AbstractSome construction laws require the integration of an open thermosyphon system having multiple functions to the building roof. In order to analyze the efficiency of this system, a numerical model was developed. This model is based on the study of the natural convection coupled with radiative heat transfer in an inclined air channel. Two configurations are studied, the first one is a simple channel formed by two parallel plates and the second one is equipped with fin blades joined to the upper plate. The air flow in the channel which is due to the buoyancy forces is fully turbulent and the turbulence was modeled using the k‐ε model. Some numerical results obtained were validated using the experimental ones of Khedari et al. (2002) and those of Nouanégué and Bilgen (2009). The effect of the radiative heat transfer on the mean Nusselt number was shown. Correlations for Nusselt numbers were obtained for the two configurations as functions of the geometric parameters and the Rayleigh number. The main objective of this study is to use these correlations in other models to facilitate the operation of this system