The characteristics of fully developed turbulent convection in a round tube

New exact differential models for fully developed turbulent flow and convec tion 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 t ime-averaged turbulent shear stress and heal flux density, and utilize a th eoretically based algebraic correlating equation for the former and a purel y empirical one for the latter rather than the customary heuristic differen tial models involving the eddy diffusivities. The predicted rates of heat t ransfer were found to be relatively insensitive to the particular empirical expressions utilized for the turbulent Prandtl number, which is the only s ignificant 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 a nd all thermal boundary conditions. (C) 2001 Elsevier Science Ltd. All righ ts reserved.