Prandtl number

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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.^[1] The Prandtl number is given as:

where:

• ${\displaystyle \nu }$ : momentum diffusivity (kinematic viscosity), ${\displaystyle \nu =\mu /\rho }$, (SI units: m²/s)
• ${\displaystyle \alpha }$ : thermal diffusivity, ${\displaystyle \alpha =k/(\rho c_{p})}$, (SI units: m²/s)
• ${\displaystyle \mu }$ : dynamic viscosity, (SI units: Pa s = N s/m²)
• ${\displaystyle k}$ : thermal conductivity, (SI units: W/(m·K))
• ${\displaystyle c_{p}}$ : specific heat, (SI units: J/(kg·K))
• ${\displaystyle \rho }$ : 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.