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 and later by Theodore von Kármán and Sol Penner in 1954. The mass-flux fraction of a species i is defined as where It satisfies the identity where is the mass production rate of species i.