# Peclet number

The **Péclet number** (**Pe**) is dimensionless number that is the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient. In the context of species or mass transfer, the Péclet number is the product of the Reynolds number and the Schmidt number. In the context of the thermal fluids, the thermal Peclet number is equivalent to the product of the Reynolds number and the Prandtl number.

The Péclet number is defined as:

For mass transfer, it is defined as:

For heat transfer, the Péclet number is defined as:

where

- is the characteristic length
- is the flow velocity
- is a diffusion coefficient
- is the thermal diffusivity

In most engineering applications the Péclet number is often very large. In such situations, the dependency of the flow upon *downstream* locations is diminished, and variables in the flow tend to become 'one-way' properties. Thus, when modelling certain situations with high Péclet numbers, simpler computational models can be adopted.