Effects of slip length and hydraulic diameter on hydraulic entrance length of microchannels with superhydrophobic surfaces

Abstract

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

References

[1] Tuckerman D B, Pease R F W. High-performance heat sinking for VLSI. IEEE Electron Device Letters, 1981, 2(5): 126–129

[2] Yang X H, Liu J. Liquid metal enabled combinatorial heat transfer science: toward unconventional extreme cooling. Frontiers in Energy, 2018, 12(2): 259–275

[3] Drummond K P, Back D, Sinanis M D, Janes D B, Peroulis D, Weibel J A, Garimella S V. A hierarchical manifold microchannel heat sink array for high-heat-flux two-phase cooling of electronics. International Journal of Heat and Mass Transfer, 2018, 117: 319–330

[4] Liu D, Wang Q, Wei J. Experimental study on drag reduction performance of mixed polymer and surfactant solutions. Chemical Engineering Research & Design, 2018, 132: 460–469

[5] Ermagan H, Rafee R. Geometric optimization of an enhanced microchannel heat sink with superhydrophobic walls. Applied Thermal Engineering, 2018, 130: 384–394

[6] Cheng Y, Xu J, Sui Y. Numerical study on drag reduction and heat transfer enhancement in microchannels with superhydrophobic surfaces for electronic cooling. Applied Thermal Engineering, 2015, 88: 71–81

[7] Ermagan H, Rafee R. Geometric optimization of an enhanced microchannel heat sink with superhydrophobic walls. Applied Thermal Engineering, 2018, 130: 384–394

[8] Andrews H G, Eccles E A, Schofield W C E, Badyal J P S. Three-dimensional hierarchical structures for fog harvesting. Langmuir, 2011, 27(7): 3798–3802

[9] Milani D, Abbas A, Vassallo A, Chiesa M, Bakri D A. Evaluation of using thermoelectric coolers in a dehumidification system to generate freshwater from ambient air. Chemical Engineering Science, 2011, 66(12): 2491–2501

[10] Khawaji A D, Kutubkhanah I K, Wie J M. Advances in seawater desalination technologies. Desalination, 2008, 221(1–3): 47–69

[11] Beér J M. High efficiency electric power generation: the environmental role. Progress in Energy and Combustion Science, 2007, 33(2): 107–134

[12] Pérez-Lombard L, Ortiz J, Pout C. A review on buildings energy consumption information. Energy and Building, 2008, 40(3): 394–398

[13] Li B, Yao R. Urbanisation and its impact on building energy consumption and efficiency in China. Renewable Energy, 2009, 34(9): 1994–1998

[14] Barthlott W, Neinhuis C. Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta, 1997, 202(1): 1–8

[15] Bhushan B, Jung Y C. Micro- and nanoscale characterization of hydrophobic and hydrophilic leaf surfaces. Nanotechnology, 2006, 17(11): 2758–2772

[16] Gao X, Jiang L. Water-repellent legs of water striders. Nature, 2004, 432(7013): 36

[17] Cassie A B D, Baxter S. Wettability of porous surfaces. Transactions of the Faraday Society, 1944, 40: 546–551

[18] Navier C. Mémoire sur les lois du mouvement des fluides. Mémoires de l’Académie des Sciences de l’Institut de France, 1823, 1823(6): 389–416

[19] Neto C, Evans D R, Bonaccurso E, Butt H J, Craig V S J. Boundary slip in Newtonian liquids: a review of experimental studies. Reports on Progress in Physics, 2005, 68(12): 2859–2897

[20] Ou J, Perot B, Rothstein J P. Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Physics of Fluids, 2004, 16(12): 4635–4643

[21] Ou J, Rothstein J P. Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Physics of Fluids, 2005, 17(10): 103606

[22] Woolford B, Jeffs K, Maynes D, Webb B W. Laminar fully-developed flow in a microchannel with patterned ultrahydrophobic walls. In: ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems, 2005: 481–488

[23] Guan N, Liu Z, Jiang G, Zhang C, Ding N. Experimental and theoretical investigations on the flow resistance reduction and slip flow in super-hydrophobic micro tubes. Experimental Thermal and Fluid Science, 2015, 69: 45–57

[24] Choi C H, Ulmanella U, Kim J, Ho C M, Kim C J. Effective slip and friction reduction in nanograted superhydrophobic microchannels. Physics of Fluids, 2006, 18(8): 087105

[25] Cheng Y P, Teo C J, Khoo B C. Microchannel flows with superhydrophobic surfaces: effects of Reynolds number and pattern width to channel height ratio. Physics of Fluids, 2009, 21(12): 122004

[26] Choi C H, Westin K J A, Breuer K S. Apparent slip flows in hydrophilic and hydrophobic microchannels. Physics of Fluids, 2003, 15(10): 2897–2902

[27] Rosengarten G, Cooper-White J, Metcalfe G. Experimental and analytical study of the effect of contact angle on liquid convective heat transfer in microchannels. International Journal of Heat and Mass Transfer, 2006, 49(21–22): 4161–4170

[28] Ermagan H, Rafee R. Effect of pumping power on the thermal design of converging microchannels with superhydrophobic walls. International Journal of Thermal Sciences, 2018, 132: 104–116

[29] Yun H, Chen B, Chen B. Numerical simulation of geometrical effects on the liquid flow and heat transfer in smooth rectangular microchannels. In: ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer, 2009: 271–277

