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 was introduced by Joseph O. Hirschfelder and Charles F. Curtiss in 1948[1] and later by Theodore von Kármán and Sol Penner in 1954.
This variable is used in steady, one-dimensional combustion problems in place of the mass fraction.
direction) steady flows, the conservation equation for the mass-flux fraction reduces to where
is the mass production rate of species i.