Undershoots in the Heat Transfer Coefficient and Friction-Factor Distributions in the Entrance Region of Turbulent Pipe Flows

Heat transfer coefficients for turbulent pipe flow are typically envisioned as axially varying from very high values at the pipe inlet to a subsequent monotonic decrease to a constant fully developed value. This distribution, although well enshrined in the literature, may not be universally true. Here, by the use of high accuracy numerical simulation, it was shown that the initially decreasing values of the coefficient may attain a local minimum before subsequently increasing to a fully developed value. This local minimum may be characterized as an undershoot. It was found that whenever a turbulent flow laminarizes when it enters a round pipe, the undershoot phenomenon occurs. The occurrence of laminarization depends on the geometry of the pipe inlet, on fluid-flow conditions in the upstream space from which fluid is drawn into the pipe inlet, on the magnitude of the turbulence intensity, and on the Reynolds number. However, the presence of the undershoot does not affect the fully developed values of the heat transfer coefficient. It was also found that the Fanning friction factor may also experience an undershoot in its axial variation. The magnitude of the heat transfer undershoot is generally greater than that of the Fanning friction factor undershoot.