Definition of Sherwood Number
Definition
In fluid mechanics, the dimensionless quantity obtained by dividing the product of the total mass transfer rate $h$ and the characteristic length $L$ by the mass diffusivity $D$ is called the Sherwood number. $$ \mathrm{Sh} := \frac{h L}{D} $$
Description
Nusselt number: In fluid mechanics, the dimensionless quantity obtained by dividing the product of the heat transfer coefficient $h$ and the characteristic length $L$ by the thermal conductivity $k$ is called the Nusselt number. $$ \mathrm{Nu} = {{h L} \over k} $$
The Sherwood number is often referred to as the Nusselt number for mass transfer — under an analogous definition it concerns mass transfer instead of heat transfer. Unlike the Nusselt number, where higher or lower values relate to heat transfer efficiency, the Sherwood number is not typically characterized as ‘good’ or ‘bad.’
$$ \mathrm{Sh} = \frac{h}{D/L} $$ If one divides both numerator and denominator of the Sherwood number by $L$, the Sherwood number effectively expresses how rapidly total mass transfer occurs relative to mass diffusion. It can be viewed as a measure of how much mass transport is produced by the fluid flow compared with the relatively slow process of diffusion.
Total mass transfer rate
The dimension of the total mass transfer rate $h$ is $[\mathsf{T} / \mathsf{L}]$. Unlike the heat transfer coefficient $h$ that appears in the definition of the Nusselt number — which arises from Newton’s law of cooling and yields a neat expression in SI units — the total mass transfer rate does not originate from a single law, so it should be specified explicitly. $$ h \left[ {\frac{ \mathrm{W} }{ \mathrm{m}^2 \cdot \mathrm{K} }} \right] $$