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Mass-flux fraction

Ratio of mass-flux of chemical species to total mass flux From Wikipedia, the free encyclopedia

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The mass-flux fraction (or Hirschfelder-Curtiss variable or Kármán-Penner variable) is the ratio of mass-flux of a particular chemical species to the total mass flux of a gaseous mixture. It includes both the convectional mass flux and the diffusional mass flux. It was introduced by Joseph O. Hirschfelder and Charles F. Curtiss in 1948[1] and later by Theodore von Kármán and Sol Penner in 1954.[2][3] The mass-flux fraction of a species i is defined as[4]

where

  • is the mass fraction
  • is the mass average velocity of the gaseous mixture
  • is the average velocity with which the species i diffuse relative to
  • is the density of species i
  • is the gas density.

It satisfies the identity

,

similar to the mass fraction, but the mass-flux fraction can take both positive and negative values. This variable is used in steady, one-dimensional combustion problems in place of the mass fraction.[5] For one-dimensional ( direction) steady flows, the conservation equation for the mass-flux fraction reduces to

,

where is the mass production rate of species i.

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