World Library  
Flag as Inappropriate
Email this Article

Schmidt number

 

Schmidt number

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).

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:

\mathrm{Sc} = \frac{\nu}{D} = \frac {\mu} {\rho D} = \frac{ \mbox{viscous diffusion rate} }{ \mbox{molecular (mass) diffusion rate} }

where:

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

Turbulent Schmidt Number

The turbulent Schmidt number is commonly used in turbulence research and is defined as:[2]

\mathrm{Sc}_\mathrm{t} = \frac{\nu_\mathrm{t}}{K}

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.[3][4]

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

where,

  • \mathrm{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

  1. ^ Incropera, Frank P.; DeWitt, David P. (1990), Fundamentals of Heat and Mass Transfer (3rd ed.),   Eq. 6.71.
  2. ^ Brethouwer, G. (2005). "The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulation". J. Fluid Mech. 542: 305–342.  
  3. ^ Schmidt Analysis (updated 12/05/07)
  4. ^ http://mac6.ma.psu.edu/stirling/simulations/isothermal/schmidt.html
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.