Sherwood Number
A dimensionless number in mass transfer that represents the ratio of convective mass transfer to diffusive mass transfer.
Sherwood Number
The Sherwood number (Sh) is a fundamental dimensionless quantity in mass transfer and transport phenomena that characterizes the ratio of convective to diffusive mass transport. Named after Thomas Kilgore Sherwood, it serves as the mass transfer analog to the Nusselt number used in heat transfer.
Mathematical Definition
The Sherwood number is defined as:
Sh = (k × L) / D
Where:
- k is the mass transfer coefficient
- L is the characteristic length
- D is the mass diffusivity
Physical Significance
The Sherwood number provides crucial insights into:
- The dominance of convective vs. diffusive mass transfer mechanisms
- The efficiency of mass transfer processes
- The behavior of boundary layers in mass transfer
Applications
Industrial Processes
Environmental Systems
- Atmospheric pollutant dispersion
- Water treatment processes
- environmental mass transfer
Correlations
The Sherwood number is often expressed in terms of other dimensionless numbers:
Sh = f(Re, Sc)
Where:
- Reynolds number (Re) represents flow characteristics
- Schmidt number (Sc) represents fluid properties
Common correlations include:
- Forced convection over a flat plate
- Flow through packed beds
- Mass transfer in pipes and tubes
Importance in Design
Engineers use the Sherwood number to:
- Scale up chemical processes
- Design mass transfer equipment
- Optimize separation operations
- Predict mass transfer rates in various systems
Related Dimensionless Numbers
The Sherwood number works in conjunction with:
- Nusselt number (heat transfer analog)
- Stanton number (mass transfer efficiency)
- Peclet number (convection/diffusion ratio)
Understanding the relationships between these dimensionless numbers enables engineers to analyze and design efficient mass transfer systems across various scales and applications.