Sherwood Number Calculator

 https://www.meracalculator.com/physics/fluid-mechanics/sherwood-number.php

The Sherwood number represents the link between convective mass transfer and diffuse mass transportation and is used in analyzing mass transfer systems such as liquid-liquid removal. This article describes the number and traditional formulations of Sherwood.

Numbers without dimensions play an important part in the study of fluid dynamics and problems with heat and mass transfer. They provide a way of characterizing complex phenomena, often through a direct comparison of the individual numbers. A summary of dimensionless numbers and formulas for their measurement can be found in this article.

 

Definition:

The number of Sherwood is a dimensionless number named after Thomas Kilgore Sherwood and defines the convective mass transfer ratio to the large mass transfer rate. It is the Nusselt Number mass transfer equivalent and is formulated as follows:

Sh=h/(D/L)

Where h is the convective mass the transfer rate and D/L is the mass diffusion rate.

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

 Sh=kRT/DP​

Heat Transfer Link

Sherwood number can be defined in accordance with the Reynolds Number and Schmidt Number by dimensional analysis. In this case, the number of Schmidt is equivalent to the number of Prandtl.

This relationship is useful because it permits heat transfer connections to be used for mass transmission analysis to calculate the Nusselt number. This is done by replacing the number of Sherwood with the number of Nusselt and the number of Schmidt with Prandtl.


Example:
Calculate the Sherwood Number for the given details.
Mass Transfer Coefficient (k) = 10 m/s
Characteristic Length (L) = 20 m
Diffusion Coefficient (D) = 10 m2/s

Solution:
Apply Formula:
Sh = kl/D
Sh = 5*15/10
Sh = 7.5
Sherwood Number (Sh) = 7.5

 

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