Expression of the time-averaged equations for the conservation of momentum and energy in terms of the fractions of the local shear stress and heat flux density, respectively, due to turbulence is shown to result in greatly simplified representations for fully developed flow and convection in round tubes and parallel-plate channels as compared to those in terms of the eddy viscosity, eddy conductivity, or mixing length. On the other hand, the turbulent Prandtl number is shown to be a fundamental characteristic of flow and convection rather than simply an artifact of the eddy diffusional model. The new simplified representations provide the basis for improved predictions of the velocity distribution, the friction factor, the temperature distribution and the Nusselt number. The adaption of these new representations for other geometries and for developing convection is discussed briefly.