Dimensionless number
Dimensionless numbers in transport phenomena are a set of dimensionless quantities that have an important role in the calculations of momentum, mass and heat transfer.
Diffusive numbers in transport phenomena
vs. | Inertial | Viscous | Thermal | Mass |
---|---|---|---|---|
Inertial | vd | Re | Pe | Pe_{AB} |
Viscous | Re^{−1} | η, μ/ρ | Pr | Sc |
Thermal | Pe^{−1} | Pr^{−1} | α | Le |
Mass | Pe_{AB}^{−1} | Sc^{−1} | Le^{−1} | D |
The classical numbers in transport phenomena of mass, momentum, and energy are principally analyzed by the ratio of effective diffusivities in each transport mechanism. The six dimensionless numbers give the relative strengths of the different phenomena of inertia, viscosity, conductive heat transport, and mass transport. (In the table, the number is the ratio of the left column quantity over top row quantity; e.g. Re = vd/η.) These same quantities may alternatively be expressed as ratios of characteristic time, length, or energy scales; these are less commonly used but can provide insight into particular applications.
List
All numbers are dimensionless quantities
Name | Standard symbol | Definition | Word definition |
---|---|---|---|
Biot number | Ratio of thermal resistance external to a boundary or surface to the internal thermal resistance | ||
Brinkman number | Ratio of heat transfer to viscous heating | ||
Darcy friction factor | Ratio of pressure drop to kinetic energy in pipe flow. | ||
Drag coefficient | Ratio of drag force to kinetic energy in external flow | ||
Fanning friction factor | Ratio of wall shear stress to kinetic energy in pipe flow. | ||
Grashof number | Ratio of bouyant to viscous forces in natural convection | ||
Mach number | Ratio of flow velocity in medium to speed of sound in medium | ||
Nusselt number | Ratio of convective to conductive heat transfer | ||
Peclet number | or | Ratio of advective transport to molecular diffusion in mass transfer or the ratio of advective transport to thermal diffusion in heat transfer. | |
Prandtl number | heat transfer (the ratio of viscous diffusion to thermal diffusion) | ||
Rayleigh number | heat transfer (buoyancy versus viscous forces in free convection) | ||
Reynolds number | fluid mechanics (ratio of fluid inertial and viscous forces) | ||
Schmidt number | mass transfer (viscous over molecular diffusion rate) | ||
Sherwood number | mass transfer (forced convection; ratio of convective to diffusive mass transport) |