Defaults (Re=50000, Pr=7.0, k=0.60 W/(m·K), D=25 mm, heating) give Nu ≈ 287.7, h ≈ 6905 W/(m²·K), heat flux at ΔT=10 K ≈ 69.0 kW/m², thermal boundary-layer ≈ 0.087 mm. Valid range is Re > 4000 and 0.6 < Pr < 160; below Re = 4000 the flow is laminar and a different correlation is required.
Forced convection in a horizontal pipe: bulk fluid in the core (blue) and a thin thermal boundary layer near the wall (red gradient). Larger Nu means a thinner boundary layer and a higher driving force. Arrows indicate the axial velocity profile, and the gap between wall temperature T_w and bulk temperature T_b drives heat transfer.
Horizontal: Reynolds number Re (4000 to 200000, log10) / Vertical: Nusselt number Nu (log10) / Blue line: Dittus-Boelter prediction with slope 0.8 / Yellow marker: current (Re, Nu) operating point / Changing Pr shifts the whole line vertically; larger Pr gives larger Nu and stronger convective heat transfer.
The Dittus-Boelter correlation is the most basic empirical equation for forced-convection heat transfer in turbulent pipe flow (Re > 4000, 0.6 < Pr < 160):
$$\mathrm{Nu} = 0.023\,\mathrm{Re}^{0.8}\,\mathrm{Pr}^{n}$$$n = 0.4$ for heating (fluid receives heat from the wall, $T_w > T_b$) and $n = 0.3$ for cooling. The Reynolds and Prandtl numbers are defined as:
$$\mathrm{Re} = \frac{\rho U D}{\mu},\quad \mathrm{Pr} = \frac{\mu c_p}{k}$$The heat-transfer coefficient $h$ follows from the definition $\mathrm{Nu} = hD/k$:
$$h = \frac{\mathrm{Nu}\,k}{D}$$The wall heat flux follows from Newton's law of cooling, and the thermal boundary-layer thickness is $\delta_T \approx D/\mathrm{Nu}$:
$$q = h\,(T_w - T_b),\quad \delta_T \approx \frac{D}{\mathrm{Nu}}$$$\rho$ is density, $U$ is the mean velocity, $D$ is the pipe diameter, $\mu$ is viscosity, $c_p$ is the specific heat at constant pressure, $k$ is the fluid thermal conductivity, $T_w$ is the wall temperature and $T_b$ is the bulk (mixing-cup) temperature.