||This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (August 2014)|
|This article needs additional citations for verification. (August 2014)|
The Prandtl number (Pr) is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. That is, the Prandtl number is given as:
- : momentum diffusivity (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 Pr are:
- 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 °C)
- 13.4 and 7.2 for seawater (At 0°C and 20°C respectively)
- between 100 and 40,000 for engine oil
- around 1×1025 for Earth's mantle.
Small values of the Prandtl number, Pr << 1, means the thermal diffusivity dominates. Whereas with large values, Pr >> 1, the momentum diffusivity dominates the behavior. For example, the listed value for liquid mercury indicates that the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. However, for engine oil, convection is very effective in transferring energy from an area in comparison to pure conduction, so 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 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.