Advertisement

Velocity Field and Pressure Drop in Single-Phase Flows

Part of the Heat and Mass Transfer book series (HMT)

Abstract

The available experimental data on the flowof incompressible fluids are generalized. These data encompass a wide range of Reynolds numbers that correspond to laminar, transient and turbulent regimes of the flow. Thermal effects due to energy dissipation are estimated. Laminar drag reduction in micro-channels using hydrophobic surfaces is discussed. Data of experimental investigations related to the flow in smooth and rough micro-channels are compared with predictions of the conventional theory. Possible sources of divergence of experimental and theoretical results are also discussed.

Keywords

Reynolds Number Pressure Drop Friction Factor Heat Mass Transfer Drag Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bailey DK, Ameel TA, Warrington RO, Savoie TI (1995) Single phase forced convection heat transfer in micro-geometries. In: Proceedings the 13th of Intersociety Energy Conversion Engineering Conference, San Diego, 20–25 August 1978. American Society of Mechanical Engineers, New York, pp 301–310Google Scholar
  2. Bastanjian SA, Merzhanov AG, Xudiaev SI (1965) On hydrodynamic thermal explosion. Sov Phys Docl 163:133–136Google Scholar
  3. Bayraktar T, Pidugu SB (2006) Characterization of liquid flows in micro-fluidic systems. Int J Heat Mass Transfer 49:815–824CrossRefzbMATHGoogle Scholar
  4. Berg van den HR, Seldom ten CA, Gulik van der PS (1993) Compressible laminar flow in a capillary. J Fluid Mech 246:1–20zbMATHCrossRefGoogle Scholar
  5. Brutin D, Tadrist L (2003) Experimental friction factor of a liquid flow in micro-tubes. Phys Fluids 15:653–661CrossRefGoogle Scholar
  6. Celata GP, Gumo M, Zummo G (2004) Thermal-hydraulic characteristics of single-phase flow in capillary pipes. Exp Thermal Fluid Sci 28:87–95CrossRefGoogle Scholar
  7. Celata GP, Morini GL, Marconi V, McPhail SS, Zummo G (2005) Using viscous heating to determine the friction factor in micro-channels: an experimental validation. In: Proceedings of ECI International Conference on Heat Transfer and Fluid Flow in Microchannel, Caste/Vecchio Pascoli, Italy, 25–30 September 2005Google Scholar
  8. Celata GP, Cumo M, McPhail S, Zummo G (2006) Characterization of fluid dynamics behavior and channel wall effects in micro-tube. Int J Heat Fluid Flow 27:135–143CrossRefGoogle Scholar
  9. Cho YI, Hartnett JP (1982) Non-Newtonian fluids in circular pipe flows. Adv Heat Transfer 15:60–141Google Scholar
  10. Cogswell FN (1981) Polymer melt rheology: a guide for industrial practice. Woodhead, CambridgeGoogle Scholar
  11. Cui HH, Silber-Li ZH, Zhu SN (2004) Flow characteristics of liquids in micro-tubes driven by high pressure. Phys Fluids 16:1803–1810CrossRefGoogle Scholar
  12. Darbyshire AG, Mullin T (1995) Transition to turbulence in constant-mass-flux pipe flow. J Fluid Mech 289:83–114CrossRefGoogle Scholar
  13. Davies J, Maynes D, Webb BW, Woolford B (2006) Laminar flow in a microchannel with super hydrophobic walls exhibiting transverse ribs. Phys Fluids 18:087110CrossRefGoogle Scholar
  14. Duncan AB, Peterson GP (1994) Review of microscale heat transfer. Appl Mech Rev 47:397–428CrossRefGoogle Scholar
  15. Frank-Kamenetskii DA (1969) Diffusion and heat transfer in chemical kinetics, 2nd edn. Plenum, New YorkGoogle Scholar
