Advertisement

The Pi-Theorem pp 103-130 | Cite as

Laminar Flows in Channels and Pipes

  • L. P. Yarin
Chapter
Part of the Experimental Fluid Mechanics book series (FLUID, volume 1)

Abstract

Fluid flow in pipes and ducts was a subject of numerous experimental and theoretical investigations performed during the last two centuries. Beginning from the seminal works of Hagen (1839) and Poiseuille (1840), a detailed data on flows of incompressible viscous fluids in pipes and ducts of different geometry was obtained. These results are presented in many review articles, monographs and textbooks. A comprehensive analysis of problems related to laminar and turbulent flows in pipes and ducts (the physical foundations of the theory and its mathematical formulation) can be found in such widely known books as Schlichting (1979), Landau and Lifshitz (1987), Loitsyanskii (1966) and Ward-Smith (1980).

Keywords

Friction Factor Volumetric Flow Rate Entrance Region Governing Parameter Dimensionless Group 
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.

References

  1. Adler M (1934) Stromung in gekruiimmeten. Rohren Z Angew Math 14:257–275zbMATHGoogle Scholar
  2. Astarita G, Marrucci G (1974) Principies of non-newtonian fluid mechanics. McGraw-Hill, New YorkGoogle Scholar
  3. Bahrami M, Yovanovich MM, Culham JR (2006) Pressure drop of fully developed laminar flow in rough microtybes. J Fluids Eng Trans ASME 128:632–637CrossRefGoogle Scholar
  4. Barua SN (1963) On secondary flow in stationary curved pipes. QJ Mech Appl Math 16:61–77MathSciNetCrossRefGoogle Scholar
  5. Berger SA, Tabol L, Yao L-S (1983) Flow in curved pipes. Annu Rev Fluid Mech 15:461–512CrossRefGoogle Scholar
  6. Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymeric liquids. In: Fluid mechanics, vol 1. Wiley&Sons, New YorkGoogle Scholar
  7. Celata GP (2000) Heat transfer and fluid flow in microchannels. Begell Hause, New YorkGoogle Scholar
  8. Dean WR (1927) Note on the motion of fluid in a curved pipe. Philos Mag 20:208–223Google Scholar
  9. Dean WR (1928) The streamline motion of fluid in a curved pipe. Philos Mag 30:673–693Google Scholar
  10. Dunkan AB, Peterson GP (1994) Review of micro-scale heat transfer. App Mech 47:397–428CrossRefGoogle Scholar
  11. Van Dyke M (1978) Extended Stokes series: Laminar flow through a loosely coiled pipe. J Fluid Mech 36:129–145CrossRefGoogle Scholar
  12. Emery AE, Chen CS (1968) An experimental investigation of possible methods to reduce laminar entry length. Trans ASME Ser D 90:134–137CrossRefGoogle Scholar
  13. Fargie D, Martin BW (1971) Developing laminar flow in a pipe of circular cross-section. Proc Roy Soc 321A:461–476Google Scholar
  14. Friedmann M, Gilis J, Liron N (1968) Laminar flow in a pipe at low and moderate Reynolds numbers. App Sci Res 19:426–438zbMATHCrossRefGoogle Scholar
  15. Gad-el-Hak M (1999) The fluid mechanics of micro-devices. The Freeman Scholar Lecture. J Fluid Eng 121:5–33CrossRefGoogle Scholar
  16. Gad-el-Hak M (2003) Comments or “critical” view on new results in micro-fluid mechanics. Int J Heat Mass Transf 46:3941–3945zbMATHCrossRefGoogle Scholar
  17. Garimella S, Sobhan C (2003) Transport in microchannels: critical review. Annu Rev Heat Transf 13:1–50Google Scholar
  18. Germano M (1989) The Dean equations extended to a helical pipe flow. J Fluid Mech 203:289–305zbMATHCrossRefGoogle Scholar
  19. Hagen G (1839) Uber die Bewegung des Wassers in engen zylindrisghen Rohren. Pogg Ann 46:423–442CrossRefGoogle Scholar
  20. Hezwig H (2002) Flow and heat transfer in micro systems. Everything different or just smaller? ZAMM 82(9):579–586Google Scholar
  21. Hezwig H, Hausner O (2003) Critical view on new results in micro-fluid mechanics: an example. Int J Heat Mass Transf 46:935–937CrossRefGoogle Scholar
  22. Hezwig H, Gloss D, Wenterodt T (2008) A new approach to understanding and modeling the influence of wall roughness on friction factors for pipe and channel flows. J Fluid Mech 613:35–53Google Scholar
