Internal-flow Nusselt numbers for the low-Reynolds-number end of the laminar-to-turbulent transition regime

For heat exchange devices that operate in the low-Reynolds-number end of the laminar-to-turbulent transition regime, logical design is thwarted by the absence of reliable Nusselt number information. The currently accepted Nusselt number correlation for the transition regime, due to Gnielinski, is restricted to the high-Reynolds-number end of that regime. This limitation results from the need for a valid friction factor—Reynolds correlation for input to the Gnielinski equation. Heretofore, such correlations have been unavailable for the low-Reynolds-number end. By the application of a new fluid flow model which is valid for all flow regimes and smoothly and automatically bridges between regimes, the needed correlations have been determined. On this basis, fully developed Nusselt number results are provided for (a) a round pipe of axially uniform cross section, (b) the downstream end of a round pipe fitted with a conical enlargement (diverging nozzle) at its upstream end, and (c) a parallel-plate channel. All results are for a fluid with Prandtl number equal to 0.7.