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

Abstract

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 μm and 25 μm were conducted in a tailored vacuum chamber with pressures from 0.03 millibar 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 scattering of 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 another parameter, in this case the Knudsen number, must be taken into account for the correlation as well. The presented results for the Nusselt number for Rayleigh numbers below 10−8 exhibit a clear departure from the available correlations in the literature. An 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 that involves very thin wires in their systems which interact with a surrounding environment with a significant level of rarefaction. Systems such as temperature sensors based on thermocouple wires for Mars atmosphere, whose measurements are affected by a low free convection heat transfer, could benefit from this study gaining a better performance in modelling with a more accurate estimation of free convection heat transfer. Results in this range of parameters have not been found in published literature.