Acta Mechanica

, Volume 218, Issue 3–4, pp 195–204 | Cite as

Blasius and Sakiadis problems in nanofluids

Article

Abstract

The classical problems of forced convection boundary layer flow and heat transfer past a semi-infinite static flat plate (Blasius problem) and past a moving semi-infinite flat plate (Sakiadis problem) using nanofluids are theoretically studied. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles such as copper (Cu), alumina (Al2O3), and titania (TiO2) in the base fluid of water with the Prandtl number Pr = 6.2 to investigate the effect of the solid volume fraction parameter φ of the nanofluids. Also, the case of conventional or regular fluid (φ = 0) with Pr = 0.7 is considered for comparison with known results from the open literature. The comparison shows excellent agreement. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles are presented and discussed in detail. It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Muthtamilselvan M., Kandaswamy P., Lee J.: Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure. Commun. Nonlinear. Sci. Numer. Simul. 15, 1501–1510 (2010)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Masuda H., Ebata A., Teramae K., Hishinuma N.: Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (Dispersion of g-Al2O3, SiO2, and TiO2 ultra-fine particles). Netsu Bussei 7, 227–233 (1999)Google Scholar
  3. 3.
    Granquist C.G., Buhrman R.A.: Ultrafine metal particles. J. Appl. Phys. 47, 2200–2219 (1976)CrossRefGoogle Scholar
  4. 4.
    Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. In: Proc. 1995 ASME Int. Mech. Engng. Congress and Exposition, San Franciscos, USA, ASME, FED 231/MD 66, pp. 99–105. (1995)Google Scholar
  5. 5.
    Choi S.U.S., Zhang Z.G., Yu W., Lockwood F.E., Grulke E.A.: Anomalously thermal conductivity enhancement in nanotube suspensions. Appl. Phys. Lett. 79, 2252–2254 (2001)CrossRefGoogle Scholar
  6. 6.
    Buongiorno J.: Convective transport in nanofluids. ASME J. Heat Transf. 128, 240–250 (2006)CrossRefGoogle Scholar
  7. 7.
    Keblinski P., Phillpot S.R., Choi S.U.S., Eastman J.A.: Mechanisms of heat flow in suspensions of nano-sized particles. Int. J. Heat Mass Transf. 45, 855–863 (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Keblinski P., Prasher R., Eapen J.: Thermal conductance of nanofluids: is the controversy over?. J. Nanopart. Res. 10, 1089–1097 (2008)CrossRefGoogle Scholar
  9. 9.
    Prasher R., Song D., Wang J., Phelan P.: Measurements of nanofluid viscosity and its implications for thermal applications . Appl. Phys. Lett. 89, 133108 (2006)CrossRefGoogle Scholar
  10. 10.
    Maïga S.E.B., Nguyen C.T., Galanis N., Roy G.: Heat transfer behaviours of nanofluids in a uniformly heated tube. Superlattices Microstruct. 35, 543–557 (2004)CrossRefGoogle Scholar
  11. 11.
    Polidori G., Fohanno S., Nguyen C.T.: A note on heat transfer modelling of Newtonian nanofluids in laminar free convection. Int. J. Thermal Sci. 46, 739–744 (2007)CrossRefGoogle Scholar
  12. 12.
    Popa C.V., Fohanno S., Nguyen C.T., Polidori G.: On heat transfer in external natural convection flows using two nanofluids. Int. J. Thermal Sci. 49, 901–908 (2010)CrossRefGoogle Scholar
  13. 13.
    Mintsa H.A., Roy G., Nguyen C.T., Doucet D.: New temperature dependent thermal conductivity data for water-based nanofluids. Int. J. Thermal Sci. 48, 363–371 (2009)CrossRefGoogle Scholar
  14. 14.
    Khanafer K., Vafai K., Lightstone M.: Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 46, 3639–3653 (2003)CrossRefMATHGoogle Scholar
  15. 15.
    Maiga S.E.B., Palm S.J., Nguyen C.T., Roy G., Galanis N.: Heat transfer enhancement by using nanofluids in forced convection flows. Int. J. Heat Fluid Flow 26, 530–546 (2005)CrossRefGoogle Scholar
