# Sherwood number

## Definition

The Sherwood number is used for the problems of mass transfer. It is basically a ratio and
a dimensionless number. This dimensionless number is significant for explaining the
effectiveness of mass convection. So, the concentration boundary layer of a specific
surface is considered by the Sherwood number^{[1]}.

## Introduction

The **Sherwood number** (**Sh**) is a dimensionless number used in mass-transfer operations It is the ratio of convective mass transfer to mass diffusion.

It is defined as follows

where

- is a characteristic length
- is a mass diffusion rate
- is the convective mass transfer coefficient

Using dimensional analysis, it can also be further defined as a function of the Reynolds and Schmidt numbers:

For example, for a single sphere it can be expressed as:

where is the Sherwood number due only to natural convection and not forced convection.

A more specific correlation is the Froessling equation:^{[2]}

This form is applicable to heat transfer from a single spherical particle. It is particularly valuable in situations where the Reynolds number and Schmidt number are readily available. Since Re and Sc are both dimensionless numbers, the Sherwood number is also dimensionless.

These correlations are the mass transfer analogies to heat transfer correlations of the Nusselt number in terms of the Reynolds number and Prandtl number. For a correlation for a given geometry (e.g. spheres, plates, cylinders, etc.), a heat transfer correlation (often more readily available from literature and experimental work, and easier to determine) for the Nusselt number (Nu) in terms of the Reynolds number (Re) and the Prandtl number (Pr) can be used as a mass transfer correlation by replacing the Prandtl number with the analogous dimensionless number for mass transfer, the Schmidt number, and replacing the Nusselt number with the analogous dimensionless number for mass transfer, the Sherwood number.

As an example, a heat transfer correlation for spheres is given by the Ranz-Marshall Correlation:^{[3]}

This correlation can be made into a mass transfer correlation using the above procedure, which yields:

In the case of falling film example, where only A is diffusing into B:^{[4]}

This is a very concrete way of demonstrating the analogies between different forms of transport phenomena.

The mass convection effectiveness is described by the Sherwood number similar to the Nusselt number that describes the heat convection effectiveness at the specific surface. The Nusselt number and Sherwood number are related to the thermal boundary layer and concentration boundary layer respectively. The Sherwood number considers the mass diffusivity, characteristic length, and convective mass transfer ^{[5]}

- ↑ [Azizi, Z. (2014). Effective diffusivity in a structured packed column: Experimental and Sherwood number correlating study. Chemical Engineering Research and Design , 43 - 53
- ↑ Froessling, N.
*Uber die Verdunstung Fallender Tropfen (The Evaporation of Falling Drops)*. Gerlands Beitrage zur Geophysik, 52:107-216, 1938 - ↑ Ranz, W. E. and Marshall, W. R.
*Evaporation from Drops*. Chemical Engineering Progress, 48:141-146, 173-180, 1952. - ↑ Green, D. W., & Perry, R. H. (2007). Heat and Mass Transfer. In Mathematics (8th ed., pp. 5-65).
- ↑ [ Burganos, V. N. (1997). Sherwood number for a swarm of adsorbing spheroidal particles at any peclet number. AIChE Journal , 844 - 846.