Model mass transfer with dimensionless clarity always. Switch between definitions and empirical correlations easily here. Use your data, get Sh, kL, and insight fast.
These sample cases demonstrate typical inputs and expected output ranges.
| Case | Correlation | Re | Sc | Computed Sh | Notes |
|---|---|---|---|---|---|
| 1 | Sphere (Ranz–Marshall) | 10,000 | 700 | ≈ 2 + 0.6·(10,000)^0.5·(700)^(1/3) | Common for particles, drops, and bubbles. |
| 2 | Flat plate laminar (avg) | 200,000 | 600 | ≈ 0.664·Re^0.5·Sc^(1/3) | Valid for laminar boundary layers. |
| 3 | Laminar pipe entry (avg) | 1,500 | 900 | ≈ 1.86·(Re·Sc·Dh/L)^(1/3) | Use when entrance effects dominate. |
The Sherwood number is the dimensionless mass transfer analog of the Nusselt number:
Sh = (kL · Lc) / DkL = (Sh · D) / LcRe = (ρ · v · Lc) / μ (optional)Sc = μ / (ρ · D) (optional)Correlation-based estimates express Sh as a function of Re and Sc. Choose a correlation that matches your geometry and flow regime.
Lc and D with appropriate units.Re and Sc, or enable property-based calculation.Dh and L.Lc consistently with the selected correlation.D matches the same fluid phase used for μ and ρ.Re can make some correlations unreliable.Sh is negative in turbulent plate mode, switch regimes.The Sherwood number (Sh) compares convective mass transfer at a surface to molecular diffusion. Higher Sh indicates a thinner concentration boundary layer and stronger renewal at the interface. In practice, increasing flow speed or mixing usually increases Sh and supports higher mass-transfer rates.
This calculator uses Sh = kL·Lc/D and the rearranged form kL = Sh·D/Lc to move between dimensionless performance and a usable coefficient. Typical diffusivities are about 10−5 m²/s for gases and about 10−9 m²/s for many liquid solutes, so D strongly influences kL.
The characteristic length Lc must match the correlation definition. Use diameter for spheres and cylinders, streamwise plate length for flat plates, and hydraulic diameter Dh for ducts. A mismatched Lc silently skews Re, Sh, and any derived kL.
Most correlations express Sh as a function of Re and Sc. Re = ρvLc/μ indicates whether inertial or viscous effects dominate. Sc = μ/(ρD) compares momentum to mass diffusion; gases often have Sc near 0.7–1, while many liquids are roughly 100–2000+ depending on viscosity and D.
For particles and droplets, a widely used estimate is Sh = 2 + 0.6Re^{1/2}Sc^{1/3}, which adds convection enhancement to the diffusion baseline. Flat-plate averages separate laminar and turbulent boundary layers; transition is often discussed around Re ≈ 5×105 based on plate length.
In laminar ducts, concentration profiles develop along the entrance region, so average transfer depends on the aspect ratio through Dh/L. The entry relation Sh = 1.86(Re·Sc·Dh/L)^{1/3} predicts higher Sh for shorter channels. Farther downstream, fully developed laminar transfer can approach a near-constant Sh.
Because correlations use fractional powers, uncertainty in inputs can still matter. A 20% change in Re changes Re^{1/2} by about 9%, and uncertainty in D directly scales kL. Compare correlations, confirm units, and export a record of assumptions for reviews.
Sherwood-based calculations appear in gas absorption, evaporation and drying, dissolution and leaching, corrosion and electrochemistry, membrane transport, and reaction engineering. They support scale-up by separating flow effects from property effects. Combined with a driving-force model such as N = kL(Cs − C∞), Sh enables defensible transfer-rate predictions. It is also useful for quick benchmarking across operating points during optimization.
Sh ranges from near 1–10 for weak convection to hundreds or more for strong forced convection. The actual value depends on geometry, Reynolds number, Schmidt number, and boundary conditions.
Use the molecular diffusivity of the transferring species in the same phase where mass transfer occurs. For gas-phase transfer, D is much larger than in liquids, so using the wrong phase can misestimate kL by orders of magnitude.
Yes. First estimate Sh from a correlation using Re and Sc, then compute kL = Sh·D/Lc. Ensure Lc matches the correlation definition and D matches the fluid properties used in Sc.
The turbulent flat-plate average form includes an offset term and is not valid at low Reynolds numbers. If it yields non-physical results, use the laminar plate option or a correlation valid for your Re range.
The constant term represents diffusion around a stagnant sphere, giving a baseline contribution even when Re approaches zero. The added Re and Sc term accounts for enhancement due to convection and boundary-layer thinning.
Use Reynolds number as a guide and consider geometry-specific transition behavior. For flat plates, transition is often discussed near Re ≈ 5×105, but surface roughness and free-stream turbulence can shift it.
No. If you have kL, Lc, and D, you can compute Sh directly from the definition. Schmidt number is mainly required for correlation-based estimation when kL is unknown.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.