Heat transfer in binary polyatomic gas mixtures over the whole range of the gas rarefaction based on kinetic deterministic modeling

Abstract

In the present work, the problem of heat conduction through binary mixtures of non-vibrating polyatomic gases is studied over the whole range of the gas rarefaction in a deterministic manner. This is achieved by applying a recently proposed kinetic model, which takes into account the internal degrees of freedom of the gas molecules. The cross and self-collision frequencies are determined based on the thermal conductivity formulas proposed in the literature for the polyatomic gas mixtures. Numerical investigation is carried out for several binary mixtures consisting of linear and nonlinear gases in a wide range of all involved parameters. The validity of the present kinetic modeling is demonstrated by performing comparisons with the corresponding numerical and experimental data. Analytical solutions for the heat flux in the free molecular and hydrodynamic regimes are formulated showing excellent agreement with the numerical estimations. The effect of the internal degrees of freedom on the heat flux, as a function of the mole fraction, is also studied. The numerical results show that the relative deviation between monatomic and polyatomic heat fluxes varies linearly with the mole fraction when the difference between the molecular masses of the species is small. However, in the case of a mixture being composed of gases with quite different molecular masses, a nonlinear behavior is observed. It is clearly shown that the heat flux problem through polyatomic gas mixture cannot be captured by monatomic modeling. Furthermore, an approximate formula for the heat flux over the whole range of the Knudsen number is examined.