Lewis number ($Le=\kappa /D$)

The ratio of thermal diffusivity $\kappa$ to molecular or solutal diffusivity $D$. In coupled heat equation and solute diffusion equation similarity problems, the thermal coordinate $z/(2\sqrt{\kappa t})$ becomes $\sqrt{Le}$ times larger in the solute complementary error function profile. This follows by substituting the thermal coordinate into $C_t=D{C}_{zz}$, giving $C^{\prime \prime }+2Le\eta C^{\prime }=0$. The definition must specify the direction of this ratio because reciprocal conventions occasionally occur.