Convective Mass Transfer: Sherwood, Schmidt, and Chilton-Colburn Analogy

Convective mass transfer is analyzed using dimensionless groups analogous to those in convective heat transfer:

Dimensionless Numbers

• Schmidt Number (\(Sc\)): Ratio of momentum diffusivity \(\nu\) to mass diffusivity \(D\). Analogous to Prandtl number:
  \[Sc = \frac{\nu}{D}\]
• Sherwood Number (\(Sh\)): Ratio of convective mass transfer to molecular diffusion. Analogous to Nusselt number:
  \[Sh = \frac{h_m L}{D}\]

Chilton-Colburn Analogy

The Chilton-Colburn J-factor analogy relates skin friction, heat transfer, and mass transfer for turbulent flows:

Where \(j_D = St_m Sc^{2/3}\) and \(j_H = St Pr^{2/3}\), with Stanton mass number \(St_m = h_m/u_m\).

References

• Chilton, T. H., & Colburn, A. P. (1934). Mass transfer (absorption) coefficients. Industrial & Engineering Chemistry, 26(11), 1183-1187.