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Sherwood number compares convective mass transfer with molecular diffusion across a characteristic length.
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Formula
Sh dimensionless; km in m/s; L in m; D in m2/s
| Symbol | Meaning | Unit |
|---|---|---|
| Sherwood number | dimensionless | |
| Mass-transfer coefficient | m/s | |
| Characteristic length for the correlation | m | |
| Molecular diffusivity | m2/s |
\mathrm{Sh}=\frac{k_mL}{D}This is the mass-transfer analogue of Nusselt number. A suitable correlation in Reynolds and Schmidt numbers is needed to find km; geometry, flow state and concentration boundary conditions matter. Flux conventions must match the definition of km.
This is the mass-transfer analogue of Nusselt number. A suitable correlation in Reynolds and Schmidt numbers is needed to find km; geometry, flow state and concentration boundary conditions matter. Flux conventions must match the definition of km.
Sherwood number compares convective mass transfer with molecular diffusion across a characteristic length.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Sherwood number for convective mass transfer” and check its unit and magnitude.
For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Sh dimensionless; km in m/s; L in m; D in m2/s.
Formula cluster
Sherwood number compares convective mass transfer with molecular diffusion across a characteristic length.
For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10.
Describe convective mass transfer at surfaces and in equipment.
Here is how to work through a typical Sherwood number for convective mass transfer (Sh = kmL/D) task step by step:
Task
Work through the numerical example for “Sherwood number for convective mass transfer” and check its unit and magnitude.
Solution path
For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10.
Sh=kmL/D mirrors Nu=hL/k. The mass-transfer coefficient plays the role of heat-transfer coefficient, and diffusivity that of conductivity. The analogy does not make all correlations identical. Select a mass-transfer coefficient and flux convention consistent with the correlation. Application: Describe convective mass transfer at surfaces and in equipment. The numerical example For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10 anchors the idea in a concrete measurement case. The corresponding units are Sh dimensionless; km in m/s; L in m; D in m2/s. For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10. This checks that the reference quantities are compatible.
Sc=ν/D compares momentum and species diffusion. Many forced mass-transfer correlations express Sh as a function of Re and Sc. Match species, temperature and concentration basis to the diffusivity and correlation. Select a mass-transfer coefficient and flux convention consistent with the correlation. The corresponding units are Sh dimensionless; km in m/s; L in m; D in m2/s. For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10. This checks that the reference quantities are compatible. Scope: This is the mass-transfer analogue of Nusselt number. A suitable correlation in Reynolds and Schmidt numbers is needed to find km; geometry, flow state and concentration boundary conditions matter. Flux conventions must match the definition of km. A practical application is Describe convective mass transfer at surfaces and in equipment.
To calculate flux, you also need a concentration driving force and a local or average mass-transfer coefficient. Interfacial reactions, multicomponent diffusion and nonideal phases can invalidate a simple film model. Select a mass-transfer coefficient and flux convention consistent with the correlation. Scope: This is the mass-transfer analogue of Nusselt number. A suitable correlation in Reynolds and Schmidt numbers is needed to find km; geometry, flow state and concentration boundary conditions matter. Flux conventions must match the definition of km. A practical application is Describe convective mass transfer at surfaces and in equipment.
Write the quantity and unit from the variable list next to every value: Sh dimensionless; km in m/s; L in m; D in m2/s. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For km=0.002 m/s, L=0.05 m and D=1.0·10−5 m2/s, Sh=10. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Select a mass-transfer coefficient and flux convention consistent with the correlation.
The background states this starting condition: This is the mass-transfer analogue of Nusselt number. A suitable correlation in Reynolds and Schmidt numbers is needed. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Select a mass-transfer coefficient and flux convention consistent with the correlation.
Quanta exam set
Curated exam set for "Sherwood number for convective mass transfer":
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Which formula describes Sherwood number for convective mass transfer?
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How do you rearrange Sherwood number for convective mass transfer for Base equation for the target quantity?
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Which common mistake happens with Sherwood number for convective mass transfer?
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Create a curated FSRS exam set for Sh = kmL/D: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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