Definition of Lewis Number
Definition
In fluid mechanics, the dimensionless quantity defined as the ratio of thermal diffusivity $\alpha$ to mass diffusivity $D$ is called the Lewis number. $$ \mathrm{Le} := {\frac{ \alpha }{ D }} $$
Explanation
The Lewis number represents the relative importance of heat transfer and mass transfer when both occur simultaneously. In particular, the Schmidt number and the Prandtl number both cancel the kinematic viscosity $\nu$, and the Lewis number can be expressed as the ratio of these two numbers. $$ \begin{align*} \mathrm{Sc} =& {\frac{ \nu }{ D }} \\ \mathrm{Pr} =& {\frac{ \nu }{ \alpha }} \\ \implies \mathrm{Le} =& = {\frac{ \nu }{ D }} \left( {\frac{ \nu }{ \alpha }} \right)^{-1} = \frac{ \mathrm{Sc} }{ \mathrm{Pr} } \end{align*} $$