Natural Convection Modeling in a Solar Tower

Objectives: We present in this study a modeling of thermal laminar convection airflow in a solar tower. Methods: To formulate with precision, the boundary conditions of the solar chimney model chosen, the Cartesian equations are transformed into hyperbolic coordinates. An orthogonal grid is elaborated. It then makes it possible to draw up the diagrams of physique and calculation fields. The computer code uses the heat equation, the vorticity, and the stream function formalism as the boundary conditions for pressure are difficult to set. We use the Boussinesq approximation, which consists in considering that the density (r) of the fluid varies only in the term of the gravity forces, whose variations with temperature, assumed to be linear, generate natural convection. These variations are then translated into an equation of state which relates density to temperature. The system of dimensionless equations is solved by using an intégro-interpolation method referring to finite differences scheme. Findings: The solutions obtained from the dimensionless equations enabled us to determine the space evolution parameters (temperatures and velocities) in the tower according to the Rayleigh number. The fluid temperature and velocity evolution in the collector increase when one moves in the direction of radius decrease. The fluid temperature evolution in the chimney showed that the highest temperature is located at the chimney base while we obtained a parabolic profile of the transverse temperature distribution within the chimney. Finally, the evolution of the fluid velocity in the chimney showed that there was a preferred zone for turbine installation. Novelty : The use of dimensionless geometric parameters is unique and in general, the approach adopted in this paper differs from that encountered in the literature.