Dimensionless Numbers
Dimensionless number | Definition | Description | Associated regime |
---|---|---|---|
Reynolds | \( Re = \frac{\rho V L}{\mu}\) | Ratio between inertial and viscous forces | Stokes / steady or unstationary laminar / turbulent |
Prandtl | \( Pr = \frac{\nu}{\alpha} = \frac{c_p \mu}{k}\) | Ratio between momentum diffusivity and thermal diffusivity | Momentum or thermal diffusivity driven flows |
Rayleigh | \( Ra = \frac{\rho \beta \Delta T g L^3}{\mu \alpha } \) | Ratio between thermal diffusion and thermal convection time scales | Associated to laminar or turbulent free convection flows (buoyancy-driven); can also be relative to pure conduction regimes or mixed convection flows |
Nusselt | \( Nu = \frac{h L}{k} \) | At a boundary, ratio between convective and conductive heat transfer | Pure conduction \( (<= 1) \), laminar or turbulent regime above |
Atwood | \( A = \frac{\rho_{heavy}-\rho_{light}}{\rho_{heavy}+\rho_{light}} \) | Normalized relative density ratio, mostly used for studying the Rayleigh-Taylor instability | Same density \( = 0 < \) massless light fluid \( = 1 \) |
With: