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Frontiers in Energy

Front. Energy    2020, Vol. 14 Issue (1) : 127-138
Effects of slip length and hydraulic diameter on hydraulic entrance length of microchannels with superhydrophobic surfaces
Wenchi GONG, Jun SHEN(), Wei DAI(), Zeng DENG, Xueqiang DONG, Maoqiong GONG
Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China
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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.

Keywords laminar flow      hydraulic entrance length      super hydrophobic surface      slip length      hydraulic diameter     
Corresponding Authors: Jun SHEN,Wei DAI   
Online First Date: 20 January 2020    Issue Date: 16 March 2020
 Cite this article:   
Wenchi GONG,Jun SHEN,Wei DAI, et al. Effects of slip length and hydraulic diameter on hydraulic entrance length of microchannels with superhydrophobic surfaces[J]. Front. Energy, 2020, 14(1): 127-138.
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Wenchi GONG
Xueqiang DONG
Maoqiong GONG
Fig.1  Schematic diagram of no-slip flow and slip flow.
Fig.2  Schematic of the geometry investigated.
Symbol Variable Value range
L Channel length/cm 1
b/a Aspect ratio 1
b× a Channel height and width/mm 100 × 100, 200 × 200, 500 × 500
ls Slip length/mm 2,5,10,12,15,20
uin Inlet velocity/(m·s1) 0.001–8
Re Reynolds number 0.1–1000
Tab.1  Summary of numerical parameters
Fig.3  Centerline velocity of 100?μm × 100?μm channel at uin = 0.5 m/s in different grid systems.
Fig.4  Determination of the hydraulic entrance length.
Fig.5  Pressure drops of numerical results compared with empirical correlation.
Fig.6  Flow characteristics of slip flow.
Fig.7  L+hy versus Re at different slip lengths in 100 mm × 100 mm channel.
Fig.8  L+hy versus Re in different square channels at ls = 2 mm.
Fig.9  Comparison of L+hy between numerical simulation and empirical correlations.
Fig.10  Comparison of L+hy between the numerical simulation and the new correlation.
Authors Correlations MRD/% MARD/% ss/%
Ahmad and Hassan [33] Lhy+= 0.61+0.14Re+0.0752 Re −9.27 13.51 14.88
Galvis et al [30]. Lhy+=0.741+0.09Re+0.0889Re 14.08 14.93 11.60
Han [49] Lhy+=0.0752Re −32.67 37.19 41.90
Wiginton and Dalton [50] Lhy+=0.09Re −19.42 43.73 50.15
Atkinson et al. [31] Lhy+=0.625+0.044Re −22.07 22.06 10.36
Chen [32] Lhy+= 0.631+0.035Re+0.044 Re −27.47 27.47 11.65
New correlation 0.05 5.69 6.32
Tab.2  Predictive performance of different correlations for square microchannels with superhydrophobic surfaces
a Channel width/m
b Channel height/m
Dh 2ab/(a+ b), hydraulic diameter/m
H Distance of parallel plates/m
ls Slip length/m
L Length of channels or parallel plates/m
Lhy Hydraulic entrance length/m
L+hy Lhy/Dh, dimensionless hydraulic entrance length
MAD Mean relative deviation
MARD Mean absolute relative deviation
n Numbers of data points
p Pressure/Pa
Δp Pressure drop/Pa
Q Flow rate/(m3·s–1)
Re Reynolds number
ui Velocity along i direction (i = x, y, z)/(m·s–1)
uin Inlet velocity/(m·s–1)
uw Wall velocity/(m·s–1)
ufd The centerline velocity of fully developed flow/(m·s–1)
x, y, z Cartesian coordinates/m
cor Correlation
no-slip No-slip flow
sim Simulation
slip Slip flow
μ Dynamic viscosity/(Pa·s)
ρ Mass density/(kg·m–3)
σs Standard deviation
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