Mass-flux fraction

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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 and later by
Theodore von Kármán Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronau ...
and Sol Penner in 1954. The mass-flux fraction of a species i is defined as :$\epsilon_i = \frac = Y_i\left\left(1+\frac\right\right)$ where *$Y_i=\rho_i/\rho$ is the mass fraction *$v$ is the mass average velocity of the gaseous mixture *$V_i$ is the average velocity with which the species i diffuse relative to $v$ *$\rho_i$ is the density of species i *$\rho$ is the gas density. It satisfies the identity :$\sum_i \epsilon_i =1$ similar to mass fraction, but, the mass-flux fraction can take both positive and negative values. This variable is used in steady, one-dimensional
combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustio ...
problems in place of mass fraction.Penner, S. S. (1957). Chemistry problems in jet propulsion (Vol. 1). Pergamon Press. For one-dimensional ($x$ direction) steady flows, the conservation equation for the mass-flux fraction reduces to :$\frac = \frac$ where $w_i$ is the mass production rate of species i.

# References

{{reflist, 30em Chemical properties Dimensionless numbers of chemistry Combustion