# Dittus-Boelter equation - Nusselt number

## Description

In heat transfer at a boundary (surface) within a fluid, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer across (normal to) the boundary. In this context, convection includes both advection and diffusion. Named after Wilhelm Nusselt, it is a dimensionless number. The conductive component is measured under the same conditions as the heat convection but with a (hypothetically) stagnant (or motionless) fluid. A similar non-dimensional parameter is Biot number, with the difference that the thermal conductivity is of the solid body and not the fluid. This number gives an idea that how heat transfer rate in convection is related to the resulting of heat transfer rates in conduction.

The Dittus-Boelter equation (for turbulent flow) is an explicit function for calculating the Nusselt number. It is easy to solve but is less accurate when there is a large temperature difference across the fluid. It is tailored to smooth tubes, so use for rough tubes (most commercial applications) is cautioned.

Related formulas## Variables

N_{u} | Nusselt number (dimensionless) |

Re_{D} | Reynolds number on the hydraulic diameter (dimensionless) |

Pr | Prandtl number (dimensionless) |

n | n= 0.4 for the fluid being heated, and n = 0.3 for the fluid being cooled (dimensionless) |