Heat transfer through rarefied gas confined between two concentric spheres

Abstract

The problem of heat transfer through a rarefied gas confined between two concentric spheres is studied on the basis of the nonlinear S-model kinetic equation. In the slip and free molecular flow regimes the analytical expressions are provided for the arbitrary temperature and radius ratios. In the transitional flow regime the S-model kinetic equation is solved numerically. The limits of the applicability of the analytical expressions are established by confronting the numerical and analytical solutions. The behavior of the macroscopic flow parameters (heat flux, temperature, pressure and number density) is examined in details for various temperature ratios between the sphere surfaces, for different sphere radius ratios and for several values of the accommodation coefficient on the internal sphere surface. The non monotonic behavior of the heat flux is observed in the case of the strong temperature ratio between the spheres. The essential pressure variations between the two spheres are found for the small and moderate values of the rarefaction parameter. The simple approximate expression for the heat flux, proposed previously, is tested with proposed here analytical expressions and the good agreement with the numerical results is found in very large range of the rarefaction parameter and different temperature ratios.