Prandtlegetal

The Prandtlgetal, or Prandtl number (Pr), is a dimensionless quantity in fluid dynamics that characterizes the relative thickness of the velocity boundary layer to the thermal boundary layer in a moving fluid. It is defined as Pr = ν/α, where ν is the kinematic viscosity and α is the thermal diffusivity. Equivalently, Pr is the ratio of momentum diffusivity to thermal diffusivity.

Physically, the Prandtl number indicates how quickly momentum diffuses relative to heat. When Pr ≪ 1, heat diffuses faster than momentum, leading to a thicker velocity boundary layer relative to the thermal layer. When Pr ≫ 1, momentum diffuses faster than heat, and the thermal boundary layer is thinner than the velocity boundary layer. Typical values: air around 0.7, water around 7, many oils in the tens to hundreds, and liquid metals around 0.01–0.1.

In engineering and physics, Pr is used to predict convective heat transfer and to scale flow problems. It interacts with the Rayleigh number in natural convection and with the Reynolds number in forced convection. It also relates to the Schmidt number for mass transfer, by analogy between heat and species diffusion.

History and usage: The concept is named after Ludwig Prandtl, who introduced it in boundary-layer theory in the early 20th century. Today it appears in analytical solutions, experimental correlations, and computational fluid dynamics as a parameter governing thermal boundary layers.