Application of a new time scale based low {kappa}-{var_epsilon} model to natural convection from a semi-infinite vertical isothermal plate

The low {kappa}-{var_epsilon} model proposed by Yang and Shih (1992) is applied to the calculation of the turbulent natural convective boundary layer over a semi-infinite, vertical, isothermal surface. Using {kappa}/{var_epsilon} as the turbulent time scale will introduce a singularity in the {var_epsilon} equation, near the wall. This model uses a modified turbulent time scale near the wall to eliminate this singularity. The constants in the equation for damping function are modified to produce better results for both, natural convection and force convection. The results are compared with available experimental data and the results obtained from Chien`s model and are found to be in reasonable agreement. Here {kappa} represents the turbulent kinetic energy and {var_epsilon} represents the dissipation rate of turbulent kinetic energy