In this study, the concepts of air exchange rate (ACH), pollutant exchange rate (PCH) and average pollutant concentration (Θ) are implemented to estimate the air and pollutant exchange for combined wind-buoyancy driven flow in an idealized 2D street canyon of building-height-to-street-width ratio of one. The flow inside the street canyon is driven simultaneously by the free-stream wind and the buoyancy dissipated by solar radiation. The wind flow pattern can be characterized by the dimensionless quantity Richardson number (Ri) which represents the relative contributions of mechanical and thermal forces. A steady-state RANS Renormalized Group (RNG) k-ε turbulence model is constructed to estimate the values of ACH, PCH and Θ as functions of Ri. It is found that the ACH increases with increasing Ri, hence, the buoyancy helps remove air pollutant from the street canyon. In addition, at Ri about 8, the mean vertical wind replaces the turbulence fluctuation that dominates the pollutant removal. The buoyancy strengthens the recirculation that in turn enhances pollutant mixing inside the street canyon. Improved air quality is observed at higher Ri that is in-line with the reduced Θ with increasing Ri. Though steady-state models have been adopted in various studies, the calculation becomes unstable for Ri larger than 10. Under this circumstance, an unsteady-state RANS RNG k-ε turbulence model is used instead of the steady-state one to look into the transient transport behaviors. Periodic wind flow at the core of street canyon is observed in the unsteady-state calculation. This finding suggests the unsteady nature of combined wind-buoyancy driven flow and signifies the limitation of steady-state assumption for street canyon air pollution problems.