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Numerical Investigation of Heat Transfer, Pressure Drop and Wall Shear Stress Characteristics of Al2O3-Water Nanofluid in a Square Duct

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Abstract

Turbulent heat transfer, pressure drop and wall shear stress behavior of the nanofluid Al2O3-water mixture in a square duct under constant wall heat flux are investigated numerically. Single-phase approach is taken into account during the simulations. All of the nanofluid properties depend on the temperature and the nanoparticle volume concentration. The renormalization group theory RNG \({k-\varepsilon}\) model is employed in order to model turbulence. Validation tests of the numerical results are done by using water as the first working fluid. Similar models and methods are chosen for the simulation of nanofluid (Al2O3-water) flow and heat transfer. A very good agreement is realized with the previous water and nanofluid related theoretical-empirical heat transfer and pressure drop correlations. The rate of heat transfer is increased by the presence of nanofluids when compared to that of water. Increasing Re number and particle’s volumetric concentration increases the convection heat transfer coefficient, pressure drop and wall shear stress along the duct. On the other hand, this study confirmed that single-phase model approach is appropriate for the simulation of Al2O3-water flow and heat transfer.

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Abbreviations

a P :

Coefficient of P cell

\({{C}_{1\varepsilon}}\) :

Turbulent model constant (= 1.42)

\({{C}_{2\varepsilon}}\) :

Turbulent model constant (= 1.68)

C p :

Constant pressure specific heat (J/kgK)

\({{C}_{\mu}}\) :

Turbulent model constant (= 0.0845)

c :

Constant part of the source term

D :

Hydraulic diameter (m)

f :

Darcy friction factor

g :

Gravitational acceleration (m/s2)

h :

Convection heat transfer coefficient (W/m2K)

I :

Turbulent intensity \({({=}{u}'/\overline u)}\)

k :

Turbulent kinetic energy (m2/s)

L :

Length of the duct (m)

l :

Turbulent mixing length (m)

\({{l}_{\varepsilon}}\) :

Length scale of turbulent kinetic energy dissipation (m)

\({{l}_{\mu}}\) :

Length scale of viscosity (m)

Nu :

Nusselt number

P :

Pressure (Pa)

Pr :

Prandtl number

\({q^{\prime\prime}}\) :

Wall heat flux (W/m2)

\({R^\prime}\) :

Effect of strain in \({\varepsilon}\) equation (kg/ms4)

Re :

Re number

S :

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

T :

Temperature (K)

\({{\overline{u}}}\) :

Time-averaged mean velocity (m/s)

\({u^\prime}\) :

Instantaneous velocity component (m/s)

u :

Velocity (m/s)

t :

Time (s)

u :

Velocity (m/s)

X :

Distance from the entrance of the duct (m)

\({y^{\ast}}\) :

Non-dimensional viscous sublayer thickness

\({y_{T}^\ast}\) :

Non-dimensional thermal sublayer thickness

\({\alpha}\) :

Inverse effective Pr number (= 1/Pr)

\({\alpha_{\varepsilon}}\) :

Inverse effective Pr number for dissipation rate of turbulent kinetic energy (= 1/\({{\rm Pr}_{\varepsilon}}\))

\({\alpha_{k}}\) :

Inverse effective Pr number for turbulent kinetic energy (= 1/Pr k )

\({\alpha_{t}}\) :

Inverse effective Pr number for turbulent flow (= 1/Pr t )

\({\beta}\) :

Model constant (= 0.012)

\({\Delta {P}}\) :

Pressure drop (Pa)

\({\varepsilon}\) :

Turbulent kinetic energy dissipation rate (m2/s3)

\({\eta}\) :

Rate of strain in turbulent flow (\({={\rm Sk}/\varepsilon)}\)

\({\tau}\) :

Wall shear stress (N/m2)

\({\eta_{0}}\) :

Model constant (= 4.38)

\({\lambda}\) :

Thermal conductivity (W/mK)

\({\mu}\) :

Molecular viscosity (kg/ms)

\({\phi}\) :

Volumetric concentration of nanoparticles

\({\rho}\) :

Density (kg/m3)

bf :

Base fluid

eff :

Effective

l :

Laminar

nb :

Neighbor cell

nf :

Nanofluid

np :

Nanoparticle

P :

P center cell

t :

Turbulent

w :

Wall

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  1. Department of Mechanical Engineering, Pamukkale University, 20070, Kinikli, Denizli, Turkey

    Okyar Kaya

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Kaya, O. Numerical Investigation of Heat Transfer, Pressure Drop and Wall Shear Stress Characteristics of Al2O3-Water Nanofluid in a Square Duct. Arab J Sci Eng 40, 3641–3655 (2015). https://doi.org/10.1007/s13369-015-1790-y

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