r,PV}}\) are \(h_{\text{c,PV}}\) in W/(m\({}^{2}\cdot\)K) and \(h_{\text{r,PV}}\) in W/(m\({}^{2}\cdot\)K), respectively. The heat transfer through the acrylic plate is carried out by forced convection between the air in the ventilation channel and the bottom surface of the acrylic plate (\(h_{\text{c,APb}}\) in W/(m\({}^{2}\cdot\)K)), conduction through the acrylic plate, and free convection between the upper surface of the acrylic plate and the ambient air (\(h_{\text{c,APu}}\) in W/(m\({}^{2}\cdot\)K)).