  16. Frenkel L (1946) Kinetic theory of liquids. Clarendon, OxfordzbMATHGoogle Scholar
  17. Gad-el-Hak M (1999) The fluid mechanics of microdevices. The Freeman Scholar Lecture. J Fluid Eng 121:5–33CrossRefGoogle Scholar
  18. Gad-el-Hak M (2003) Comments or critical view on new results in micro-fluid mechanics. Int J Heat Mass Transfer 46:3941–3945zbMATHCrossRefGoogle Scholar
  19. Goldstein S (1965) Modern developments in fluid dynamics, vol 2. Dover, New York, pp 676–680Google Scholar
  20. Gruntfest IJ, Young JP, Jhonson NL (1964) Temperatures generated by the flow of liquids in pipes. J Appl Phys 35:18–23zbMATHCrossRefGoogle Scholar
  21. Guo ZY, Li ZX (2002) Size effect on micro-scale single phase flow and heat transfer. In: Proceedings of the 12th International Heat Transfer Conference, Grenoble, France, 18–23 August 2002Google Scholar
  22. Guo ZY, Li ZX (2003) Size effect on micro-scale single-phase flow and heat transfer. Int J Heat Mass Transfer 46:149–159CrossRefMathSciNetGoogle Scholar
  23. Hagen G (1839) Über die Bewegung des Wassers in engen zylindrischen Rohren. Pogg Ann 46:423–442CrossRefGoogle Scholar
  24. Hao PF, Zhang XW, Yao FHe (2007) Transitional and turbulent flow in circular micro-tube. Exp. Thermal and Fluid Science 32:423-431CrossRefGoogle Scholar
  25. Harley JC, Huang Y, Bau HH, Zewel JN (1995) Gas flow in micro-channels. J Fluid Mech 284:257–274CrossRefGoogle Scholar
  26. Herwig H (2000) Flow and heat transfer in micro systems. Is everything different or just smaller. ZAMM 82:579–586CrossRefMathSciNetGoogle Scholar
  27. Herwig H, Hausner O (2003) Critical view on new results in micro-fluid mechanics: an example. Int J Heat Mass Transfer 46:935–937CrossRefGoogle Scholar
  28. Hetsroni G, Gurevich M, Mosyak A, Rozenblit R (2004) Drag reduction and heat transfer of surfactants flowing in a capillary tube. Int J Heat Mass Transfer 47:3797–3869CrossRefGoogle Scholar
  29. Hetsroni G, Zakin JL, Lin Z, Mosyak A, Pancallo EA, Rozenblit R (2001) The effect of surfactants on bubble grows, wall thermal patterns and heat transfer in pool boiling. Int J Heat Mass Transfer 44:485–497CrossRefGoogle Scholar
  30. Hetsroni G, Mosyak A, Pogrebnyak E, Yarin LP (2005) Fluid flow in micro-channels. Int J Heat Mass Transfer 48:1982-1998CrossRefGoogle Scholar
  31. Ho C-M, Tai Y-C (1998) Micro-electro-mechanical systems (MEMS) and fluid flows. Ann Rev Fluid Mech 30:579–612CrossRefGoogle Scholar
  32. Hsieh SS, Tsai HH, Lin CY, Huang CF, Chien CM (2004) Gas flow in long micro-channel. Int J Heat Mass Transfer 47:3877–3887CrossRefGoogle Scholar
  33. Hwang YW, Kim MS (2006) The pressure drop in microtubes and correlation development. Int J Heat Mass Transfer 49:1804–1812CrossRefGoogle Scholar
  34. Incropera FP (1999) Liquid cooling of electronic devices by single-phase convection. Wiley, New YorkGoogle Scholar
  35. Jones OC (1976) An improvement in the calculation of turbulent friction factor in rectangular ducts. Trans ASME J Fluid Eng 98:173–181Google Scholar
  36. Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45:3477–3489CrossRefGoogle Scholar
  37. Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24:4–16CrossRefGoogle Scholar
  38. Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47:3159–3169CrossRefGoogle Scholar
