Péclet number

In continuum mechanics, the Péclet number (Pe, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum.

The Péclet number is defined as For mass transfer, it is defined as Such ratio can also be re-written in terms of times, as a ratio between the characteristic temporal intervals of the system: For

the diffusion happens in a much longer time compared to the advection, and therefore the latter of the two phenomena predominates in the mass transport.

For heat transfer, the Péclet number is defined as where L is the characteristic length, u the local flow velocity, D the mass diffusion coefficient, Re the Reynolds number, Sc the Schmidt number, Pr the Prandtl number, and α the thermal diffusivity, where k is the thermal conductivity, ρ the density, and cp the specific heat capacity.

[2] The Péclet number also finds applications beyond transport phenomena, as a general measure for the relative importance of the random fluctuations and of the systematic average behavior in mesoscopic systems.