## What is Sherwood Number

The **Sherwood number** is a dimensionless number, named after Thomas Kilgore Sherwood. The **Sherwood number** is defined as the ratio of the convective mass transfer to the mass diffusivity.

The Nusselt and Sherwood numbers represent the effectiveness of heat and mass convection at the surface. The **Sherwood number** is to the concentration boundary layer what the Nusselt number is to the thermal boundary layer.

The Sherwood number is defined as:

where:

k_{m} is convective mass transfer coefficient [m/s]

L is a characteristic length [m]

D is the mass diffusivity [m^{2}/s]

For example, the Sherwood number for a single sphere can be expressed as:

Sh = Sh_{0} + C.Re^{m}Sc^{1/3}

where Sh_{0} is the Sherwood number due only to natural convection and not forced convection.

Diffusivity is encountered in Fick’s law, which states:

*If the concentration of a solute in one region is greater than in another of a solution, the solute diffuses from the region of higher concentration to the region of lower concentration, with a magnitude that is proportional to the concentration gradient.*

In one (spatial) dimension, the law is:

where:

*J*is the diffusion flux,*D*is the**diffusion coefficient,***φ*(for ideal mixtures) is the concentration.

The use of this law in **nuclear reactor theory** leads to the **diffusion approximation**.

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