  39. Leite RJ (1959) An experimental investigation of the stability of Poiseuille flow. J Fluid Mech 5:81–96zbMATHCrossRefGoogle Scholar
  40. Lelea D, Nishio S, Takano K (2004) The experimental research on micro-tube heat transfer and fluid flow of distilled water. Int J Heat Mass Transfer 47:2817–2830CrossRefGoogle Scholar
  41. Li ZX, Du DX, Guo ZY (2003) Experimental study on flow characteristics of liquid in circular micro-tubes. Microscale Thermophys Eng 7:253–265CrossRefGoogle Scholar
  42. Lindgren ER (1958) The transition process and other phenomena in viscous flow. Arkiv für Physik 12:1–169Google Scholar
  43. Loitsianskii LG (1966) Mechanics of liquid and gases. Pergamon, OxfordGoogle Scholar
  44. Lumley JL (1969) Drag reduction by additives. Ann Rev Fluid Mech 1:367–384CrossRefGoogle Scholar
  45. Ma HB, Peterson GP (1997) Laminar friction factor in microscale ducts of irregular cross section. Microscale Thermophys Eng 1:253–265CrossRefGoogle Scholar
  46. Mala GM, Li D (1999) Flow characteristics of water in micro-tubes. Int J Heat Fluid Flow 20:142–148CrossRefGoogle Scholar
  47. Maynes D, Webb AR (2002) Velocity profile characterization in sub-diameter tubes using molecular tagging velocimetry. Exp Fluids 32:3–15CrossRefGoogle Scholar
  48. Morini GL (2004) Laminar-to-turbulent transition in microchannels. Microscale Thermophys Eng 8:15–30CrossRefGoogle Scholar
  49. Obot NT (1988) Determination of incompressible flow friction in smooth circular and noncircular passages. A generalized approach including validation of the century old hydraulic diameter concept. Trans ASME J Fluid Eng 110:431–440CrossRefGoogle Scholar
  50. Ou J, Perot B, Rothstein JP (2004) Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys Fluids 16(12):4635–4643CrossRefGoogle Scholar
  51. Papautsky I, Brazzle J, Ameel T, Frazier B (1999) Laminar fluid behavior in micro-channels using micro-polar fluid theory. Sens Actuators 73:101–108CrossRefGoogle Scholar
  52. Peng XF, Peterson GP (1996) Convective heat transfer and friction for water flow in micro-channel structures. Int J Heat Mass Transfer 39:2599–2608CrossRefGoogle Scholar
  53. Peng XF, Wang BX (1998) Forced convection and boiling characteristics in micro-channels. In: Heat Transfer 1998 Proceedings of the 11th IHTC, Kyongju, Korea, 23–28 August 1998, vol 11, pp 371–390Google Scholar
  54. Pfund D, Rector D, Shekarriz A (2000) Pressure drop measurements in a micro-channel. AIChE J 46:1496–1507CrossRefGoogle Scholar
  55. Plam B (2000) Heat transfer in microchannels. In: Heat Transfer and Transport Phenomena in Microscale. Banff Oct:54–64Google Scholar
  56. Poiseuille JLM (1840) J Recherches experimentelles tubes de tris petits diameters. Comptes Rendus 11:961–967, 1041–1048Google Scholar
  57. Qu W, Mala GM, Li D (2000) Pressure driven water flows in trapezoidal silicon micro-channels. Int J Heat Mass Transfer 43:353–364zbMATHCrossRefGoogle Scholar
  58. Rands C, Webb BW, Maynes D (2006) Characterization of transition to turbulence in micro-channels. Int J Heat Mass Transfer 49:2924–2930CrossRefGoogle Scholar
  59. Ren L, Qu W, Li D (2001) Interfacial electrokinetic effects on liquid flow in micro-channels. Int J Heat Mass Transfer 44:3125–3134zbMATHCrossRefGoogle Scholar
  60. Schlichting H (1979) Boundary layer theory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  61. Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC, Boca RatonGoogle Scholar
