Skip to main content
SpringerLink
Log in

Laminar natural convection of Cu-water nanofluid in concentric annuli with radial fins attached to the inner cylinder

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Laminar natural convection of Cu-water nano-fluid between two horizontal concentric cylinders with radial fins attached to the inner cylinder is studied numerically. The inner and outer cylinders are maintained at constant temperature. The governing equations in the polar two-dimensional space with the respective boundary conditions are solved using the finite volume method. The hybrid-scheme is used to discretize the convection terms. In order to couple the velocity field and the pressure in the momentum equations, the well known semi-implicit method for pressure linked equation reformed algorithm is adopted. Using the developed code, a parametric study is undertaken, and the effects of the Rayleigh number, Number of fins, length of the fins and the volume fraction of nano-particles on the fluid flow and heat transfer inside the annuli are investigated. In this study, two cases with different number of fins are considered. It is observed from the results that the average Nusselt number increases with increasing both the Rayleigh number and the volume fraction of the nano-particles. Moreover, the average Nusselt number decreases by increasing the fins’ length and the number of fins. Heat transfer rate increases by increasing the fins’ length at all Rayleigh numbers, but it increases by increasing the number of fins at high Rayleigh numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

c p :

Specific heat (kJ kg−1 K−1)

D :

Inner cylinder diameter

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2 K−1)

l :

Gap width between cylinders

L :

Dimensionless length

l fin :

Fin length

k :

Thermal conductivity (W m−1 K−1)

kr :

Ratio of fin conductivity to the conductivity of base fluid

Nu :

Nusselt number

p :

Pressure (Nm−2)

P :

Dimensionless pressure

Pr :

Prandtl number

r :

Radial coordinate

R :

Dimensionless radial distance

Ra :

Rayleigh number

T :

Temperature (K)

\( \bar{T} \) :

Dimensionless temperature

u, v :

Velocity components

U, V :

Dimensionless velocity components

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

φ :

Nano-particle volume fraction

ν :

Kinematic viscosity (m2 s−1)

θ :

Angle

ψ :

Stream function (m2 s−1)

Ψ :

Dimensionless stream function

ρ :

Density (kg m−3)

μ :

Dynamic viscosity (N s m−2)

Avg :

Average

f :

Fluid

i :

Inner

nf :

Nano-fluid

o :

Outer

References

  1. Kuhen TH, Goldstein RJ (1976) An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. Fluid Mech J 74:695–719

    Article  Google Scholar 

  2. Kuhen TH, Goldstein RJ (1978) An experimental study of natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli. ASME J Heat Transf 100:635–640

    Article  Google Scholar 

  3. Kumar R (1988) Study of natural convection in horizontal annuli. Int J Heat Mass Transf 31:1137–1148

    Article  Google Scholar 

  4. Ho CJ, Li YH, Chen TC (1989) A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions. Int J Heat Fluid Flow 10:40–47

    Article  Google Scholar 

  5. Yeh CL (2002) Numerical investigation of three-dimensional natural convection inside horizontal concentric annulus with specified wall temperature or heat flux convection in a horizontal annulus driven by inner heat generating solid cylinder. Int J Heat Mass Transf 45:775–784

    Article  MATH  Google Scholar 

  6. Chai JC, Patankar SV (1993) Laminar natural convection in internally finned horizontal annulus. Numer Heat Transf 24:67–87

    Article  Google Scholar 

  7. Rahnama M, Farhadi M (2004) Effect of radial fins on two-dimensional turbulent natural convection in a horizontal annulus. Int J Therm Sci 43:255–264

    Article  Google Scholar 

  8. Maxwell JC (1873) Electricity and magnetism. Clarendon Press, Oxford, UK

    Google Scholar 

  9. Choi SUS (1995) Enhancing thermal conductivity of fluid with nanoparticles, developments and applications of non-Newtonian flow. ASME FED 231:99–105

    Google Scholar 

  10. Behzadmehr A, Saffar-Avval M, Galanis N (2007) Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach. Int J Heat Fluid Flow 28:211–219

