In a novel desalination system previously proposed by the authors, solar thermal energy is trapped in a glass covered water chamber/basin to provide the heat for evaporation of seawater in the basin. A chimney is integrated with the water basin, which allows the warm and humidified air to flow and ventilate due to the buoyance force. Heat dissipation through the thermal conductive chimney wall makes the water vapor in the humid air to condense while flowing up in the chimney. The condensate at the chimney wall flows downward and is collected as clean water. In the present work, mathematical modeling and numerical computation have been carried out to delineate the coupling of the buoyance-force-driven flow with the heat and mass transfer of the water evaporation in the solar collection water basin and water vapor condensation in the heat dissipating chimney. Through the modeling analysis and computation, one can find the adequate diameter of the water chamber with given conditions including the chimney dimensions, the temperatures of the water and ambient air, and the space between the water surface and cover glass of the water chamber. The objective of the optimal design is to find the best match of the water chamber with given chimney and other conditions for the system to maximize the production of clean water using solar thermal energy.