Skip to main content
SpringerLink
Log in

Numerical investigation of the heat transfer enhancement using various viscosity models in chamber filled with water–CuO nanofluid

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Heat transfer enhancement in two-dimensional lid-driven chamber, filled with water–cupric oxide nanofluid is investigated numerically. Different viscosity models are used to evaluate heat transfer enhancement and the increase in the average Nusselt number on hot wall. The horizontal boundaries of the square domain are assumed to be insulated, and the vertical ones are considered to be isothermal. The model of Chon et al. is exerted for heat conduction coefficient. The standpoint of each viscosity model fundamentally varies in terms of whether it takes different variables such as temperature effects, Brownian motion of the nanoparticles, the radii of aggregated particles, and the volume fraction of nanoparticles into account. The governing stream-vorticity equations are solved using a second-order central finite difference scheme, coupled to the conservation of mass and energy. The main sensitive parameters of interest to investigate the viscosity models are chosen as volume fraction of the nanoparticles φ, and Richardson number Ri. The performance study of the viscosity models and the interpretation of the corresponding results of streamlines, isothermal lines, and velocity components are done in a different range of φ and Ri for forced, mixed and natural convections. It is found that higher heat transfer is predicted when Brownian motion and temperature effects are considered.

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.

Institutional subscriptions

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

Similar content being viewed by others

Abbreviations

C P :

Specific heat at constant pressure (J kg−1 K−1)

d :

Diameter of nanoparticle (m)

g:

Gravitational acceleration (m s−2)

Gr :

Grashof number, Gr = gβ f L 3 (T H−T C)/ν 2 f

k B :

Boltzmann constant (J/K)

k :

Thermal conductivity (W/m K)

L :

Length of cavity (m)

Nu :

Nusselt number, Nu = qL/k f ΔT

p :

Dimensional pressure (Pa)

P :

Dimensionless pressure, P = p ρ −1 nf U −2 m

Pr :

Prandtl number, Pr = ν f /α f

Ra :

Rayleigh number, Ra = Gr Pr

Re :

Reynolds number, Re = U m L/ν f

Ri :

Richardson number, Ri = Gr/Re 2

R s :

Radios of nanoparticle (nm)

T :

Dimensional temperature (°C)

u, v :

Dimensional x and y components of velocity (m s−1)

U, V :

Dimensionless velocities, V = v/U m , U = u/U m

U m :

Lid velocity (m s−1)

x, y :

Dimensional coordinates (m)

X, Y :

Dimensionless coordinates, X = x/L, Y = y/L

α :

Fluid thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

γ :

Transport quantity

ε :

Numerical tolerance

ζ :

Modeling function, Eq. (17)

η :

Intrinsic viscosity

θ :

Dimensionless temperature, θ = T−T C /T H−T C

λ :

Modeling function, Eq. (25)

μ :

Dynamic viscosity (N s m−2)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

φ :

Nanoparticle volume fraction

ψ :

Dimensional stream function (m2 s−1)

Ψ:

Dimensionless stream function, Ψ = ψ/U m L

ω :

Dimensional vorticity (s−1)

Ω:

Dimensionless vorticity Ω = ωL/U m

avg:

Average

eff:

Effective

f :

Fluid

H :

Hot

C :

Cold

m :

Maximum

nf :

Nanofluid

s :

Solid particle

*:

Normalized

References

  1. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. ASME Fluids Eng Div 231:99–105

    Google Scholar 

  2. Kakac S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187–3196

    Article  MATH  Google Scholar 

  3. Saidur R, Leong KY, Mohammad HA (2011) A review on applications and challenges of nanofluids. Renew Sustain Energy Rev 15:1646–1668

    Article  Google Scholar 

  4. Mahbubul IM, Saidur R, Amalina MA (2012) Latest developments on the viscosity of nanofluids. Int J Heat Mass Transf 55:874–885

    Article  Google Scholar 

  5. Mukesh Kumar PC, Kumar J, Suresh S (2012) Review on nanofluid theoretical viscosity models. Int J Eng Innov Res 1(2):128–134

    Google Scholar 

  6. Khanafer K, Vafai K, Lightstone M (2003) Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 46:3639–3653

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Talebi F, Mahmoudi AH, Shahi M (2010) Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid. Int Commun Heat Mass Transf 37:79–90

    Article  Google Scholar 

  9. Mahmoodi M (2011) Numerical simulation of free convection of a nanofluid in L-shaped cavities. Int J Therm Sci 50:1731–1740

    Article  Google Scholar 

  10. Abu-Nada E, Masoud Z, Oztop HF, Campo A (2010) Effect of nanofluid variable properties on natural convection in enclosures. Int J Therm Sci 49:479–491

