The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. It is named after Ludwig Prandtl.

It is defined as:

$\backslash mathit\{Pr\}\; =\; \backslash frac\{\backslash nu\}\{\backslash alpha\}$

where:

• $\backslash nu$ is the kinematic viscosity
• α is the thermal diffusivity

Typical values for Pr are:

• around 0.7 for air and many other gases,
• between 100 and 40,000 for engine oil,
• between 4 and 5 for R-12 refrigerant
• around 0.015 for mercury

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.

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

Dimensionless numbers | Fluid mechanics

Prandtl-Zahl | nombre de Prandtl | numero di Prandtl | プラントル数 | 프란틀 수 | Getal van Prandtl | Liczba Prandtla | Prandtlin luku