Péclet number

The Péclet number (according to Jean Claude Eugène Péclet ) is a dimensionless number which shows the ratio of advective to diffusive flows over a characteristic length in transport processes . It is used both for questions of heat and of mass transfer . ${\displaystyle Pe}$ ${\displaystyle L}$

Heat transfer

In thermodynamics , the Péclet number corresponds to the product of the Reynolds number and Prandtl number and is defined as: ${\displaystyle Re}$ ${\displaystyle Pr}$

${\displaystyle Pe={L\cdot v \over a}={L\cdot v\cdot \rho \cdot c_{p} \over \lambda }={Re\cdot Pr}}$

With

• ${\displaystyle L}$- characteristic length (SI units: m)
• ${\displaystyle v}$- speed (SI units: m / s)
• ${\displaystyle a}$- Thermal diffusivity (SI units: m ² / s)
• ${\displaystyle \rho }$- Density (SI units: kg / m ³ )
• ${\displaystyle c_{p}}$- specific heat capacity (SI units: J / (kg K))
• ${\displaystyle \lambda }$- Thermal conductivity (SI units: W / (m K)).

See also: heat transfer , heat transfer coefficient

Material transport

Due to the analogy between heat and mass transfers, a Péclet number is defined to describe mass transfer processes, which is the product of the Reynolds number and Schmidt number : ${\displaystyle Re}$ ${\displaystyle Sc}$

${\displaystyle Pe^{\prime }={L\cdot v \over D}={Re\cdot Sc}}$

With

• the diffusion coefficient (SI units: m ² / s). ${\displaystyle D}$

This Péclet number is deleted here just to make the difference to heat transfer clear.

Numerics

The Péclet number is z. B. used in the numerical calculation of transport processes. Due to the simultaneous occurrence of advective and diffusive flows, the descriptive differential equations are of a mixed hyperbolic - parabolic type. The calculation of the Péclet number then allows an estimate to be made as to which type is predominant and therefore the choice of a suitable numerical method.