Lewis number

In

• α is the thermal diffusivity,
• D is the mass diffusivity,
• λ is the
  thermal conductivity
  ,
• ρ is the density,
• D_im is the mixture-averaged diffusion coefficient,
• c_p is the specific heat capacity at constant pressure.

In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition.^[3][4]

The Lewis number can also be expressed in terms of the Prandtl number (Pr) and the Schmidt number (Sc):^[5]

${\displaystyle \mathrm {Le} ={\frac {\mathrm {Sc} }{\mathrm {Pr} }}}$

It is named after

The Lewis number is large for water ${\displaystyle (\mathrm {Le} \approx 90\gg 1)}$, and this is likely the reason why mammals do not have gills.^[8] In gills, oxygen is extracted from seawater into the mammal. Since the Lewis number for water is high, this means that during this diffusion process, a relatively large amount of heat would also be extracted from the animal, as heat diffuses faster than oxygen. This would cause the animal to cool down too much while breathing.