An extended Enskog asymptotic expansion method is used to find approximate
solutions of the Boltzmann equation in the cases of strong thermal nonequil
ibrium. The formalism to determine thermal conductivities in the expanding
Row of a binary mixture of a diatomic and its parent atoms through a supers
onic nozzle is applied. Results show that the diffusion of highly excited v
ibrational levels, which become overpopulated during the expansion, substan
tially contributes to the transport of energy. This effect cannot be repres
ented by simplified theories such as the multitemperature model.