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.

Key words： laminar flow; hydraulic entrance length; super hydrophobic surface; slip length; hydraulic diameter

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).

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