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Nanofluids thermal behavior analysis using a new dispersion model along with single-phase

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Abstract

A numerical study has been performed to analyze nanofluids convective heat transfer. Laminar α-Al2O3-water nanofluid flows in an entrance region of a horizontal circular tube with constant surface temperature. Numerical analysis has been carried out using two different single-phase models (homogenous and dispersion) and two-phase models (Eulerian–Lagrangian and mixture). A new model is developed to consider the nanoparticles dispersion. The transport equations for the tube with constant surface temperature were solved numerically using a control volume approach. The effects of nanoparticles volume fraction (0.5, 1 %) and Reynolds number (650 ≤ Re ≤ 2300) on nanofluid convective heat transfer coefficient were studied. The results are compared with the experimental data and it is shown that the homogenous single-phase model is underestimated and the mixture model is overestimated. Although the Eulerian–Lagrangian model gives a reasonable prediction for the thermal behavior of nanofluids, the dispersion single-phase model gives more accurate prediction despite its simplicity.

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Abbreviations

Bc :

Boltzmann constant (J K−1)

C:

Dispersion coefficient

Cc :

Cunningham correction factor

Cm :

Coefficient

Cp :

Specific heat (J kg−1 K−1)

Cs :

Coefficient

Ct :

Coefficient

dp :

Particle diameter (m)

dij :

Deformation tensor

D:

Tube diameter (m)

F:

Total force (N kg−1)

FB :

Brownian force (N kg−1)

FD :

Drag force (N kg−1)

FG :

Gravity force (N kg−1)

FL :

Saffman’s lift force (N kg−1)

FP :

Pressure gradient force (N kg−1)

FT :

Thermophoretic force (N kg−1)

FV :

Virtual mass force (N kg−1)

g:

Gravity acceleration (N m−2)

h:

Convective heat transfer coefficient (W m−2 K−1)

H:

Enthalpy (J kg−1)

k:

Thermal conductivity (W m−1 K−1)

Kn:

Knudsen number

Ks :

Coefficient

l:

Mean free path (m)

L:

Tube length (m)

mp :

Particle mass (kg)

Nu:

Nusselt number

p:

Pressure (Pa)

Pr:

Prandtl number

\(\dot{Q}\) :

Rate of total transferred energy (W)

r:

Radial coordinate

R:

Tube radius (m)

Re:

Reynolds number

S0 :

Spectral intensity basis (W kg−1)

Sp :

Source term

t:

Time (s)

T:

Temperature (K)

V:

Velocity (m s−1)

α :

Thermal diffusivity (m2 s−1)

ρ :

Density (kg m−3)

φ :

Particle volume fraction

ς i :

Unit-variance-independent Gaussian random number

μ :

Dynamic viscosity (kg m−1 s−1)

bf:

Base fluid

d:

Dispersed

eff:

Effective

i:

Inlet

m:

Mixture

nf:

Nanofluid

p:

Particle

w:

Wall

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, No. 15, Pardis St, MollaSadra Ave, Vanak Sq, 19991-43344, Tehran, Iran

    Mohammad Salemi Mojarrad, Ali Keshavarz & Azin Shokouhi

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  1. Mohammad Salemi Mojarrad
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  2. Ali Keshavarz
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  3. Azin Shokouhi
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Correspondence to Ali Keshavarz.

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Mojarrad, M.S., Keshavarz, A. & Shokouhi, A. Nanofluids thermal behavior analysis using a new dispersion model along with single-phase. Heat Mass Transfer 49, 1333–1343 (2013). https://doi.org/10.1007/s00231-013-1182-3

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  • DOI: https://doi.org/10.1007/s00231-013-1182-3

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