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How It Works
The Sherwood number is the mass-transfer analogue of the Nusselt number. It compares the total (convective) mass transfer at a surface to what pure molecular diffusion alone would provide. A Sh of 1 means there is no convective enhancement; in turbulent flows Sh can reach hundreds or thousands, indicating that convective mixing dominates.
Chemical engineers use Sherwood correlations -- functions of Reynolds and Schmidt numbers -- to predict mass-transfer coefficients for reactor design, gas absorption columns, and separation membranes without running full experiments.
Example Problem
A 0.05 m sphere dissolves in water. The mass-transfer coefficient is measured at k = 3.6 × 10⁻⁵ m/s and the diffusion coefficient of the solute in water is 1.2 × 10⁻⁹ m²/s. What is the Sherwood number?
- Sh = kL / D = 3.6 × 10⁻⁵ × 0.05 / 1.2 × 10⁻⁹
- Sh = 1.8 × 10⁻⁶ / 1.2 × 10⁻⁹ = 1,500
Sh = 1,500 means convective mass transfer is 1,500 times more effective than diffusion alone, typical for a sphere in a moderate liquid flow.
Frequently Asked Questions
What is the Sherwood number used for in chemical engineering?
It predicts the mass-transfer coefficient from known flow conditions and fluid properties. Engineers use Sh correlations (e.g., Sh = 2 + 0.6 Re½ Sc³') to design gas-liquid contactors, packed columns, and catalytic reactors without requiring expensive pilot-plant tests.
How is the Sherwood number related to the Nusselt number?
Both have the same mathematical form: Nu = hL/k for heat transfer and Sh = kₘL/D for mass transfer. The Chilton-Colburn analogy relates them directly, allowing heat-transfer data to estimate mass-transfer rates and vice versa.
What is the minimum Sherwood number for a sphere?
For a sphere in a stagnant fluid, the exact solution gives Sh = 2. This represents pure diffusion from the sphere surface into an infinite medium. Any fluid motion increases Sh above this minimum value.
Related Calculators
- Nusselt Number Calculator — the heat-transfer analogue of the Sherwood number.
- Schmidt Number Calculator — momentum vs. mass diffusivity, a key input to Sh correlations.
- Lewis Number Calculator — thermal vs. mass diffusivity ratio for coupled transport.
- Reynolds Number Calculator — flow regime classification needed for Sh correlations.
- Viscosity Converter — convert viscosity units used in dimensionless number calculations.