It is shown that formulas developed previously for the thermal diffusion factor imply a close relation between it and the translational and internal heat conductivities, hi trans and k~ ~,t, of each species in a multicomponent mixture. This suggests a phenomenological relationship that is more difficult to calculate than the translational heat conductivity of a multicomponent mixture. The calculation in fact uses the same set of inputs and collision integrals that enter the calculation of k~tms and seems to be as accurate as the first Chapman-Cowling approximation of s 0. Further approximations lead to a "back-of-the-envelope" approximation for the high-temperature limit. Coupled with the binary trace approximation, this allows extremely fast estimates of thermal diffusion fluxes.
Several sample calculations demonstrate the accuracy of these formulas for systems containing rare gas atoms, molecules with internal degrees of freedom, and polar molecules. When an old set of flame structure data is reanalyzed with the inclusion of thermal diffusive fluxes calculated with these formulas, several anomalies previously attributed to experimental error disappear. A comparison with a standard flame structure calculation shows that here even the "back-of-the-envelope" approximation is semiquantitative.