Kinetic theory of thermal transpiration and mechanocaloric effect. III. Flow of a polyatomic gas between parallel plates

The phenomenological coefficients for one-dimensional mass and energy flows between infinite parallel plates containing polyatomic gases at all degrees of rarefaction are reported. The polyatomic gas model equations developed by Hansen and Morse were used in the linearized Wang Chang and Uhlenbeck equation with Maxwell’s diffuse scattering boundary conditions. The solutions reproduce the molecular flow results at large Knudsen numbers and the continuum fluid properties for small Knudsen numbers. The phenomenological coefficients are functions of the Eucken factor, the internal constant volume heat capacity, and the translational Eucken factor. Calculations for the Gross–Jackson and the BGK model are reported and compared to the polyatomic gas results. We find the thermal transpiration effect depends on the translational Eucken factor and is independent of the inelastic collisions. The monatomic gas results can be used to estimate the thermal transpiration effect by ’’scaling’’ the Knudsen numbers used to compute the 𝒥MQ coefficient. This scaling is not uniform and errors become large for large Knudsen numbers. The cross coefficients 𝒥MQ=𝒥QM for all calculations but the energy flux near the wall was found to be negative for inverse Knudsen numbers greater than 3.