Finite-difference computation of turbulent free convection from an isothermal vertical plate using a two-equation model of turbulence

A two equation, low-Reynolds-number model of turbulence was applied to turbulent natural convection from an isothermal vertical plate. This case differs from forced convection problems in that the thermal and velocity fields are coupled. First a transformation of coordinates which allows growth of the boundary layer thickness was devised. Then the time-averaged equations of conservation for mass, momentum, turbulent kinetic energy and turbulence-energy dissipation were approximated by nonlinear finite difference equations which were implicit in the x direction and in the conservative form. These coupled nonlinear equations were solved by means of a double-loop iterative scheme in which the method of successive relaxation was used in the inner loops and the method of simultaneous relaxation in the outer loop.