A numerical analysis has been made for the buoyancy-induced turbulent thermal convection between two flat plates. The bottom plate is maintained at a higher temperature $T_H$, and the upper plate is at a lower temperature $T_L$. The governing equations are closed with the Reynolds stress model. The turbulent momentum diffusivity is modeled by considering the buoyancy effect. The third-order transport models are based on the concept of simple gradient transport. The wall damping function on the pressure-strain correlation term near the wall is formulated to take account of the effect of heat flux. The calculations are performed with the true wall boundary conditions at the wall. Results show that the predicted mean temerature profiles are in good agreement with experimental data. The computed vertical profiles of velocity and temperature fluctuations also reveal consistent trend with experimental observations. Power law relations between fluctuating levels of the velocity and the temperature at the center and the Rayleigh numbers are fairly predicted. The overall heat transfer correlation obtained by this work may be represented by Nu=0.135 $Ra^{0.294}$ for air, which is in good agreement with experimental one.
