The effects of free convection on turbulent transport for a liquid flowing in a vertical channel

Model equations for the turbulent stresses and heat fluxes are used in deriving expressions for the turbulent viscosity and thermal diffusivity for the liquid flowing in a vertical channel under conditions of free convection. The values are shown to differ from the analogous ones introduced by Boussinesq's method and as usually determined by experiment. Allowance is made for the effects of the wall on these quantities, and also for the effects of free convections on the mixing length. It is shown that in the limiting case of marked influence from free convection, the turbulent viscosity and thermal diffusivity differ from the analogous Boussinesq values in being described by the same limiting relationship for rising and descending flows.