Schmidt number


In fluid dynamics, the Schmidt number of a fluid is a dimensionless number defined as the ratio of momentum diffusivity and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt.
The Schmidt number is the ratio of the shear component for diffusivity to the diffusivity for mass transfer. 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. The ratio of thermal diffusivity to mass diffusivity is the Lewis number.

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. It is related to the turbulent Prandtl number, which is concerned with turbulent heat transfer rather than turbulent mass transfer. It is useful for solving the mass transfer problem of turbulent boundary layer flows. The simplest model for Sct is the Reynolds analogy, which yields a turbulent Schmidt number of 1. From experimental data and CFD simulations, Sct ranges from 0.2 to 6. Studies have shown that the turbulent Schmidt number varies locally within a flow, depending on both turbulence characteristics and flow parameters. Formulations have been derived to estimate it locally based on these quantities, providing a means to relate concentration and turbulence fields more directly.

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: