Lewis number#

Named after: Warren K. Lewis (1882-1975).

$$\text{Le} \stackrel{\text{def}}{=} \frac{\alpha}{D} \sim \frac{\text{thermal diffusion}}{\text{mass diffusion}}$$

Measures thermal diffusivity relative to mass diffusivity. It indicates whether heat or species concentration spreads faster.

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

Coupled heat and mass transfer

Range	Regime	Description
0 – 1	mass diffuses faster	Species concentration disturbances spread faster than temperature disturbances. Mass transfer boundary layers tend to be thicker than thermal boundary layers.
1 – ∞	heat diffuses faster	Temperature disturbances spread faster than species concentration disturbances. Thermal boundary layers tend to be thicker than concentration boundary layers.

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