    Article  Google Scholar 

  11. Brinkman HC (1952) The viscosity of concentrated suspensions and solutions. J Chem Phys 20:571–581

    Article  Google Scholar 

  12. Nguyen CT, Desgranges F, Roy G, Galanis N, Mare T, Boucher S, Angue Minsta H (2007) Temperature and particle-size dependent viscosity data for water based nanofluids- hysteresis phenomenon. Int J Heat Fluid Flow 28:1492–1506

    Article  Google Scholar 

  13. Nasrin R, Alim MA, Chamkha AJ (2012) Combined convection flow in triangular wavy chamber filled with water–CuO nanofluid: effect of viscosity models. Int Commun Heat Mass Transf 39:1226–1236

    Article  Google Scholar 

  14. Pak BC, Cho Y (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle. Exp Heat Transf 11:151–170

    Article  Google Scholar 

  15. Sheikhzadeh GA, Ebrahim Qomi M, Hajialigol N, Fattahi A (2012) Numerical study of mixed convection flows in a lid-driven enclosure filled with nanofluid using variable properties. Results Phys 2:5–13

    Article  Google Scholar 

  16. Chamkha AJ, Abu-Nada E (2012) Mixed convection flow in single and double-lid driven square cavities filled with water–Al2O3 nanofluid: effect of viscosity models. Eur J Mech B Fluids 36:82–96

    Article  MathSciNet  MATH  Google Scholar 

  17. Abu-Nada E (2011) Rayleigh-Bénard convection in nanofluids: effect of temperature dependent properties. Int J Therm Sci 50:1720–1730

    Article  Google Scholar 

  18. Chon CH, Kihm KD, Lee SP, Choi S (2005) Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett 87(15): 153107-1-3

    Google Scholar 

  19. Angue Minsta H, Roy G, Nguyen CT, Doucet D (2008) New temperature and conductivity data for water-based nanofluids. Int J Therm Sci 48(2):363–373

    Google Scholar 

  20. 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 57:152–162

    Article  Google Scholar 

  21. Krieger IM, Dougherty TJ (1959) A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans Soc Rheol 3:137–152

    Article  Google Scholar 

  22. Chen H, Ding Y, Tan C (2007) Rheological behavior of nanofluids. New J Phys 9(10):267

    Article  Google Scholar 

  23. Nielsen LE (1970) Generalized equation for the elastic moduli of composite materials. J Appl Phys 41:4626–4627

    Article  Google Scholar 

  24. Wang X, Xu X, Choi SUS (1999) Thermal conductivity of nanoparticle–fluid mixture. J Thermophys Heat Transf 13(4):474–480

    Article  Google Scholar 

  25. Batchelor G (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech 83(01):97–117

    Article  MathSciNet  Google Scholar 

  26. Koo J, Kleinstreuer C (2005) Laminar nanofluid flow in microheat-sinks. Int J Heat Mass Tranf 48(13):2652–2661

    Article  MATH  Google Scholar 

  27. Abu-Nada E (2010) Effects of variable viscosity and thermal conductivity of CuO–water nanofluid on heat transfer enhancement in natural convection: mathematical model and simulation. J Heat Tranf 132:052401

    Article  Google Scholar 

  28. Krane RJ, Jessee J (1983) Some detailed field measurements for a natural convection flow in a vertical square enclosure. In: 1st ASME-JSME thermal engineering joint conference, vol 1, pp 323–329

  29. Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336

    Article  Google Scholar 

  30. Fusegi T, Hyun JM, Kuwahara K, Farouk B (1991) A numerical study of three dimensional natural convection in a differentially heated cubical enclosure. Int J Heat Mass Transf 34:1543–1557

    Article  Google Scholar 

  31. Markatos NC, Pericleous KA (1984) Laminar and turbulent natural convection in an enclosed cavity. Int J Heat Mass Transf 27:772–775

    Google Scholar 

  32. De Vahl Davis G (1983) Natural convection of air in a square cavity, a benchmark numerical solution. Int J Numer Methods Fluids 3:249–264

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

    Ashkan Ghafouri & Mehdi Salari

Authors
  1. Ashkan Ghafouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehdi Salari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashkan Ghafouri.

Additional information

Technical Editor: Horacio Vielmo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghafouri, A., Salari, M. Numerical investigation of the heat transfer enhancement using various viscosity models in chamber filled with water–CuO nanofluid. J Braz. Soc. Mech. Sci. Eng. 36, 825–836 (2014). https://doi.org/10.1007/s40430-013-0091-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-013-0091-1

Keywords

Search

Navigation