# What is L in the Nusselt number

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### Nusselt number

For these similarity considerations, Nusselt introduced the dimensionless form of the heat transfer coefficient, the so-called Nusselt number:

- Tab. 1
- Legend

symbol | description | unit |
---|---|---|

Nusselt number | ||

Heat transfer coefficient | W K ^{-1} · M^{-2} | |

constructive length | m | |

Coefficient of thermal conductivity | W K ^{-1} · M^{-1} |

It represents the relationship between heat flow and heat conduction through a layer of thickness l. If the Nusselt number can be determined, the heat transfer coefficient can be calculated, because the thermal conductivity coefficient of the fluid and the structural length l (e.g. inside diameter of a pipe with a flow through it ) are assumed to be known.

The dimensionless Nusselt index, in turn, is a function of a few dimensionless indexes that characterize the flow and heat conduction processes. For estimating calculations, the criteria equations can be expressed in the form of a potential approach (equation applies to forced convection):

- Tab. 2
- Legend

symbol | description |
---|---|

Constant: depends on the type of heat exchanger, the type of phases involved, the type of flow and the direction of flow | |

the exponents are usually at: 0.4 ≤ m ≤ 0.8; 0.33 ≤ n ≤ 0.43 and have the same dependencies as the constant C. | |

Nusselt number | |

Reynolds number | |

Prandtl number |

The following table provides a list of equations for the rough calculation of heat transfer coefficients for turbulent flow in geometrically similar apparatus:

- Tab. 3

Heat transfer | Simplified criteria equation |
---|---|

in smooth pipes with longitudinal flow | Nu = 0.02 * Re^{0,80 }· Pr^{0,43} |

on cross-flow individual pipes | Nu = 0.21 x Re^{0,62}· Pr^{0,38} |

on pipe bundles with cross flow - pipes in alignment - pipes offset | Nu = 0.23 x Re^{0,65}· Pr^{0,33}Nu = 0.41 * Re^{0,60}· Pr^{0,33} |

on plates exposed to the flow | Nu = 0.04 * Re^{0,80}· Pr^{0,43} |

in flowed-through embankments | Nu = 0.58 x Re^{0,70}· Pr^{0,33} |

Gmehling, J .; Brehm, A. (** 1996**):

*Basic Operations - Textbook of Technical Chemistry, Volume 2*.

*Georg Thieme Publishing House*,

When using these equations, attention must be paid to the characteristic dimensions of the system, to which the dimensionless parameters refer.

- Tab. 4

with pipes, drops, particles, bubbles | Diameter d |

for stirred tanks | Diameter D |

with flat walls | Length or height h |

in the case of bulk layers | mean particle diameter d_{m} |

### Nusselt code for free convection

The calculation equations for the Nusselt number were previously only valid for forced convection. Should thermal lift forces cause the flow (free convection), the Grashof number Gr is used instead of the Reynolds number, which represents the quotient of thermal lift force and internal inertial force. The following then applies to the Nusselt number:

- Tab. 5
- Legend

symbol | description |
---|---|

Constant: depends on the type of heat exchanger, the type of phases involved, the type of flow and the direction of flow | |

the exponents are usually at: 0.4 ≤ m ≤ 0.8; 0.33 ≤ n ≤ 0.43 and have the same dependencies as the constant C. | |

Nusselt number | |

Grass yard number | |

Prandtl number |

Grass yard number

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