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The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate (convection + diffusion) to the rate of diffusive mass transport, [1] and is named in honor of Thomas Kilgore Sherwood. It is defined as follows
In 1969 he retired from MIT to become professor of chemical engineering at the University of California, Berkeley. Sherwood's primary research area was mass transfer, and in 1937 he published the first major textbook in the field, Absorption and Extraction (republished 1974 as Mass Transfer). The Sherwood number is named in his honor:
The same restrictions described in the heat transfer definition are applied to the mass transfer definition. The Sherwood number can be used to find an overall mass transfer coefficient and applied to Fick's law of diffusion to find concentration profiles and mass transfer fluxes.
A significant experiment was carried out in 1934 by Edwin R. Gilliland and Thomas Kilgore Sherwood that used a falling-film column to study the mass transfer phenomenon between a liquid phase and a gas phase, obtaining an experimental correlation between the Sherwood number, Reynolds number and Schmidt number. [3]
Mass transfer in a system is governed by Fick's first law: 'Diffusion flux from higher concentration to lower concentration is proportional to the gradient of the concentration of the substance and the diffusivity of the substance in the medium.' Mass transfer can take place due to different driving forces. Some of them are: [12]
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A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. [2] A similar non-dimensional property is the Biot number, which concerns thermal conductivity for a solid body rather than a fluid. The mass transfer analogue of the Nusselt number is the Sherwood number.