A model for predicting fluid flow and convective heat transfer in all flow regimes has been implemented for steady mainflows in pipes and ducts of constant cross section. The key feature of the model is its capability to predict transitions between purely laminar and purely turbulent flow, while the latter flows are also predicted with high accuracy. The flow regime need not be specified in advance but is determined automatically as the flow evolves during its passage along the pipe or duct. Intermittently in the transition regime is fully accounted. It was shown that fully developed flows are necessarily restricted to either the laminar regime or the turbulent regime, but that a fully developed intermittent regime exists. The effects of the flow conditions at the inlet of the pipe or duct, velocity profile shape and turbulence intensity, on the subsequent transitions were quantified. To facilitate the heat transfer analysis, the turbulent-Prandtl-number concept, widely used to inter-relate the turbulent viscosity and thermal conductivity, was extended to encompass both intermittent and laminar flows. The presented results include all-flow-regime fully developed friction factors and fully developed Nusselt numbers. The locations where laminar-flow breakdown occurs and where fully developed begins are also presented.