  23. Hetsroni H, Mosyak A, Pogrebnyak E, Yarin LP (2005a) Fluid flow in microchannels. Int J Heat Mass Transf 48:1982–1998CrossRefGoogle Scholar
  24. Hetsroni G, Mosyak A, Pogrebnyak E, Yarin LP (2005b) Heat transfer in micro-channels: comparison of experiments with theory and numerical results. Int J Heat Mass Transf 48:5580–5601CrossRefGoogle Scholar
  25. Ho C-M, Tai Y-C (1988) Micro-electro-mechanical systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612CrossRefGoogle Scholar
  26. Incropera FP (1999) Liquid cooling of electronic devices by single-phase convection. John Wiley&Sons, New YorkGoogle Scholar
  27. Ito H (1959) Friction factors for turbulent flow in curved pipes. Trans ASME J Basic Eng 81:123–134Google Scholar
  28. Kakas S, Vasiliev LL, Bayazitoglu Y, Yener Y (2005) Micro-scale heat transfer. Springer, BerlinGoogle Scholar
  29. Kandlicar SG (2005) Roughness effects at microscale-reassessing Nikuradse’s experiments on liquid flow in rough tubes. B Pol Acad Sci Tech Sci 53:343–349Google Scholar
  30. Landau LD, Lifshitz EM (1987) Fluid mechanics, 2nd edn. Pergamon, New YorkGoogle Scholar
  31. 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
  32. Li Z, He Y-L, Tang G-H, Tao W-Q (2007) Experimental and numerical studies of liquid flow and heat transfer in microtubes. Int J Heat Mass Transf 50:3442–3460Google Scholar
  33. Loitsyanskii LG (1966) Mechanics of liquids and gases. Pergamon Press, OxfordGoogle Scholar
  34. Ma HB, Peterson GP (1997) Laminar friction factor in micro-scale ducts of irregular cross-section. Micro-scale Thermophys Eng 1:253–265CrossRefGoogle Scholar
  35. Moody LF (1948) Friction factors for pipe flow. Trans ASME 66:671–684Google Scholar
  36. Mori Y, Nakayama W (1965) Study on forced convective heat transfer in curved pipes (1st Report, Laminar flow). Int J Heat Mass Transf 8:67–82zbMATHCrossRefGoogle Scholar
  37. Nikuradse J (1930) Turbulente stromung in nicht kreisfozmigen rohren. Ing Arch 1:306–332Google Scholar
  38. Nikuradse J (1933) Stromungsgesetze in rauhen. Rihren Forschg Arb Ing-Wes 361. Translated in NACA Memo. N1292, (1950)Google Scholar
  39. Pfund D, Rector D, Shekarriz A (2000) Pressure drop measurements in micro-channel. AIChE 46:1496–1507CrossRefGoogle Scholar
  40. Plam B (2000) Heat transfer in micro-channels. In: Heat transfer and transport phenomena in microscale. Banff Oct, pp 54–64Google Scholar
  41. Poiseuille J (1840) Recherches experimentelles sur le mouvements des liquides dans les tubes de tres petits diameters. Comptes Rendus 11:961–967, 1041–1048Google Scholar
  42. Qu W, Mala GM, Li D (2000) Pressure driven water flows in trapezoidal silicon micro-channels. Int J Heat Mass Transf 43:353–364zbMATHCrossRefGoogle Scholar
  43. Schlichting H (1979) Boundary layer theory, 8th edn. Springer, BerlinGoogle Scholar
  44. Schiller L (1923) Uber den Stromungswiderrstand von Rohren verschiedenen Querschnitts-und Rauhigkeitsgrades. ZAMM 3:2–13MathSciNetCrossRefGoogle Scholar
  45. Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New YorkGoogle Scholar
  46. Wang HL, Wang Y (2007) Flow in microchannels with rough walls: flow pattern and pressure drop. J Micromech Microeng 17:586–596CrossRefGoogle Scholar
  47. Ward-Smith AS (1980) Internal fluid flow (The fluid dynamics of flow in pipes and ducts). Clarendon, OxfordGoogle Scholar
  48. White CM (1929) Streamline flow through curved pipes. Proc R Soc London Ser 123A:645–663CrossRefGoogle Scholar
  49. White FM (2008) Viscous fluid flow, 7th edn. McGraw-Hill, New YorkGoogle Scholar
  50. Wilkinson WL, Chen AML (1960) Non-Newtonian fluids (Fluid mechanics, mixing and heat transfer). Pergamon Press, New YorkGoogle Scholar
  51. Yarin LP, Mosyak A, Hetsroni G (2009) Fluid flow, Heat transfer and boiling in micro-channels. Springer, BerlinzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • L. P. Yarin
    • 1
  1. 1.Dept. of Mechanical Engineering Technion CityTechnion-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations