# Lewis Number

on . Posted in Dimensionless Numbers

Lewis number, abbreviated as Le, a dimensionless number, is the ratio of thermal diffusivity to mass diffusivity.  It is used to characterize fluid flows where there is simultaneous heat and mass transfer.  The Lewis number is often used to characterize heat and mass transfer processes, particularly in situations involving simultaneous heat and mass transfer, such as in combustion, chemical reactions, or natural convection.  It provides information about the relative importance of thermal and mass diffusion in a system.

### Key points about the Lewis number

• Le < 1  -  Thermal diffusion is much faster than mass diffusion.  In this case, heat transfer dominates over mass transfer, and temperature variations occur more rapidly than concentration variations.
• Le ≈ 1  -  Heat and mass transfer are comparable in magnitude, and both processes influence the system behavior.
• Le > 1  -  Mass diffusion is much faster than thermal diffusion.  Mass transfer dominates over heat transfer, and concentration variations occur more rapidly than temperature variations.

The Lewis number is particularly relevant in fields such as combustion, chemical engineering, and atmospheric science, where the interaction between heat and mass transfer plays a significant role.  It helps researchers and engineers understand the interplay between diffusion processes and how they affect the overall behavior of fluid flows with coupled heat and mass transfer.

## Lewis number formula

$$\large{ Le = \frac{ \alpha }{ D_m } }$$

### Lewis Number - Solve for Le

$$\large{ Le = \frac{ \alpha }{ D_m } }$$

 thermal diffusivity, α mass diffusivity, Dm

### Lewis Number - Solve for α

$$\large{ \alpha = Le \; D_m }$$

 Lewis number, Le mass diffusivity, Dm

### Lewis Number - Solve for Dm

$$\large{ D_m = \frac{ \alpha }{ Le } }$$

 thermal diffusivity, α Lewis number, Le

Symbol English Metric
$$\large{ Le }$$ = Lewis number  $$\large{dimensionless}$$
$$\large{ \alpha }$$  (Greek symbol alpha) = thermal diffusivity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$
$$\large{ D_m }$$ = mass diffusivity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$ 