  16. 16.
    Abu-Nada E.: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat Fluid Flow 29, 242–249 (2008)CrossRefGoogle Scholar
  17. 17.
    Hwang K.S., Lee Ji-Hwan, Jang S.P.: Buoyancy-driven heat transfer of water-based Al2 O3 nanofluids in a rectangular cavity. Int. J. Heat Mass Transf. 50, 4003–4010 (2007)CrossRefMATHGoogle Scholar
  18. 18.
    Jou R.Y., Tzeng S.C.: Numerical research of natural convective heat transfer enhancement filled with nanofluids in rectangular enclosures. Int. Commun. Heat Mass Transf. 33, 727–736 (2006)CrossRefGoogle Scholar
  19. 19.
    Tiwari R.K., Das M.K.: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50, 2002–2018 (2007)CrossRefMATHGoogle Scholar
  20. 20.
    Oztop H.F., Abu-Nada E.: Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow 29, 1326–1336 (2008)CrossRefGoogle Scholar
  21. 21.
    Das S.K., Choi S.U.S., Yu W., Pradet T.: Nanofluids: Science and Technology. Wiley, New Jersey (2007)CrossRefGoogle Scholar
  22. 22.
    Kakaç S., Pramuanjaroenkij A.: Review of convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transf. 52, 3187–3196 (2009)CrossRefMATHGoogle Scholar
  23. 23.
    Nield D.A., Kuznetsov A.V.: The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transf. 52, 5792–5795 (2009)CrossRefMATHGoogle Scholar
  24. 24.
    Cheng P., Minkowycz W.J.: Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82, 2040–2044 (1977)CrossRefGoogle Scholar
  25. 25.
    Kuznetsov A.V., Nield D.A.: Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Thermal Sci. 49, 243–247 (2010)CrossRefGoogle Scholar
  26. 26.
    Blasius H.: Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. Phys. 56, 1–37 (1908)Google Scholar
  27. 27.
    Sakiadis B.C.: Boundary-layer behaviour on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J. 7, 26–28 (1961)CrossRefGoogle Scholar
  28. 28.
    Xuan Y., Li Q.: Heat transfer enhancement of nanofluid. Int. J. Heat Fluid Flow 21, 58–64 (2000)CrossRefGoogle Scholar
  29. 29.
    Brinkman H.C.: The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 20, 571–581 (1952)CrossRefGoogle Scholar
  30. 30.
    Abu-Nada E.: Effects of variable viscosity and thermal conductivity of CuO-water nanofluid on heat transfer enhancement in natural convection: mathematical model and simulation. ASME J. Heat Transf. 132, 052401-1–052401-9 (2010)CrossRefGoogle Scholar
  31. 31.
    Ghasemi B., Aminossadati S.M.: Mixed convection in a lid-driven triangular enclosure filled with nanofluids. Int. Commun. Heat Mass Transf. 37, 1142–1148 (2010)CrossRefGoogle Scholar
  32. 32.
    Tsou F.K., Sparrow E.M., Goldstein R.J.: Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transf. 10, 219–235 (1967)CrossRefGoogle Scholar
  33. 33.
    Takhar H.S., Nitu S., Pop I.: Boundary layer flow due to a moving plate: variable fluid properties. Acta Mechanica 90, 37–42 (1991)CrossRefMATHGoogle Scholar
  34. 34.
    Pop I., Gorla R.S.R., Rashidi M.: The effect of variable viscosity on the flow and heat transfer to a continuous moving flat plate. Int. J. Eng. Sci. 30, 1–6 (1992)CrossRefGoogle Scholar
  35. 35.
    Pantokratoras A.: Further results on the variable viscosity on flow and heat transfer to a continuous moving flat plate. Int. J. Eng. Sci. 42, 1891–1896 (2004)CrossRefGoogle Scholar
  36. 36.
    Andersson H.I., Aarseth J.B.: Sakiadis flow with variable fluid properties revisited. Int. J. Eng. Sci. 45, 554–561 (2007)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversiti Sains Malaysia, USMPenangMalaysia
  2. 2.UUM College of Arts and Sciences, Physical Science Division, Building of Quantitative SciencesUniversiti Utara MalaysiaSintokMalaysia
  3. 3.Faculty of MathematicsUniversity of ClujClujRomania

Personalised recommendations