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Concept# Prandtl number

Summary

The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:
where:
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 scale variable, the Prandtl number contains no such length scale and is dependent only on the fluid and the fluid state. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.
The mass transfer analog of the Prandtl number is the Schmidt number and the ratio of the Prandtl number and the Schmidt number is the Lewis number.
For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents.
Typical values for Pr are:
0.003 for molten potassium at 975 K
around 0.015 for mercury
0.065 for molten lithium at 975 K
around 0.16–0.7 for mixtures of noble gases or noble gases with hydrogen
0.63 for oxygen
around 0.71 for air and many other gases
1.38 for gaseous ammonia
between 4 and 5 for R-12 refrigerant
around 7.56 for water (At 18 °C)
13.4 and 7.2 for seawater (At 0 °C and 20 °C respectively)
50 for n-butanol
between 100 and 40,000 for engine oil
1000 for glycerol
10,000 for polymer melts
around 1 for Earth's mantle.
For air with a pressure of 1 bar, the Prandtl numbers in the temperature range between −100 °C and +500 °C can be calculated using the formula given below. The temperature is to be used in the unit degree Celsius. The deviations are a maximum of 0.1 % from the literature values.

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