## 1 Introduction
The operating performance of PV panels cooled by a natural draft cooling system under typical hot dry conditions was investigated in [30]. The results of the yield analysis of a BIPV facade prototype can be found in [31]. Finally, based on this state-of-the-art review, as well as a few hundred older and newer references reviewed in [32; 33; 34; 35], it was found that there is no analytical thermal model that simultaneously and iteratively determines the air velocities at the inlet and at the outlet of a solar chimney and the average temperature of PV modules integrated with that chimney. In particular, the existing analytical thermal models cannot calculate analytically the air velocities at the inlet and at the outlet of a solar chimney. Therefore, this is recognized as a research gap. The model proposed here is based on the analytical thermal model developed in [36] for the purpose of analyzing the cooling of PV modules integrated in a roof inclined at an angle of 37\({}^{\circ}\). The model is obtained by replacing empirical correlations for free convection heat transfer from the upper surface of an inclined plate used in [36] with empirical correlations for free convection heat transfer from one surface of a vertical isothermal plate [37]. This represents the main difference in the proposed model, when compared to the model used in [36]. Specifically, the proposed model is a combination of the model from [36], the existing empirical correlations for radiation, laminar free convection, forced convection, sky temperature, and velocity of air along the solar chimney channel, and the proposed empirical correlations for turbulent free convection from a vertical flat plate. The excellent accuracy of the correlations used in the proposed model was previously validated by a large amount of experimental data and the large number of relevant comparisons [37; 38; 39; 40; 41; 42]. For this reason, the associated validation processes do not have to be repeated. Addressing the research gap identified previously represents another contribution. In addition, the third contribution is the use of empirical correlations for forced convection to model the heat transfer from the back surfaces of PV modules integrated with the solar chimney channel, based on estimated air velocity in it. On the other hand, the limitations of the proposed model refer to the impossibility of taking into account the effects of wind, daily variation in solar irradiance, and daily variation in the ambient air temperature on the heating of the PV modules, as well as wind on the velocity of air along the solar chimney channel. In this paper, a vertical segment of the facade of a building composed of the top section of a solar chimney, a maximum of six PV modules mounted on the channel of the solar chimney (i.e., PV section), and an absorber section installed above the PV section is considered. It is assumed that the dimensions of these three sections are known. The air velocities at the inlet and at the outlet of the chimney channel and the average temperature of the PV section are estimated iteratively using the proposed steady-state thermal model. For the purpose of comparisons, it is assumed that the dimensions of the chimney channel are identical to the dimensions of the one from [37]. Comparisons are made between the performance parameters calculated for the air velocity along the chimney channels that are inclined at angles of 90\({}^{\circ}\) and 37\({}^{\circ}\) with regard to the horizontal plane. In addition, the effects of the solar irradiance, the height of the solar chimney, the height difference between the two openings of a ventilation channel, the solar irradiance, the number of PV modules on the air velocities (at the inlet and at the outlet of the solar chimney channel), and the average PV section temperature are quantified.