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| {{Unreferenced|date=December 2009}}
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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 [[convection|convective]] to [[diffusion|diffusive]] mass transport, and is named in honor of [[Thomas Kilgore Sherwood]]. | |
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| It is defined as follows
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| :<math>\mathrm{Sh} = \frac{K L}{D} = \frac{\mbox{Convective mass transfer coefficient}}{\mbox{Diffusive mass transfer coefficient}} </math>
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| where
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| * ''L'' is a characteristic length (m)
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| * ''D'' is [[mass diffusivity]] (m<sup>2</sup>.s<sup>−1</sup>)
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| * ''K'' is the [[mass transfer coefficient]] (m<sup></sup>.s<sup>−1</sup>)
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| Using dimensional analysis, it can also be further defined as a function of the [[Reynolds number|Reynolds]] and [[Schmidt number|Schmidt]] numbers:
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| :<math>\mathrm{Sh} = f(\mathrm{Re}, \mathrm{Sc})</math> | |
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| For example, for a single sphere it can be expressed as:
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| :<math>\mathrm{Sh} = \mathrm{Sh}_0 + C\, \mathrm{Re}^{m}\, \mathrm{Sc}^{\frac{1}{3}}</math>
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| where <math>\mathrm{Sh}_0</math> is the Sherwood number due only to natural convection and not forced convection.
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| A more specific correlation, the Froessling equation:
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| :<math>\mathrm{Sh} = 2 + 0.552\, \mathrm{Re}^{\frac{1}{2}}\, \mathrm{Sc}^{\frac{1}{3}}</math>
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| This form is particularly valuable to chemical engineers 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.
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| These correlations are the mass transfer analogs 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.
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| As an example, a heat transfer correlation for spheres is given by the Ranz-Marshall Correlation:
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| :<math>\mathrm{Nu} = 2 + 0.6\, \mathrm{Re}^{\frac{1}{2}}\, \mathrm{Pr}^{\frac{1}{3}}, ~ 0 \le ~ \mathrm{Re} <200, ~ 0 \le \mathrm{Pr} < 250</math>
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| This correlation can be made into a mass transfer correlation using the above procedure, which yields:
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| :<math>\mathrm{Sh} = 2 + 0.6\, \mathrm{Re}^{\frac{1}{2}} \, \mathrm{Sc}^{\frac{1}{3}}, ~ 0 \le ~ \mathrm{Re} < 200, ~ 0 \le \mathrm{Sc} < 250</math>
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| This is a very concrete way of demonstrating the [[Transport phenomena#Analogy between phenomena|analogies between different forms of transport phenomena]].
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| ==See also==
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| * [[Churchill-Bernstein Equation]]
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| {{NonDimFluMech}}
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| {{DEFAULTSORT:Sherwood Number}}
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| [[Category:Dimensionless numbers]]
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