Sherwood Number Calculator

Understanding Sherwood Number Calculator

The Sherwood number is the mass transfer analog of the Nusselt number. It represents the ratio of total mass transfer to diffusive mass transfer.

How to use this calculator

1. Enter the mass transfer coefficient \(k_c\).
2. Enter the characteristic length \(L\) for the surface or object.
3. Enter the diffusivity \(D\) of the species in the fluid.
4. Click calculate to get \(Sh\), then review the result and the steps.

The formula explained

The calculator uses \(Sh = \frac{k_c L}{D}\), which computes a dimensionless ratio of convective mass transfer to diffusive transport. A larger \(Sh\) means convection is more important compared with diffusion.

• Sh = Sherwood number, a dimensionless mass transfer number
• \(k_c\) = Mass transfer coefficient, usually in units like \(\mathrm{m/s}\)
• L = Characteristic length, such as diameter or plate length, in \(\mathrm{m}\)
• D = Diffusivity of the species in the fluid, in \(\mathrm{m^2/s}\)

Step by step method

1. Write the formula \(Sh = \frac{k_c L}{D}\).
2. Multiply \(k_c\) by \(L\).
3. Divide that product by \(D\).

Worked example

Problem. A sphere has a mass transfer coefficient of \(k_c = 0.020\,\mathrm{m/s}\), a characteristic length of \(L = 0.10\,\mathrm{m}\), and a diffusivity of \(D = 1.5 \times 10^{-5}\,\mathrm{m^2/s}\). Find the Sherwood number.

1. Substitute the values into \(Sh = \frac{k_c L}{D}\): \(Sh = \frac{(0.020)(0.10)}{1.5 \times 10^{-5}}\).
2. Compute the numerator: \((0.020)(0.10) = 0.002\).
3. Divide: \(Sh = \frac{0.002}{1.5 \times 10^{-5}} = 133.3\).

Tips and common mistakes

• Make sure all units are consistent, especially \(L\), \(k_c\), and \(D\), so the result is truly dimensionless.
• Do not confuse the Sherwood number with the Sherwood correlation, because this calculator only evaluates \(Sh\) from \(\frac{k_c L}{D}\).

Frequently asked questions