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Scale-adaptive simulation of turbulent mixed convection of nanofluids in a vertical duct

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Abstract

The present paper focuses on the turbulent mixed convection of nanofluids through a vertical square duct. The prediction accuracy of scale-adaptive simulation (SAS) approach is investigated versus RANS-based models (k − ε and k − ω), in terms of Nusselt number and friction factor. A thermal-dependent model is considered to determine the effective thermal conductivity and effective dynamic viscosity of nanofluids. The present numerical simulations are performed for CuO–water and SiO2–water nanofluids and compared with various experimental data. Results indicate that the SAS approach can predict the unsteady flow and heat transfer of nanofluids more accurately than the k − ε and k − ω models. Moreover, it is found that the turbulent velocity fluctuations enhance in streamwise, spanwise and wall-normal directions with an increasing nanoparticle volume fraction, whilst this increment is higher in streamwise direction. Also, in the near-wall region the effect of the presence of nanoparticles on the turbulent velocity fluctuations is more considerable, which increases the turbulence content of the flow field.

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Abbreviations

a :

Duct width (m)

c P :

Specific heat (J kg−1 K−1)

d p :

Particle diameter (nm)

D h :

Hydraulic diameter (m)

f :

Peripherally averaged friction factor \(( = 2{{\Delta }}PD_{\text{h}} /(Lu^{2} ))\)

g :

Gravitational acceleration (= 9.80665 m s−2)

Gr :

Grashof number \(( = g\beta q'' D_{\text{h}}^{4} /(\lambda \nu^{2} ))\)

h :

Convective heat transfer coefficient (W m−2 K−1) \(( = q'' /(T_{\text{wall}} - T_{\text{bulk}} ))\)

i, j, k :

Coordinate index

k :

Turbulence kinetic energy (m2 s−2)

L :

Duct length (m)

MCP:

Mixed convection parameter \(( = Ra^{1/4} /(Re^{1/2} pr^{1/3} ))\)

Nu :

Nusselt number \(( = hD_{\text{h}} /{{\lambda }})\)

P :

Pressure (Pa)

Pr :

Prandtl number \(( = \nu /\alpha )\)

Q :

Second invariant of the velocity gradient tensor (s−2)

q″:

Uniform heat flux (W m−2)

Ra :

Rayleigh number (= Gr Pr)

RANS:

Reynolds-averaged Navier–Stokes

Re :

Reynolds number (\(= (uD_{\text{h}} /\nu )\))

S :

Strain rate tensor (s−1)

SAS:

Scale-adaptive simulation

t :

Time (s)

T :

Temperature (K)

URANS:

Unsteady Reynolds-averaged Navier–Stokes

u i :

Velocity vector (m s−1)

\(\bar{u}\) :

Mean velocity component (m s−1)

u′:

Fluctuating velocity component (m s−1)

u, v, w :

Velocity along x, y, z (m s−1)

u * :

Friction velocity (m s−1)

x, y, z :

Coordinate system

x + :

Dimensionless wall distance in x direction

z + :

Dimensionless wall distance in z direction

α :

Thermal diffusivity (m2s−1)

β :

Volumetric expansion coefficient (K−1)

\(\delta_{\text{ij}}\) :

Kronecker delta

\(\varepsilon\) :

Dissipation rate (m2s−3)

\(\kappa\) :

Boltzmann constant (= 1.3807 × 10– 23 J K−1)

\(\lambda\) :

Thermal conductivity (\({\text{W m}}^{ - 1} {\text{K}}^{ - 1}\))

\(\mu\) :

Dynamic viscosity (\({\text{Nsm}}^{ - 2}\))

\(\mu_{\text{t }}\) :

Turbulent (eddy) viscosity (\({\text{Nsm}}^{ - 2}\))

\(\rho\) :

Density (kg m−3)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\varphi\) :

Particle volume fraction

\({{\Omega }}\) :

Rotation rate tensor (s−1)

\(\omega\) :

Specific dissipation rate (s−1)

b:

Bulk

bf:

Base fluid

nf:

Nanofluid

p:

Particle

rms:

Root mean square

w:

Water

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    Farzad Bazdidi-Tehrani, Seyed Iman Vasefi & Arash Khabazipur

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  1. Farzad Bazdidi-Tehrani
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Correspondence to Farzad Bazdidi-Tehrani.

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Bazdidi-Tehrani, F., Vasefi, S.I. & Khabazipur, A. Scale-adaptive simulation of turbulent mixed convection of nanofluids in a vertical duct. J Therm Anal Calorim 131, 3011–3023 (2018). https://doi.org/10.1007/s10973-017-6747-9

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