Péclet number

The Peclet number ( after Jean Claude Eugène Péclet ) is a dimensionless parameter which the ratio of advective to diffusive fluxes reproduces in transport processes on a characteristic length. It takes place both in matters of heat as well as the mass transport use and is abbreviated.

Heat transport

In thermodynamics, the Peclet number is the product of the Reynolds number and Prandtl number and is defined as:

With:

• - Temperature conductivity ( in SI units: m2 / s)
• - Thermal conductivity ( in SI units: W / ( m K) )
• - Density ( in SI units: kg/m3)
• - Specific heat capacity ( in SI units: J / ( kg K) )
• - Characteristic length ( in SI units: m )
• - Characteristic time (in SI units: s)
• - Speed ​​( in SI units: m / s)

Mass transport

For solute transport, the Peclet number is calculated as the product of Reynolds number and Schmidt number and is defined as:

With:

• - Diffusion constant ( in SI units: m2 / s)

Common applications for the Peclet number, for example, in the numerical calculation of transport processes. Due to the simultaneous occurrence of advective and diffusive fluxes are the differential equations describing a mixed hyperbolic - parabolic type. The calculation of the Peclet number then allows an estimate of what type prevails, and therefore the selection of a suitable numerical method.

Numerics

Dissolving now advective - convective transport equation by a finite difference or finite element method on a discrete grid, defined is a so-called cell Peclet number in which then represents the characteristic length of the cell size of the grid. It results so as

Which must be guaranteed for the guarantee of the stability of the numerical scheme that the cell Peclet number ( depending on the nature of the numerical method mostly <2) is always smaller than an upper bound. This then means that, for convective transport dominant, ie large or small, or the cell size may need to be very small in the above formula, which can increase the numerical effort considerably.