Four-equation turbulence model for prediction of the turbulent boundary layer affected by buoyancy force over a flat plate

Turbulent convective heat transfer with appreciable buoyancy effect over a heated or cooled horizontal flat plate is numerically analyzed by solving four equations for mean square temperature variance , its rate of destruction _θ, turbulent kinetic energy κ and the rate of kinetic energy dissipation . Turbulent time-scale ratio R of temperature fluctuations relative to velocity fluctuations defined by is found to vary widely across the boundary layer. For both highly stable and highly unstable conditions, the ‘four-equation’ model yields better results for mean temperature profile and surface heat flux than the two-equation model. It is also found that the magnitude of thermal von Karman constant κ_θ is not a universal constant but it depends on the thermal stratification of the boundary layer.