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Heat and Mass Transfer

, Volume 49, Issue 11, pp 1549–1563 | Cite as

Numerical study of turbulent flow and heat transfer of Al2O3–water mixture in a square duct with uniform heat flux

  • Okyar KayaEmail author
Original

Abstract

Turbulent flow and convective heat transfer of a nanofluid made of Al2O3 (1–4 vol.%) and water through a square duct is numerically studied. Single-phase model, volumetric concentration, temperature-dependent physical properties, uniform wall heat flux boundary condition and Renormalization Group Theory k-ε turbulent model are used in the computational analysis. A comparison of the results with the previous experimental and numerical data revealed 8.3 and 10.2 % mean deviations, respectively. Numerical results illustrated that Nu number is directly proportional with Re number and volumetric concentration. For a given Re number, increasing the volumetric concentration of nanoparticles does not have significant effect on the dimensionless velocity contours. At a constant dimensionless temperature, increasing the particle volume concentration increases the size of the temperature profile. Maximum value of dimensionless temperature increases with increasing x/Dh value for a given Re number and volumetric concentration.

Keywords

Heat Transfer Heat Transfer Coefficient Wall Shear Stress Base Fluid Skin Friction Coefficient 
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.

List of symbols

aP

Coefficient of P cell

C

Turbulent model constant = 1.42

C

Turbulent model constant = 1.68

Cp

Specific heat of nanofluid under constant pressure (J/kg K)

Cpnp

Specific heat of nanoparticle under constant pressure (J/kg K)

Cμ

Turbulent model constant = 0.0845

C

Constant part of the source term

dh

Hydraulic diameter (m)

g

Gravitational acceleration (m/s2)

I

Turbulent intensity = \({\text{u}}^{\prime } /\overline{\text{u}}\)

k

Turbulent kinetic energy (m2/s)

l

Turbulent mixing length (m)

lε

Length scale of turbulent kinetic energy dissipation (m)

lμ

Length scale of viscosity (m)

Nu

Nusselt number

P

Pressure (Pa)

Pr

Prandtl number of nanofluid

q″

Wall heat flux (W/m2)

R′

Effect of strain in ε equation (kg/ms4)

Re

Re number

Rey

Re number for a cell having distance y from the nearest wall

S

Modulus of mean rate of strain tensor (1/s)

T

Temperature (K)

Tb

Cross-sectional weighted average of the local fluid temperature (K) \(\left( { = \frac{1}{UA}\int {uTdA} } \right)\)

T

Mixed mean temperature (K)

\(\overline{\text{u}}\)

Time averaged mean velocity (m/s)

u′

Instantaneous velocity component (m/s)

u

Velocity (m/s)

\({\text{y}}^{*}\)

Non-dimensional viscous sublayer thickness

Greek symbols

α

Inverse effective Pr number \(\left( { = \frac{1}{Pr}} \right)\)

αε

Inverse effective Pr number for dissipation rate of turbulent kinetic energy \(\left( { = \frac{1}{{Pr_{\varepsilon } }}} \right)\)

αk

Inverse effective Pr number for turbulent kinetic energy \(\left( { = \frac{1}{{Pr_{k} }}} \right)\)

αt

Inverse effective Pr number for turbulent flow \(\left( { = \frac{1}{{Pr_{t} }}} \right)\)

ε

Turbulent kinetic energy dissipation rate (m2/s3)

κ

Von Karman constant = 0.42

η

Rate of strain in turbulent flow = Sk/ε

λ

Thermal conductivity of nanofluid (W/mK)

μ

Molecular viscosity of nanofluid (kg/ms)

ν

Kinematic viscosity of nanofluid (m2/s)

ϕ

Conservation of mass, momentum and energy equations

Φv

Volume concentration of nanoparticles

ρ

Density of nanofluid (kg/m3)

Subscripts

bf

Base fluid

eff

Effective

i

Inlet

m

Mean

nb

Neighbor cell

np

Nanoparticle

t

Turbulent

References

  1. 1.
    Namburu PK, Das DK, Tanguturi KM, Vajjha RS (2009) Numerical study of turbulent flow and heat transfer characteristics of nanofluids considering variable properties. Int J Therm Sci 4:290–302CrossRefGoogle Scholar
  2. 2.
    Yadav D, Bhargava R, Agrawal GS (2012) Boundary and internal heat source effects on the onset of Darcy-Brinkman convection in a porous layer saturated by nanofluid. Int J Therm Sci 60:244–254CrossRefGoogle Scholar
  3. 3.
    Xuan Y, Li Q (2003) Investigation on convective heat transfer and flow features of nanofluids. J Heat Transfer 125:151–155CrossRefGoogle Scholar
  4. 4.
    Pak BC, Cho YI (1998) Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf 11:151–170CrossRefGoogle Scholar
  5. 5.
    Luciu RS, Mateescu T, Cotorobai V, Mare T (2009) Nusselt number and convection heat transfer coefficient for a coaxial heat exchanger using Al2O3–Water pH = 5 nanofluid. Buletinul Inst Polit Iaşi, t.LV (LIX), f.2:71–80Google Scholar
  6. 6.
    Maiga SB, Nguyen CT, Galanis N, Roy G, Mare T, Coqueux M (2006) Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension. Int J Numer Methods Heat Fluid Flow 16:275–292CrossRefGoogle Scholar
  7. 7.
    Ghaffari O, Behzadmehr A, Ajam H (2010) Turbulent mixed convection of a nanofluid in a horizontal curved tube using a two-phase approach. Int Commun Heat Mass Transf 37:1551–1558CrossRefGoogle Scholar
  8. 8.
    Lotfi R, Saboohi Y, Rashidi AM (2010) Numerical study of forced convective heat transfer of nanofluids: comparision of different approaches. Int Commun Heat Mass Transf 37:74–78CrossRefGoogle Scholar
  9. 9.
    Zeinali Heris S, Nasr Esfahany M, Etemad SGh (2007) Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube. Int J Heat Fluid Flow 28:203–210CrossRefGoogle Scholar
  10. 10.
    Mirmasoumi S, Behzadmehr A (2008) Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model. Appl Therm Eng 28:717–727CrossRefGoogle Scholar
  11. 11.
    Mirmasoumi S, Behzadmehr A (2008) Effect of nanoparticles mean diameter on mixed convection heat transfer of a nanofluid in a horizontal tube. Int J Heat Fluid Flow 29:557–566CrossRefGoogle Scholar
  12. 12.
    Rashmi W, Ismail AF, Khalid M (2011) CFD studies on natural convection heat transfer of Al2O3–water nanofluids. Heat Mass Transf 47:1301–1310CrossRefGoogle Scholar
  13. 13.
    Fluent 5 User Manual (1998) Fluent Incorporated Centerra Resource Park, Lebanon Google Scholar
  14. 14.
    Nguyen CT, Roy G, Lajoie PR (2005) Refroidissement des microprocesseurs a haute performance en utilisant des nano fluides. Congres Français de Thermique, SFT, Reims, 30 mai–2 juin 2005Google Scholar
  15. 15.
    Dittus FW, Boelter LMK (1930) Heat transfer for automobile radiators of the tubular type. Univ Calif Publ Eng 2:443zbMATHGoogle Scholar
  16. 16.
    Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16:359–367Google Scholar
  17. 17.
    Bejan A (1993) Heat transfer. Wiley, New JerseyzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringPamukkale UniversityKinikli, DenizliTurkey

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