Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (viscosity) and mass diffusivity, and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after the German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975).
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The Schmidt number is the ratio of the shear component for diffusivity viscosity/density to the diffusivity for mass transfer D. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer.
It is defined as:
where:
The heat transfer analog of the Schmidt number is the Prandtl number (Pr).
Turbulent Schmidt Number
The turbulent Schmidt number is commonly used in turbulence research and is defined as:
where:
The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar). It is related to the turbulent Prandtl number which is concerned with turbulent heat transfer rather than turbulent mass transfer.
Stirling engines
For Stirling engines, the Schmidt number is related to the specific power. Gustav Schmidt of the German Polytechnic Institute of Prague published an analysis in 1871 for the now-famous closed-form solution for an idealized isothermal Stirling engine model.
where,