The characteristics of fully developed turbulent convection in a round tube

New exact differential models for fully developed turbulent flow and convection were solved numerically for both uniformly heated and isothermal round tubes for a wide range of the Reynolds number and a complete range of the Prandtl number. These models are expressed directly in terms of the local time-averaged turbulent shear stress and heat flux density, and utilize a theoretically based algebraic correlating equation for the former and a purely empirical one for the latter rather than the customary heuristic differential models involving the eddy diffusivities. The predicted rates of heat transfer were found to be relatively insensitive to the particular empirical expressions utilized for the turbulent Prandtl number, which is the only significant source of uncertainty. The predicted Nusselt numbers are closely represented by a single, simple, generic correlating equation that is free of any explicit empiricism and is directly applicable for all geometries and all thermal boundary conditions.