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Prandtl number

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The Prandtl number is defined as

Pr = \frac{\mu C_p}{k}


  • \mu is the dynamic viscosity coefficient
  • C_p is the specific heat at constant pressure
  • k is the coefficient of thermal conduction

It is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It can be related to the thickness of the thermal and velocity boundary layers. It is actually the ratio of velocity boundary layer to thermal boundary layer. When Pr=1, the boundary layers coincide. When Pr is small, it means that heat diffuses very quickly compared to the velocity (momentum). This means the thickness of the thermal boundary layer is much bigger than the velocity boundary layer for liquid metals.

The parameter is named after the German physicist Ludwig Prandtl (1875 - 1953), a pioneer of aerodynamics; developed the mathematical basis for the fundamental principles of subsonic aerodynamics in the earlier 20th century. His studies identified the boundary layer, thin-airfoils, and lifting-line theories.

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