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# Péclet number

In fluid dynamics, the Péclet number is a dimensionless number relating the rate of advection of a flow to its rate of diffusion, often thermal diffusion. It is equivalent to the product of the Reynolds number with the Prandtl number in the case of thermal diffusion, and the product of the Reynolds number with the Schmidt number in the case of mass diffusion.

For thermal diffusion, the Péclet number is defined as: $\mathrm{Pe}_L = \frac{L V}{\alpha} = \mathrm{Re}_L \cdot \mathrm{Pr}.$

For mass diffusion, it is defined as: $\mathrm{Pe}_L = \frac{L V}{D} = \mathrm{Re}_L \cdot \mathrm{Sc}$

where

• L - characteristic length
• V - Velocity
• α - Thermal diffusivity $= \frac{k}{\rho c_p}$
• D - mass diffusivity

and

In 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.

A flow will often have different Péclet numbers for heat and mass. This can lead to the phenomenon of Double-diffusive convection.