Microfluidics and Nanofluidics

, Volume 17, Issue 2, pp 401–412 | Cite as

Boundary layer analysis and heat transfer of a nanofluid

Research Paper


A theoretical model for nanofluid flow, including Brownian motion and thermophoresis, is developed and analysed. Standard boundary layer theory is used to evaluate the heat transfer coefficient near a flat surface. The model is almost identical to previous models for nanofluid flow which have predicted an increase in the heat transfer with increasing particle concentration. In contrast our work shows a marked decrease indicating that under the assumptions of the model (and similar ones) nanofluids do not enhance heat transfer. It is proposed that the discrepancy between our results and previous ones is due to a loose definition of the heat transfer coefficient and various ad hoc assumptions.


Nanofluid Convective heat transfer Boundary layer Heat transfer coefficient 


  1. Acheson DJ (1990) Elementary fluid dynamics. Oxford University Press, OxfordMATHGoogle Scholar
  2. Astumian RD (2007) Coupled transport at the nanoscale: the unreasonable effectiveness of equilibrium theory. Proc Natl Acad Sci 104(1):3–4CrossRefGoogle Scholar
  3. Bejan A (2004) Convection heat transfer, 3rd edn. Wiley, Hoboken, NJGoogle Scholar
  4. Bird R, Stewart W, Lightfoot E (2007) Transport phenomena. Wiley, Hoboken, NJGoogle Scholar
  5. Buongiorno J (2006) Convective transport in nanofluids. J Heat Transf 128:240–250CrossRefGoogle Scholar
  6. Buongiorno J, Venerus D, Prabhat N, McKrell T, Townsend J et al (2009) A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 106:094312CrossRefGoogle Scholar
  7. Brenner H, Bielenberg JR (2005) A continuum approach to phoretic motions: thermophoresis. Phys A 355:251–273CrossRefGoogle Scholar
  8. Chhabra RP, Richardson JF (2008) Non-Newtonian flow and applied rheology, 2nd edn. Butterworth-Heinemann, OxfordGoogle Scholar
  9. Corcione M (2011) Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag 52:789–793CrossRefGoogle Scholar
  10. Das S, Putra N, Thiesen P, Roetzel W (2003) Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transf 125:567–574CrossRefGoogle Scholar
  11. Daungthongsuk W, Wongwises S (2007) A critical review of convective heat transfer of nanofluids. Renew Sustain Energy Rev 11:797–817CrossRefGoogle Scholar
  12. Ding Y, Chen H, He Y, Lapkin A, Yeganeh A, Siller L, Butenko YV (2007) Forced convective heat transfer of nanofluids. Adv Powder Technol 18:813–824CrossRefGoogle Scholar
  13. Duhr S, Braun D (2006) Why molecules move along a temperature gradient. Proc Natl Acad Sci 103(52):19678–19682CrossRefGoogle Scholar
  14. Evans W, Fish J, Keblinski P (2006) Role of Brownian motion hydrodynamics on nanofluid thermal conductivity. Appl Phys Lett 88:093116CrossRefGoogle Scholar
  15. Haddad Z, Abu-Nada E, Oztop HF, Mataoui A (2012) Natural convection in nanofluids: are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement? Int J Therm Sci 57:152–162CrossRefGoogle Scholar
  16. Hwang KS, Jang SP, Choi SUS (2009) Flow and convective heat transfer characteristics of water-based Al 2 O 3 nanofluids in fully developed laminar flow regime. Int J Heat Mass Transf 52:193–199CrossRefMATHGoogle Scholar
  17. Jang SP, Choi SUS (2006) Cooling performance of a microchannel heat sink with nanofluids. Appl Therm Eng 26(17–18):2457–2463CrossRefGoogle Scholar
  18. Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483CrossRefMATHGoogle Scholar