  62. Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New YorkGoogle Scholar
  63. Shapiro AK (1953) The dynamics and thermodynamics of compressible fluid flow. Wiley, New YorkGoogle Scholar
  64. Sharp KV, Adrian RJ (2004) Transition from laminar to turbulent flow in liquid filled microtubes. Exp Fluids 36:741–747CrossRefGoogle Scholar
  65. Sharp KV, Adrian R, Santiago J, Molho JI (2001) Liquid flows in micro-channels. In: CRC Handbook of MEMS. CRC, Boca Raton, pp 6.1–6.38Google Scholar
  66. Tani I (1969) Boundary layer transition. Ann Review of Fluid Mech 1:169–196CrossRefGoogle Scholar
  67. Tso CP, Mahulikar SP (1998) The use of the Brinkman number for single phase forced convective heat transfer in micro-channels. Int J Heat Mass Transfer 41:1759–1769zbMATHCrossRefGoogle Scholar
  68. Tso CP, Mahulikar SP (1999) The role of the Brinkman number in analysis flow transition in micro-channel. Int J Heat Mass Transfer 42:1813–1833CrossRefGoogle Scholar
  69. Tso CP, Mahulikar SP (2000) Experimental verification of the role of Brinkman number in micro-channels using local parameters. Int J Heat Mass Transfer 43:1837–1849CrossRefGoogle Scholar
  70. Tuckerman DB (1984) Heat transfer micro-structure for integrated circuits. Dissertation, Department of Electrical Engineering, Stanford UniversityGoogle Scholar
  71. Vargaftik NB, Vinogradov YK, Vargin VS (1996) Handbook of physical properties of liquids and gases. Pure substances and mixtures, 3rd augm. rev. edn. Begell House, New YorkGoogle Scholar
  72. Virk PS, Mickley HS, Smith KA (1970) The ultimate asymptote and mean flow structure in Toms’ phenomenon. ASME J Appl Mech 37:488–493CrossRefGoogle Scholar
  73. Warholic MD, Schmidt GM, Hanratty TJ (1999) The influence of a drag-reducing surfactant on a turbulent velocity field. J Fluid Mech 388:1–20zbMATHCrossRefGoogle Scholar
  74. Watanabe K, Udagawa Y, Udagawa H (1999) Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J Fluid Mech 381:225–238zbMATHCrossRefGoogle Scholar
  75. White FM (1994) Fluid mechanics, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  76. Wu HY, Cheng P (2003) Friction factors in smooth trapezoidal silicon micro-channels with different aspect ratio. Int J Heat Mass Transfer 46:2519–2525CrossRefMathSciNetGoogle Scholar
  77. Wygnanskii IJ, Champagne FH (1973) On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J Fluid Mech 59:281–351CrossRefGoogle Scholar
  78. Xu B, Ooi KT, Wong NT, Choi WK (2000) Experimental investigation of flow friction for liquid flow in micro-channels. Int Comm Heat Transfer 27(8):1165–1176CrossRefGoogle Scholar
  79. Yang CY, Wu JC, Chien HT, Lu SR (2003) Friction characteristics of water, R-134a, and air in small tubes. Microscale Thermophys Eng 7:335–348CrossRefGoogle Scholar
  80. Zakin JL, Myska J, Chara Z (1996) New limiting drag reduction and velocity profile asymptotes for nonpolymeric additives systems. AIChE J 42:3544–3546CrossRefGoogle Scholar
  81. Zakin JL, Qi Y, Zhang Y (2002) In: Proceedings of 15th International Congress of Chemical and Process Engineering, CHISA 2002, Prague, Czech Republic, 25–29 August 2002Google Scholar
  82. Zel’dovich JaB, Barenblatt GI, Librovich VB, Makhviladze GM (1985) Mathematical theory of combustion and explosion. Plenum, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Personalised recommendations