# Summary

The Sherwood number is a dimensionless number that represents the ratio of convective mass transfer to the rate of diffusive mass transport and is used in the analysis of mass transfer systems such as liquid-liquid extraction. This article describes the Sherwood number and typical formulations.

# Definitions

D | : | Mass diffusivity, m^{2}.s^{-1} |

h | : | Convective mass transfer film coefficient, m.s^{-1} |

k | : | Gas phase mass transfer coefficient, mol/(m^{2}.s.mole fraction) |

L | : | Characteristic length, m |

Nu | : | Nusselt Number |

P | : | Pressure, Pa |

Pr | : | Prandtl Number |

R | : | Gas Constant, L/mol.K |

Re | : | Reynolds Number |

Sc | : | Schmidt Number |

Sh | : | Sherwood Number |

T | : | Temperature, K |

# Introduction

The Sherwood number is a dimensionless number named in honour of Thomas Kilgore Sherwood and describes the ratio of convective mass transfer to the rate of diffusive mass transfer. It is the mass transfer equivalent of the Nusselt Number and is formulated as follows:

Where is the convective mass transfer rate and is the mass diffusion rate.

For gas systems an alternative formulation utilising the gas phase mass transfer coefficient k can be used:

## Relationship with Heat Transfer

Dimensional analysis indicates that Sherwood number can be defined as a function of the Reynolds Number and Schmidt Number. In this case the Schmidt number is analogous to the Prandtl Number.

This relationship is useful as it allows heat transfer relationships developed for the determination of the Nusselt number to be utilised for mass transfer analysis. This is achieved by substituting the Sherwood number for the Nusselt number, and the Schmidt Number for the Prandtl Number.

An example substitution using heat transfer over a sphere is as follows:

# Further Reading

- Chemical Engineering Volume 1, Sixth Edition: Fluid Flow, Heat Transfer and Mass Transfer
- Perry’s Chemical Engineers’ Handbook, Eighth Edition
- Fundamentals of Heat and Mass Transfer, 7th Edition

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