A free convection heat transfer correlation for very thin horizontal wires in rarefied atmospheres

Mars and upper Earth atmosphere missions are booming in recent years increasing the interest in heat transfer in rarefied gases. At these low pressures, the heat transfer problems involving small geometries whose characteristic length is of the order of the mean free path of the gas molecules, raises new difficulties. This being especially severe in the case of free convection, where the velocity of the gas is closely linked to the heat transfer problem. Experiments with horizontal wires with diameters of $12.7\ \mu\mathrm{m}$ and $25\ \mu\mathrm{m}$ were conducted in a tailored vacuum chamber with pressures from $0.03$ milibar to ambient pressure, reaching temperature differences of up to $80$ K between the wire and the air. Experimental data is comprised of Rayleigh numbers from $10^{-13}$ to $10^{-5}$ that cover a wide range from free molecular flow to continuum regime. Particularly for the transition regime, with Knudsen numbers ranging between 0.1 and 10, the experimental data shows that the free convection heat transfer cannot be represented solely as a function of the Rayleigh number, but a dependence on Knudsen number must be introduced into the correlation as well. The presented results for the Nusselt number below Rayleigh numbers of $10^{-8}$ exhibit a clear departure from the available correlations in the literature. A new empirical correlation for free convection from horizontal thin wires from the transition to continuum regime is presented. The present work sheds light on current thermal engineering problems which involves very thin wires in their systems which interact with a surrounding environment with a significant level of rarefaction.