[30] Galvis E, Yarusevych S, Culham J R. Incompressible laminar developing flow in microchannels. Journal of Fluids Engineering, 2012, 134(1): 014503

[31] Atkinson B, Brocklebank M P, Card C C H, Smith J M. Low Reynolds number developing flows. AIChE Journal, 1969, 15(4): 548–553

[32] Chen R Y. Flow in the entrance region at low Reynolds numbers. Journal of Fluids Engineering, 1973, 95(1): 153–158

[33] Ahmad T, Hassan I. Experimental analysis of microchannel entrance length characteristics using microparticle image velocimetry. Journal of Fluids Engineering, 2010, 132(4): 041102

[34] Duan Z, Muzychka Y S. Slip flow in the hydrodynamic entrance region of circular and noncircular microchannels. Microfluidics and Nanofluidics, 2010, 132(1): 011201

[35] Renksizbulut M, Niazmand H. Laminar flow and heat transfer in the entrance region of trapezoidal channels with constant wall temperature. Journal of Heat Transfer, 2006, 128(1): 63–74

[36] Ma N, Duan Z, Ma H, Su L, Liang P, Ning X, He B, Zhang X. Lattice Boltzmann simulation of the hydrodynamic entrance region of rectangular microchannels in the slip regime. Micromachines, 2018, 9(2): 87

[37] Hsieh S S, Lin C Y. Convective heat transfer in liquid microchannels with hydrophobic and hydrophilic surfaces. International Journal of Heat and Mass Transfer, 2009, 52(1–2): 260–270

[38] Chakraborty S, Anand K D. Implications of hydrophobic interactions and consequent apparent slip phenomenon on the entrance region transport of liquids through microchannels. Physics of Fluids, 2008, 20(4): 043602

[39] Ranjith S K, Patnaik B S V, Vedantam S. Hydrodynamics of the developing region in hydrophobic microchannels: a dissipative particle dynamics study. Physical Review. E, 2013, 87(3): 033303

[40] Yu K H, Tan Y X, Aziz M S A, Abdullah M Z. The Developing plane channel fow over water-repellent surface containing transverse grooves and ribs. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2018, 45: 141–148

[41] Xu J, Li Y. Boundary conditions at the solid–liquid surface over the multiscale channel size from nanometer to micron. International Journal of Heat and Mass Transfer, 2007, 50(13–14): 2571–2581

[42] Williams A. Enhanced laminar convective heat transfer using microstructured superhydrophobic surfaces. Dissertation for the Doctoral Degree. Albuquerque: University of New Mexico, 2016

[43] Solomon B R, Khalil K S, Varanasi K K. Drag reduction using lubricant-impregnated surfaces in viscous laminar flow. Langmuir, 2014, 30(36): 10970–10976

[44] Lee C, Kim C J C J. Maximizing the giant liquid slip on superhydrophobic microstructures by nanostructuring their sidewalls. Langmuir, 2009, 25(21): 12812–12818

[45] Enright R, Eason C, Dalton T, Hodes M. Friction factors and Nusselt numbers in microchannels with superhydrophobic walls. In: ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, American Society of Mechanical Engineers, 2006: 599–609

[46] Enright R, Hodes M, Salamon T, Muzychka Y. Isoflux nusselt number and slip length formulae for superhydrophobic microchannels. Journal of Heat Transfer, 2014, 136(1): 012402

[47] Sahar A M, Wissink J, Mahmoud M M, Karayiannis T G, Ashrul Ishak M S. Effect of hydraulic diameter and aspect ratio on single phase flow and heat transfer in a rectangular microchannel. Applied Thermal Engineering, 2017, 115: 793–814

[48] Kandlikar S, Garimella S, Li D, Colin S, King M R. Heat transfer and fluid flow in minichannels and microchannels. Butterworth-Heinemann: Elsevier, 2005

[49] Han L S. Hydrodynamic entrance lengths for incompressible laminar flow in rectangular ducts. Journal of Applied Mechanics, 1960, 27(3): 403–409

[50] Wiginton C L, Dalton C. Incompressible laminar flow in the entrance region of a rectangular duct. Journal of Applied Mechanics, 1970, 37(3): 854–856

[51] Maynes D, Crockett J. Apparent temperature jump and thermal transport in channels with streamwise rib and cavity featured superhydrophobic walls at constant heat flux. Journal of Heat Transfer, 2014, 136(1): 011701

[52] Cowley A, Maynes D, Crockett J. Effective temperature jump length and influence of axial conduction for thermal transport in superhydrophobic channels. International Journal of Heat and Mass Transfer, 2014, 79: 573–583

[53] Maynes D, Webb B W, Crockett J, Solovjov V. Analysis of laminar slip-flow thermal transport in microchannels with transverse rib and cavity structured superhydrophobic walls at constant heat flux. Journal of Heat Transfer, 2013, 135(2): 021701

[54] Enright R, Eason C, Dalton T, Hodes M. Friction factors and Nusselt numbers in microchannels with superhydrophobic walls. In: ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, 2006: 599–609

[55] Choi C H, Ulmanella U, Kim J, Ho C M, Kim C J. Effective slip and friction reduction in nanograted superhydrophobic microchannels. Physics of Fluids, 2006, 18(8): 087105

Acknowledgments

This work was supported by the National Key Research and Development Plan (No. 2016YFB0402102) and the Critically Arranged Project, of Chinese Academy of Sciences (No. KGZD-SW-T01-1).

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