# Prandtl Number

The Prandtl number is a dimensionless number; the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is named after the German physicist Ludwig Prandtl.

It is defined as:

where:

• : kinematic viscosity, (SI units : m2/s)
• : thermal diffusivity, (SI units : m2/s)
• : dynamic viscosity, (SI units : Pa s = (N s)/m2)
• : thermal conductivity, (SI units : W/(m K) )
• : specific heat, (SI units : J/(kg K) )
• : density, (SI units : kg/m3 ).

Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, the Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.

Typical values for are:

(Low - conductive transfer strong)

• around 0.015 for mercury
• around 0.16-0.7 for mixtures of noble gases or noble gases with hydrogen
• around 0.7-0.8 for air and many other gases,
• between 4 and 5 for R-12 refrigerant
• around 7 for water (At 20 degrees Celsius)
• 13.4 and 7.2 for seawater (At 0 degrees Celsius and 20 degrees Celsius respectively)
• between 100 and 40,000 for engine oil
• around 1×1025 for Earth's mantle.

(High - convective transfer strong)

For mercury, heat conduction is very effective compared to convection: thermal diffusivity is dominant. For engine oil, convection is very effective in transferring energy from an area, compared to pure conduction: momentum diffusivity is dominant.

In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. When Pr is small, it means that the heat diffuses very quickly compared to the velocity (momentum). This means that for liquid metals the thickness of the thermal boundary layer is much bigger than the velocity boundary layer.

The mass transfer analog of the Prandtl number is the Schmidt number.

### Other articles related to "prandtl number, prandtl, number, numbers":

Turbulent Prandtl Number
... The turbulent Prandtl number is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity ... The simplest model for is the Reynolds analogy, which yields a turbulent Prandtl number of 1 ... of 0.85, but ranges from 0.7 to 0.9 depending on the Prandtl number of the fluid in question ...
Boundary Layer - Aerodynamics
... The aerodynamic boundary layer was first defined by Ludwig Prandtl in a paper presented on August 12, 1904 at the third International Congress of Mathematicians in Heidelberg, Germany ... The ratio of the two thicknesses is governed by the Prandtl number ... If the Prandtl number is 1, the two boundary layers are the same thickness ...
Sherwood Number
... The Sherwood number, (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation ... analysis, it can also be further defined as a function of the Reynolds and Schmidt numbers For example, for a single sphere it can be expressed as where is the ... chemical engineers in situations where the Reynolds number and Schmidt number are readily available ...
Turbulent Prandtl Number - Consequences
... In the special case where the Prandtl number and turbulent Prandtl number both equal unity (as in the Reynolds analogy), the velocity profile and ... If the Prandtl number and turbulent Prandtl number are different from unity, then a solution is possible by knowing the turbulent Prandtl number so that one can ... Consequently, the turbulent Prandtl number has no meaning ...

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