# 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
symboldescriptionunit
Nusselt number
Heat transfer coefficientW K -1 · M-2
constructive lengthm
Coefficient of thermal conductivityW 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
symboldescription
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 transferSimplified criteria equation
in smooth pipes with longitudinal flowNu = 0.02 * Re0,80 · Pr0,43
on cross-flow individual pipes Nu = 0.21 x Re0,62· Pr0,38
on pipe bundles with cross flow - pipes in alignment - pipes offset Nu = 0.23 x Re0,65· Pr0,33Nu = 0.41 * Re0,60· Pr0,33
on plates exposed to the flow Nu = 0.04 * Re0,80· Pr0,43
in flowed-through embankmentsNu = 0.58 x Re0,70· Pr0,33

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 tanksDiameter D
with flat walls Length or height h
in the case of bulk layersmean particle diameter dm