Conductive heat transfer in a gas confined between two concentric spheres: from free-molecular to continuum flow regime

The conductive heat transfer through a gas confined between two concentric spherical shells maintained at different temperatures is investigated from the free-molecular to the continuum flow regime. The heat flux, measured using a recently proposed experimental system to extract the thermal accommodation coefficient, is compared with analytical expressions and numerical results. From this comparison it is found that in the free-molecular flow limit, the experimental data are well explained by the analytical expression for the arbitrary radius and temperature ratios of the spherical surfaces. In the continuum limit, the temperature dependence of the thermal conductivity coefficient should be considered in the analytical expression. In the transitional flow regime, a revised function for the heat flux interpolation is proposed to give better fitting to the numerical results. By employing these knowledge, the thermal accommodation coefficient extraction procedure for the system is revised, and it is shown that the re-calculated accommodation coefficient allows to reproduce well the measured heat flux.