Natural ventilation of building provides improvement of internal comfort and air quality conditions leading to a significant reduction of cool-ing energy consumption. Design of natural ventilation systems for many types of building is based on buoyancy forces. However, external wind flow can have significant effects on buoyancy- driven natural ventilation. The paper was concerned with transient investigation of airflow through two vents in the absence of opposing flow in the upper opening. A flow of this type represents a new class of boundary- layer flow problems in the building. Moreover, this is an exact solution of the complete Navier- Stokes Equations (including, buoyancy force term), which were then Non Dimensionalised using some dimensionless parameters and then solved analytically by separation of variable methods in which, the behavior of parameters in the results were predicts the velocity, temperature profiles together with volumetric airflow and mass transfer. The results were then evaluated numerically for several sets of values of the parameters in order to ascertain the best for optimal ventilation.