Schmidt number

For the measure of the quantum entanglement of a density matrix, see Schmidt decomposition.

Schmidt number 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).

Schmidt number is the ratio of the rana 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: \[\mathit{Sc} = \frac{\nu}{D} = \frac {\mu} {\rho D} = \frac{ \mbox{viscous diffusion rate} }{ \mbox{molecular (mass) diffusion rate} }\]

where:

• \(\nu\) is the kinematic viscosity or (\({\mu}\)/\({\rho}\,\)) in units of (m²/s)
• \(D\) is the mass diffusivity (m²/s).
• \({\mu}\) is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s)
• \(\rho\,\) is the density of the fluid (kg/m³).

The heat transfer analog of the Schmidt number is the Prandtl number.

Stirling engines

For Stirling engines, the Schmidt number represents dimensionless 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.

\[ Sc = \frac{\sum {\left | {Q} \right |}}{\bar p V_{sw}}\]

where,

• \(Sc\) is the Schmidt number
• \(Q\) is the heat transferred into the working fluid
• \(\bar p\) is the mean pressure of the working fluid
• \(V_{sw}\) is the volume swept by the piston.

Notes

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