Abstract
Heat transfer in fully developed pipe flows is investigated and combinations of laminar, turbulent, and transitional flow and heat transfer are identified. The analysis is based on governing equations conserving mass, momentum and energy and are also informed by Direct Numerical Simulation (DNS). Six regimes are identified: 1. Laminar flow and laminar heat transfer (LamF-LamH); 2. Transitional flow and laminar heat transfer (TraF-LamH); 3. Transitional flow and transitional heat transfer (TraF-TraH); 4. Turbulent flow with laminar heat transfer (TurF-LamH); 5. Turbulent flow with transitional heat transfer (TurF-TraH); and 6. Turbulent flow with turbulent heat transfer (TurF-TurH). The subdivisions of flow is based on the Reynolds number and the fluid Prandtl number. One finding is that the TurF-LamH regime only exists for very low Prandtl number flows (Pr << 1). Another critical demarcation for this type of flow exists for Re tau Pr1/2 less than or similar to 50. The friction-Reynolds number Re-tau is based on the pipe radius and the friction velocity. The model used here was based on the approach, already used with success, for flow in parallel-plate channels. The simplified model predicts a Nusselt number of 8 in the TurF-LamH regime; recommended Nusselt correlations are provided for other regimes. A discussion of the demarcation for the transitional regimes is also included along with guidance for Nusselt numbers within those ranges.