Solar energy is an important renewable energy resource for many Arabic countries. The solar chimney is considered as one of the feasible solar energy conversion techniques. The present work introduces a detailed numerical investigation and optimization of the solar chimney power density under different operating conditions. The finite volume CFD code ANSYS Fluent was implemented in the present work. The solar irradiance was modeled using the discrete ordinates (DO) radiation model. The present numerical simulation shows that the chimney collector has an optimum radius that strongly depends on the operating solar irradiance. Moreover, the turbine pressure drop significantly affects the collector performance. Increasing the turbine pressure drop increases the value of the optimum collector radius. Equations for estimating the optimum collector radius, efficiency, and power density were obtained and presented. The present investigation shows an optimum collector radius of 17 times the chimney radius at an irradiance of 500 W/m(2) using a turbine with a pressure drop of 160 Pa. An aero-economical optimization of the collector radius is recommended for future work.