Time-dependent conductive heat transfer in rarefied polyatomic gases confined between parallel plates

Abstract

The transient conductive heat transfer through a rarefied gas confined between two infinite parallel plates due to a sudden jump in the temperature of one of the plates is investigated in the whole range of the Knudsen number via kinetic theory. More specifically, the time-dependent heat transfer flow is modelled by the Holway kinetic model subject to diffuse boundary conditions. The governing integro-differential equation is numerically solved using the discrete velocity method in the molecular velocity space and typical finite control volume schemes in time and physical spaces. The time evolution of the density and temperature distributions as well as of the translational and rotational heat fluxes in terms of the two parameters characterizing the heat flow, namely the Knudsen number and the imposed temperature ratio between the plates is provided. The investigation is focused on the effect of the rotational degrees of freedom and a comparison between monatomic and polyatomic gases is performed. It is found that the time needed to reach the steady-state conditions varies between monatomic and polyatomic gases. In all cases the total time to recover the stationary solution in terms of the rarefaction parameter exhibits a minimum close to the well-known Knudsen minimum.