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.

中文翻译：

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稀薄大气中非常细的水平线的自由对流热传递相关性

近年来，火星和地球上层大气任务蓬勃发展，增加了对稀薄气体传热的兴趣。在这些低压下，涉及特征长度为气体分子平均自由程数量级的小几何形状的传​​热问题提出了新的困难。这在自由对流的情况下尤其严重，其中气体的速度与传热问题密切相关。直径为 $12.7\\mu\mathrm{m}$ 和 $25\\mu\mathrm{m}$ 的水平线实验在定制的真空室中进行，压力从 $0.03$ 毫巴到环境压力，达到高达到电线和空气之间的 $80$K。实验数据由从 $10^{-13}$ 到 $10^{-5}$ 的瑞利数组成，涵盖从自由分子流到连续体的广泛范围。特别是对于过渡区，克努森数介于 0.1 和 10 之间，实验数据表明，自由对流传热不能仅表示为瑞利数的函数，但必须将与克努森数的相关性引入相关性中，如出色地。所呈现的 Nusselt 数低于 10^{-8}$ 瑞利数的结果与文献中可用的相关性明显不同。提出了从过渡到连续体状态的水平细线自由对流的新经验相关性。