Prandtl number

The Prandtl number (Pr) is a named after Ludwig Prandtl dimensionless parameter of fluids, ie gases or liquids. It is defined as the ratio between kinematic viscosity and thermal diffusivity:

  • - Dynamic viscosity of the fluid in kg · m-1 · s -1
  • - Kinematic viscosity in m2 · s- 1
  • - Thermal conductivity in W · m -1 · K-1
  • - Thermal diffusivity in m2 · s- 1
  • - Specific heat capacity in J · kg -1 · K-1 at constant pressure.

The Prandtl number is the link of the velocity field with the temperature field of a fluid dar. While the kinematic viscosity of the transport of momentum due to friction represents the Temperaturleitkoeffizient for the stands (possibly transient ) heat transfer due to conduction. Since the momentum transfer is determined by the velocity field, the heat transport through the temperature field, the Prandtl number for the relevant connecting the two heat transfer areas. The Prandtl number is thus a measure of the ratio of the thickness of flow boundary layer to temperature.

The Prandtl number is a pure, generally temperature-and density-dependent stock size ( material parameters ) of the fluid.

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

For a model gas of uniform hard spheres with attractive dipole interaction ( hard-sphere gas) is independent of the temperature gives the value Pr = 2/ 3 = 0.667 (see kinetic theory of gases ). This is for monatomic gases helium, neon, argon, krypton, and xenon in very good agreement with the experimental values ​​.

For gases and vapors applies for pressures from 0.1 to 10 bar approximately:

Where the isentropic exponent is.

Prandtl numbers of important heat transfer media

  • Air: 0.7179 (0 ° C, 1 bar abs); 0.7194 (500 ° C, 1 bar abs)
  • Water vapor: 0.973 (100 ° C); 0,869 (500 ° C)
  • Water: 13.44 (0 ° C); 11.16 (5 ° C); 6.99 (20 ° C); 4.34 (40 ° C ); 3.00 (60 ° C); 2.20 ( 80 ° C); 1.75 (100 ° C)
  • Sodium: 0.0114 (100 ° C); 0.00535 ( 350 ° C)

General:

  • The Prandtl numbers of liquids decrease with increasing temperature.
  • Liquid metals have very small Prandtl numbers.

Examples of the Prandtl number liquids:

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