Which dimensionless number is defined as the ratio of convective mass transfer to diffusive mass transfer?

Which dimensionless number is defined as the ratio of convective mass transfer to diffusive mass transfer?

• A. Reynolds number
• B. Nusselt number
• C. Sherwood number
• D. Prandtl number

Answer: (C)

This is about a dimensionless group that measures how effective convection is at moving mass compared with diffusion. The number that does this is the Sherwood number. It is defined as Sh = k_m L / D_AB, where k_m is the mass-transfer coefficient, L a characteristic length, and D_AB the diffusion coefficient of species A in B. A larger Sh indicates convection is dominating the transport, while an Sh near 1 means diffusion is the primary mechanism. This is the mass-transfer analogue of the Nusselt number for heat transfer, which compares convective to conductive heat transfer. The other numbers describe different physical balances: Reynolds compares inertial to viscous forces, and Prandtl compares momentum diffusivity to thermal diffusivity.

This is about a dimensionless group that measures how effective convection is at moving mass compared with diffusion. The number that does this is the Sherwood number. It is defined as Sh = k_m L / D_AB, where k_m is the mass-transfer coefficient, L a characteristic length, and D_AB the diffusion coefficient of species A in B. A larger Sh indicates convection is dominating the transport, while an Sh near 1 means diffusion is the primary mechanism. This is the mass-transfer analogue of the Nusselt number for heat transfer, which compares convective to conductive heat transfer. The other numbers describe different physical balances: Reynolds compares inertial to viscous forces, and Prandtl compares momentum diffusivity to thermal diffusivity.