Schmidt number

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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 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 ^[1] as:

$\mathit{Sc} = \frac{\nu}{D} = \frac {\mu} {\rho D}$

where:

$ν$ is the kinematic viscosity
$D$ is the mass diffusivity.
$μ$ is the Viscosity
$ρ$ is the Density

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

[edit] 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.^[2] ^[3]

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