  19. Khanafer K, Vafai K (2011) A critical synthesis of thermophysical characteristics of nanofluids. Int J Heat Mass Transf 54:4410–4428CrossRefMATHGoogle Scholar
  20. Kleinstreuer C, Feng Y (2011) Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res Lett 6:229CrossRefGoogle Scholar
  21. Koo J, Kleinstreuer C (2005) Laminar nanofluid flow in microheat-sinks. Int J Heat Mass Transf 48:2652–2661CrossRefMATHGoogle Scholar
  22. Kuznetsov AV, Nield DA (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243–247CrossRefGoogle Scholar
  23. Li CH, Peterson GP (2010) Experimental studies of natural convection heat transfer of Al2O3/DI water nanoparticle suspensions (nanofluids). Adv Mech Eng 2010, Article ID 742739Google Scholar
  24. Maiga SEB, Nguyen CT, Galanis N, Roy G (2004) Heat transfer behaviors of nanofluids in a uniformly heated tube. Superlattices Microstruct 35:543–557CrossRefGoogle Scholar
  25. McNab GS, Meisen A (1973) Thermophoresis in liquids. J Colloid Interface Sci 44(2):339–346 CrossRefGoogle Scholar
  26. Myers TG (2009) Optimizing the exponent in the heat balance and refined integral methods. Int Commun Heat Mass Transf 36(2):143–147CrossRefGoogle Scholar
  27. Myers TG (2010a) Optimal exponent heat balance and refined integral methods applied to Stefan problems. Int J Heat Mass Transf 53:1119–1127CrossRefMATHGoogle Scholar
  28. Myers TG (2010b) An approximate solution method for boundary layer flow of a power law fluid over a flat plate. Int J Heat Mass Transf 53:2337–2346CrossRefMATHGoogle Scholar
  29. Myers TG, Mitchell SL, Font F (2012) Energy conservation in the one-phase supercooled Stefan problem. Int Commun Heat Mass Transf 39:1522–1525CrossRefGoogle Scholar
  30. Myers TG, MacDevette MM, Ribera H (2013) A time dependent model to determine the thermal conductivity of a nanofluid. J Nanopart Res 15:1775CrossRefGoogle Scholar
  31. Popa C, Polidori G, Arfaoui A, Fohanno S (2011) Heat and mass transfer in external boundary layer flows using nanofluids. In: Hossain M (ed) Heat and Mass Transfer - Modeling and Simulation. InTech. http://www.intechopen.com/download/get/type/pdfs/id/20408
  32. Prasher R, Bhattacharya P, Phelan PE (2006) Brownian-motion-based convective-conductive model or the effective thermal conductivity of nanofluids. J Heat Transf 128:588–595CrossRefGoogle Scholar
  33. Putra N, Roetzel W, Das SK (2003) Natural convection of nano-fluids. Heat Mass Transf 39(8–9):775–784CrossRefGoogle Scholar
  34. Savino R, Paterna D (2008) Thermodiffusion in nanofluids under different gravity conditions. Phys Fluids 20:017101CrossRefGoogle Scholar
  35. Vigolo D, Rusconi R, Stone HA, Piazza R (2010) Thermophoresis: microfluidics characterization and separation. Soft Matter 6:3489–3493CrossRefGoogle Scholar
  36. Wang X, Xu X, Choi SUS (1999) Thermal conductivity of nanoparticle-fluid mixture. J Thermophys Heat Transfer 13:474–480CrossRefGoogle Scholar
  37. Xuan Y, Li Q (2000) Heat transfer enhancement of nanofluids. Int J Heat Fluid Flow 21(1):58–64MathSciNetCrossRefGoogle Scholar
  38. Xuan Y, Roetzel W (2000) Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf 43(19):3701–3707CrossRefMATHGoogle Scholar
  39. Yang Y, Zhong ZG, Grulke EA, Anderson WB, Wu G (2005) Heat transfer properties of nanoparticle-in-fluid dispersion (nanofluids) in laminar flow. Int J Heat Mass Transf 48:1107–1116CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Centre de Recerca MatemàticaBellaterra, BarcelonaSpain
  2. 2.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada

Personalised recommendations