What is L in the Nusselt number

to directory mode

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

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
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
Grass yard number
Prandtl number

Grass yard number