This article presents gas kinetic calculation methods for the energy t
ransport in hydrogen/ air and methane/air mixtures. The total molecula
r heat conductivity as well as its various shares are calculated and d
iscussed for a temperature range of 400 to 3500 K and for a pressure o
f 10(5) Pa. The variation of the air/fuel ratio under the conditions o
f chemical equilibrium is also investigated. As opposed to our previou
s article, an extension of the Chapman-Enskog method which goes beyond
the classical Ist approximation for elastic collisions is applied for
the evaluation of suitable calculation methods. This is carried out f
ollowing the method for strong relaxing thermal nonequilibrium accordi
ng to Brun. The equations applied in this work are simplified formulat
ions for the proximity to equilibrium. The method for the evaluation o
f the parameters of the inelastic collision and some chosen results ar
e presented. A discussion of the various shares of the molecular heat
conductivity emphasizes the considerable influence of the diffusion an
d the thermal diffusion processes in fuel/air mixtures compared to the
Fourier heat conductivity.