This paper investigated effects of slip length and hydraulic diameter on the hydraulic entrance length of laminar flow in superhydrophobic microchannels. Numerical investigations were performed for square microchannels with Re ranging between 0.1 and 1000. It is found that superhydrophobic microchannels have a longer hydraulic entrance length than that of conventional ones by nearly 26.62% at a low Re. The dimensionless hydraulic entrance length slightly increases with the increasing slip length at approximately Re<10, and does not vary with the hydraulic diameter. A new correlation to predict the entrance length in square microchannels with different slip lengths was developed, which has a satisfying predictive performance with a mean absolute relative deviation of 5.69%. The results not only ascertain the flow characteristics of superhydrophobic microchannels, but also suggest that super hydrophobic microchannels have more significant advantages for heat transfer enhancement at a low Re.

中文翻译：

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滑移长度和水力直径对超疏水微通道水力入口长度的影响

本文研究了滑移长度和水力直径对超疏水微通道层流水力入口长度的影响。对Re介于0.1和1000之间的方形微通道进行了数值研究。发现，在Re低的情况下，超疏水微通道的水力入口长度比常规的长，接近26.62％。无量纲的液压入口长度随着滑移长度的增加而略有增加，大约为Re<10，并且不会随液压直径而变化。建立了一种新的相关性，以预测具有不同滑动长度的方形微通道中的入口长度，该相关性具有令人满意的预测性能，平均绝对相对偏差为5.69％。结果不仅确定了超疏水微通道的流动特性，而且还暗示了超疏水微通道在低Re的传热方面具有更显着的优势。