Sherwood Number Calculator
Enter mass-transfer coefficient, characteristic length and mass diffusivity to compute the Sherwood number Sh=k·L/D. k=1e-4, L=0.05, D=1e-9 → Sh=5000 (high mass transfer).
Input Data
Results
At a glance:The Sherwood number (Sh) is the key dimensionless number in mass transfer, the exact analog of the Nusselt number (Nu) in heat transfer: Sh=k·L/D, where Sh is dimensionless, k the mass-transfer coefficient (m/s), L the characteristic length (m) and D the mass diffusivity (m²/s). Term by term: k is the empirical convective mass-transfer coefficient (from the boundary-layer theory that the actual flux=−k·Δc, c concentration); L and D set the diffusive scale. Physical meaning: Sh is the ratio of total (convective+diffusive) mass transfer to purely diffusive transfer — Sh=1 means pure molecular diffusion (no convection), Sh≫1 means convection dominates the transfer. The mass transfer and heat transfer are fully analogous: replace Nu by Sh and Pr by Sc, giving Sh=C·Reᵐ·Scⁿ (forced convective mass transfer), like Nu=C·Reᵐ·Prⁿ. Example: k=1e-4 m/s, L=0.05 m, D=1e-9 m²/s → Sh=1e-4×0.05/1e-9=5000 (convection strongly dominates). Uses: (1) core dependent variable of mass-transfer correlations (find k from Sh); (2) absorption, distillation, drying, evaporation; (3) catalytic reactor and packed-bed design; (4) membrane separation and biomedical transport. Notes: (1) take the same characteristic length L across the correlation (pipe diameter, sphere diameter, plate length); (2) D is the species diffusivity in the medium at the operating temperature; (3) keep SI units (k m/s, L m, D m²/s) to get dimensionless Sh; (4) Sh is an output of a correlation — you then back out k. In short, Sh=k·L/D is the mass-transfer analog of Nu and the twin of Sc in every convective mass-transfer correlation.
Formula
Sherwood: Sh = k·L / D.
k transfer coefficient (m/s), L length (m), D diffusivity (m²/s); Sh dimensionless.
Mass-transfer analog: Nu→Sh, Pr→Sc, Sh=C·Reᵐ·Scⁿ.
$$\mathrm{Sh} = \frac{k\,L}{D}$$How to Use
- Enter mass-transfer coefficient k (m/s).
- Enter characteristic length L (m) and mass diffusivity D (m²/s).
- The tool computes Sh=k·L/D to judge convection vs diffusion.
Case Studies
Absorption tower and drying
Absorption tower: gas SO₂ into liquid, measure k back-calculate Sh=Sh(Re,Sc) to size the packing.
Drying: a wet surface Sh=C·Reᵐ·Scⁿ gives k, then moisture flux=−k·Δc.
Membrane: L is the membrane thickness, Sh tells how much convection helps over pure diffusion.
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.