Thermal entry effects in turbulent pipe flows

Well-resolved simulations of passive-scalar turbulent pipe flow in the thermal entry region are presented. We quantify thermal entry lengths of several quantities, such as the Nusselt number $\mathrm{Nu}$ and temperature variance, and show that they depend strongly on $\mathrm{Re}_b$ and $\mathrm{Pr}$ and that no single thermal entry length exists: higher-order statistics require much longer distances to reach their fully developed asymptote. To analyse the underlying mechanisms, we present a $\mathrm{Nu}$-decomposition, the heat transfer counterpart of the Fukagata-Iwamoto-Kasagi (FIK) identity (Fukagata et al., 2002, Physics of Fluids) applicable in thermally developing flow.