    Article  Google Scholar 

  11. Bianco V, Chiacchio F, Manca O, Nardini S (2009) Numerical investigation of nanofluids forced convection in circular tubes. J Appl Therm Eng 29:3632–3642

    Article  Google Scholar 

  12. Santra AK, Sen S, Chakraborty N (2009) Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates. Int J Therm Sci 48:391–400

    Article  Google Scholar 

  13. Putra N, Roetzel W, Das SK (2003) Natural convection of nanofluids. Heat Mass Transf 39(8–9):775–784

    Article  Google Scholar 

  14. Wen D, Ding Y (2005) Formulation of nanofluids for natural convective heat transfer applications. Int J Heat Fluid Flow 26(6):855–864

    Article  Google Scholar 

  15. Jou RY, Tzeng SC (2006) Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures. Int Commun Heat Mass Transf 33:727–736

    Article  Google Scholar 

  16. Ho CJ, Liu WK, Chang YS, Lin CC (2010) Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. Int J Therm Sci 49(8):1345–1353

    Article  Google Scholar 

  17. Aminossadati SM, Ghasemi B (2011) Enhanced natural convection in an isosceles triangular enclosure filled with a nanofluid. Comput Math Appl 61(7):1739–1753

    Article  MathSciNet  MATH  Google Scholar 

  18. Cho CC, Chen CL, Chen CK (2012) Natural convection heat transfer performance in complex-wavy-wall enclosed cavity filled with nanofluid. Int J Therm Sci 60:255–263

    Article  Google Scholar 

  19. Arefmanesh A, Amini M, Mahmoodi M, Najafi M (2012) Buoyancy-driven heat transfer analysis in two-square duct annuli filled with a nanofluid. Eur J Mech B Fluids 33:95–102

    Article  MathSciNet  Google Scholar 

  20. Mokhtari Moghari R, Akbarinia A, Shariat M, Talebi F, Laur R (2011) Two phase mixed convection Al2O3–water nanofluid flow in an annulus. Int J Multiph Flow 37(6):585–595

    Article  Google Scholar 

  21. Parvin S, Nasrin R, Alim MA, Hossain NF, Chamkha AJ (2012) Thermal conductivity variation on natural convection flow of water–alumina nanofluid in an annulus. Int J Heat Mass Transf 55(19–20):5268–5274

    Article  Google Scholar 

  22. Soleimani Sl, Sheikholeslami M, Ganji DD, Gorji-Bandpay M (2012) Natural convection heat transfer in a nanofluid filled semi-annulus enclosure. Int Commun Heat Mass Transf 39(4):565–574

    Article  Google Scholar 

  23. Abu-Nada E, Masoud Z, Hijazi A (2008) Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. Int Commun Heat Mass Transf 35:657–665

    Article  Google Scholar 

  24. Abu-Nada E (2009) Effect of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection. Int J Heat Fluid Flow 30:679–690

    Article  Google Scholar 

  25. Incropera DP, Witt D (2005) Introduction to heat transfer, 3rd edn. Wiley, London

    Google Scholar 

  26. Kenjeres S, Hanjalic K (1995) Prediction of turbulent thermal convection in concentric and eccentric horizontal annuli. Int J Heat Fluid Flow 16:429–439

    Article  Google Scholar 

Download references

Acknowledgment

The authors wish to thank the Energy Research Institute of the University of Kashan for their support regarding this research (Grant No. 65473).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Energy Research Institute, University of Kashan, Kashan, Iran

    G. A. Sheikhzadeh & M. Arbaban

  2. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    M. A. Mehrabian

Authors
  1. G. A. Sheikhzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Arbaban
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Mehrabian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Sheikhzadeh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sheikhzadeh, G.A., Arbaban, M. & Mehrabian, M.A. Laminar natural convection of Cu-water nanofluid in concentric annuli with radial fins attached to the inner cylinder. Heat Mass Transfer 49, 391–403 (2013). https://doi.org/10.1007/s00231-012-1084-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-012-1084-9

Keywords

Search

Navigation