Conductive heat transfer in rarefied binary gas mixtures confined between parallel plates based on kinetic modeling

Abstract

The kinetic model introduced by Kosuge (2009) is implemented to solve heat transfer through rarefied binary gas mixtures confined between two parallel plates maintained at different temperatures. The results have been found to be in very good agreement with corresponding ones obtained by the Boltzmann equation, the DSMC method and the Chapman-Enskog analysis. The efficiency of the Kosuge model for this problem is clearly demonstrated in the whole range of the Knudsen number for various heat flow setups, even when the temperature difference between the plates is large. The following three intermolecular models have been implemented: Hard Sphere (HS), Lennard Jones (LJ), Realistic Potential (RP). The computed HS heat fluxes in the transition and viscous regimes vary significantly with the corresponding ones of the LJ and RP models, which are close to each other. Also, the intermolecular model has a significant effect on the distribution of the mole fraction between the plates, while it has a minor effect on the density and temperature distributions. Concerning the partial heat flux distributions of the light and heavy species it has been found that moving from the hot towards the cold plate the former one is decreasing, while the latter one is increasing with the total heat flux being always constant. Heat fluxes with partial thermal accommodation at the walls are reported for He-Ne and He-Xe. For the same mixtures dimensional heat fluxes in terms of the reference pressure are plotted indicating that the total heat fluxes of the mixture with various mole fractions are always bounded from below and above by the heat flux of the heavy and light species respectively. These data may be useful for comparisons with experiments. Applying the equivalent single gas approach, it is deduced that this concept is not useful in rarefied binary gas mixture heat flow problems, which should be treated by two coupled kinetic equations. Finally, the effective thermal conductivity approximation has been successfully applied, provided that the system Knudsen number remains adequately small. © 2017 Elsevier Ltd