The parameters of micro-nano structured superhydrophobic surfaces is significant to the dropwise condensation heat transfer of steam with non-condensable gas but the theoretical model has not been structured completely. A theoretical model is structured based on the thermal resistance analysis in this study and applied to analyze the effect of the parameters of the micro-nano structures. The results clearly illustrate that an optimum relative micro-pillar spacing exists and strongly depends of the volumetric fraction of non-condensable gas. The optimum relative micro-pillar spacing increases with the increase of the volumetric fraction of non-condensable gas when the volumetric fraction is lower than 20% but an opposite trend is found when the volumetric fraction is higher than 20%. Moreover, the relative nano-pillar spacing can also significantly affect the optimum relative micro-pillar spacing. Smaller relative nano-pillar spacing induces higher optimum relative micro-pillar spacing. Surface subcooling causes more complicated influence to the relative optimum micro-pillar spacing. Subsequently, the results supply the primary information for optimizing the micro-nano structured surfaces that can induce the condensation heat transfer enhancement of steam with random volumetric fraction of non-condensable gas.

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