Prandtlnummeret

Prandtlnummeret, or the Prandtl number, is a dimensionless quantity used in fluid dynamics and heat transfer to describe the relative thickness of the velocity and temperature boundary layers in a fluid flow. It is defined as the ratio of momentum diffusivity to thermal diffusivity.

Mathematically, Pr = ν/α = (μ/ρ) / (k/(ρ c_p)) = μ c_p / k, where ν is the kinematic viscosity, α is the thermal diffusivity, μ is the dynamic viscosity, ρ is the density, k is the thermal conductivity, and c_p is the specific heat at constant pressure. The Prandtl number therefore compares how quickly momentum diffuses through a fluid to how quickly heat diffuses.

Physically, a high Prandtl number indicates that momentum diffusion dominates over thermal diffusion, so the velocity boundary layer tends to be thicker than the thermal boundary layer. Conversely, a low Prandtl number means heat diffuses more readily than momentum, so the thermal boundary layer is relatively thicker.

Typical values vary with temperature and fluid. Air at room temperature has Pr ≈ 0.7, water around 7, and many oils have Pr values well above 100. Since Pr depends on fluid properties that change with temperature, it is often treated as a temperature-dependent parameter in engineering calculations.

Applications of the Prandtl number include analyzing laminar and turbulent convection, formulating Nusselt-number correlations, and modeling heat transfer in heat exchangers. It is related to other dimensionless numbers such as the Schmidt number and the Lewis number, and is named after Ludwig Prandtl, who introduced it in the early 20th century.