Péclet number#

Named after: Jean Claude Eugène Péclet (1793-1857).

$$\text{Pe} \stackrel{\text{def}}{=} \frac{U L}{\alpha} \sim \frac{\text{advection}}{\text{thermal diffusion}}$$

Measures advective heat transport relative to thermal diffusion. It indicates whether temperature is carried mainly by flow or smoothed by diffusion.

Name	Symbol	SI units	Dimension
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
thermal diffusivity	$\alpha$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Heat transfer

Range	Regime	Description
0 – 1	diffusion dominated	Thermal diffusion dominates. Temperature gradients are smoothed quickly relative to the flow timescale.
1 – ∞	advection dominated	Advection dominates heat transport. Thermal boundary layers are thin and temperature variations are convected downstream.

Name	Symbol	SI units	Dimension
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
thermal diffusivity	\(\alpha\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)