## Péclet number $\rm{Pe} = \frac{advective \: transport \: rate}{diffusive \: transport \: rate}$ Péclet number is defined as the 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**. For mass flow, it has the form $\mathrm{Pe}=\frac{uL}{D}=\mathrm{Re \ Sc}$ Here $u$ is velocity, $L$ is characteristic length, $D$ is diffusivity, $\mathrm{Re}$ is [[Reynolds number]], $\mathrm{Sc}$ is the [[Schmidt number]]. If rewrite as a ratio of time, we have $\mathrm{Pe}=\frac{u/L}{D/l^{2}} = \frac{\mathrm{diffusion \ time}}{\mathrm{advection \ time}}$ For thermal flow, it is $\mathrm{Pe}=\frac{uL}{\alpha}=\mathrm{Re \ Pr}$ $\alpha$ is [thermal diffusivity](https://en.wikipedia.org/wiki/Thermal_diffusivity); $\mathrm{Pr}$ is the [[Prandtl number]]. >[!Info] >See more on wiki: https://en.wikipedia.org/wiki/P%C3%A9clet_number