Estimate k values from Reynolds and Schmidt numbers. Pick a correlation for your geometry today. Get Sherwood results, flux estimates, and downloadable reports instantly.
The calculator uses dimensionless groups to estimate the mass transfer coefficient. First compute Reynolds number and Schmidt number:
Then select a Sherwood correlation for your geometry:
Finally compute the mass transfer coefficient: k = (Sh · D) / L. If concentrations are provided, the flux is N = k (Cs − Cb).
| Case | Geometry | L (m) | v (m/s) | ρ (kg/m³) | μ (Pa·s) | D (m²/s) | Correlation | Re | Sc | Sh | k (m/s) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Flat plate | 0.05 | 1.50 | 1000 | 0.001 | 1.0×10⁻⁹ | Plate (laminar) | 75000 | 1000 | 12154 | 2.43×10⁻⁴ |
| 2 | Pipe | 0.02 | 2.00 | 997 | 0.001 | 2.0×10⁻⁹ | Pipe (turbulent) | 39880 | 501 | 680 | 6.80×10⁻⁵ |
| 3 | Sphere | 0.01 | 0.80 | 1.20 | 1.8×10⁻⁵ | 2.0×10⁻⁵ | Sphere / external | 533 | 0.75 | 15.4 | 3.08×10⁻² |
Examples are illustrative and depend on assumed properties.
The mass transfer coefficient, k, links fluid motion to species transport across a boundary layer. It is used in absorption, evaporation, dissolution, membrane operations, corrosion, and catalytic processes. A realistic k improves scale-up, helps size equipment, and supports mass balance closure.
This calculator combines geometry, flow speed, and properties to estimate k in m/s. The characteristic length L is plate length, pipe diameter, or particle diameter. You enter velocity v, density ρ, viscosity μ, and diffusivity D, then the tool converts inputs to consistent SI units.
The approach is based on Re, Sc, and Sh. Reynolds number reflects inertial-to-viscous forces, while Schmidt number compares momentum to mass diffusivity. Sherwood number represents convection relative to diffusion, and it connects directly to k through k = Sh·D/L.
Useful reference values help validate inputs. Gas-phase diffusivities commonly fall near 10⁻⁵ m²/s, while liquid-phase molecular diffusivities often range from 10⁻⁹ to 10⁻¹⁰ m²/s. At room temperature, air has μ ≈ 1.8×10⁻⁵ Pa·s and ρ ≈ 1.2 kg/m³, while water has μ ≈ 1.0×10⁻³ Pa·s and ρ ≈ 1000 kg/m³. These magnitudes strongly influence Re and Sc.
For external flow over a plate, L is the streamwise length over which the boundary layer grows. For internal pipe flow, L is the hydraulic diameter, typically the inside diameter for a round tube. For particles, L is the particle diameter. A smaller L usually increases k because diffusion distances are shorter.
The calculator offers widely used Sherwood correlations. For plates, laminar behavior is often assumed below Re ≈ 5×10⁵, while internal pipe flow transitions around Re ≈ 2300. The sphere correlation includes a baseline of Sh = 2 to represent diffusion in the limit of very low flow. If your system has roughness, strong buoyancy, or reactions, consider using experimental data to refine k.
Once k is computed, the optional flux estimate uses N = k(Cs − Cb). This is a driving-force form suitable for thin film models, where Cs is the interfacial concentration and Cb is the bulk concentration. If Cs − Cb is negative, the predicted flux reverses direction, which can be physically correct for desorption.
Review the reported Re and Sc. Very small Re suggests creeping flow where external correlations may overpredict. Extremely large or tiny Sc can indicate wrong viscosity, density, or diffusivity units. When results look off, confirm L matches the chosen geometry and ensure D is for the correct species and temperature.
1) What is a mass transfer coefficient?
It is a proportionality factor that relates mass flux to a concentration driving force across a boundary layer. It summarizes how flow conditions and diffusion combine to move species between a surface and the bulk fluid.
2) Which characteristic length should I use?
Use plate length along the flow for external plates, inside diameter for round pipes, and particle diameter for spheres. The same length is used in Reynolds number and in k = Sh·D/L, so consistency is critical.
3) Why do I see different correlations for the same geometry?
Boundary layers behave differently in laminar and turbulent flow. Turbulence enhances mixing and typically increases Sherwood number, producing larger k values. Correlations also vary by assumptions, such as fully developed conditions.
4) What does the Schmidt number tell me?
Schmidt number compares momentum diffusivity to mass diffusivity. Large Sc often occurs in liquids with small D, meaning concentration boundary layers can be thinner than velocity boundary layers, affecting Sherwood correlations.
5) Can I compute mass flux with this tool?
Yes. Provide surface concentration Cs and bulk concentration Cb, and the calculator estimates flux using N = k(Cs − Cb). Ensure Cs and Cb are in the same units and represent the same species and phase.
6) My result seems too large or too small. What should I check first?
Verify unit selections and typical magnitudes: liquids often have D near 10⁻⁹ m²/s and gases near 10⁻⁵ m²/s. Also confirm L matches the geometry and that the selected regime is appropriate for your Reynolds number.
7) Does this replace experimental validation?
No. Correlations are estimates based on idealized conditions. Use them for scoping, comparisons, and preliminary design, then validate with experiments or trusted references when accuracy and safety margins are important.
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.