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A Type-I model of a multicomponent system of fluids with non-constanttemperature is derived as the high-friction limit of a Type-II model via aChapman-Enskog expansion. The asymptotic model is shown to fit into the generaltheory of hyperbolic-parabolic systems, by exploiting the entropy structureinherited through the asymptotic procedure. Finally, by deriving the relativeentropy identity for the Type-I model, two convergence results for smoothsolutions are presented, from the system with mass-diffusion and heatconduction to the corresponding system without mass-diffusion but includingheat conduction and to its hyperbolic counterpart.

Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion