Turbulent Natural Convection in a Horizontal Layer of Small-Prandtl-Number Fluid

Turbulent natural convection in a horizontal layer of liquid metal confined between two infinite rigid plates is studied theoretically. The layer, with uniformly distributed energy sources in the fluid, is heated from below and cooled from above. An approximate analysis of the Boussinesq equations of motion is performed for the case of small-Prandtl-number fluids to determine the temperature profiles in three different thermal regions of the layer. By matching these profiles in the regions of overlap, analytical expressions are derived for the lower and upper surface Nusselt numbers and the dimensionless turbulent core temperature as functions of the internal and external Rayleigh numbers defined respectively in terms of the volumetric heating rate and surface-to-surface temperature difference of the layer. Comparison of the present results with heat transfer data for liquid mercury is made and found to be good.