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Numerical study of nanofluid mixed convection in a horizontal curved tube using two-phase approach

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Abstract

Laminar mixed convection of nanofluid consisting of water/Al2O3 in a horizontal curved tube is investigated numerically. Three dimensional elliptical governing equations have been solved to study the simultaneous effect of the buoyancy and centrifugal forces throughout the curved tube. The effects of nanoparticle concentrations on the secondary flow and also on the contours of temperature are presented and discussed. Axial velocity profiles with respect to the horizontal and vertical diameter are shown. In addition, the effects of nanoparticle volume fractions on the axial evolution of the local peripheral average convective heat transfer coefficient and the local peripheral average skin friction coefficient are studied. It is shown that the average convective heat transfer coefficient augments with the nanoparticle concentrations. However, its effect on the average skin friction coefficient is negligible.

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Abbreviations

a:

Acceleration (m/s2)

Cf :

Peripheral average skin friction coefficient

C:

Specific heat (J/kg K)

De:

Dean number (Re(a/R)0.5)

d:

Tube diameter (m)

dp :

Nanoparticle diameter (nm)

df :

Molecular diameter of base fluid

g:

Gravitational acceleration (m s−2)

Gr:

Grashof number \( \left( { = {\frac{{\rho_{\rm eff} {\rm g}\beta_{\rm eff} q^{\prime\prime}{\rm d^{4}} }}{{{\rm K}_{\rm eff} \mu_{\rm eff}^{2} }}}} \right) \)

h:

Peripheral average convection heat transfer coefficient

K:

Thermal conductivity (W/m K)

Kb :

Boltzmann Constant (=1.3807e−23 J/K)

P:

Pressure (pa)

Pr:

Prandtl number

q ′′ :

Uniform heat flux (W m−2)

R:

Curvature radius of tube

r:

Radial direction

r0 :

Tube radial (m)

Re:

Reynolds number \( \left( {={\frac{{\rho_{\rm eff} V_{\rm m} D}}{{\mu_{\rm eff} }}}} \right) \)

Ri:

Richardson number (Gr/Re2)

T:

Temperature (K)

V:

Velocity (m s−1)

Z:

Axial direction

α:

Thermal diffusivity

β:

Volumetric expansion coefficient (K−1)

θ:

Angular coordinate

μ:

Dynamic viscosity (N s m−2)

ρ:

Density (Kg m−3)

τ:

Shear stress

ϕ:

Volume fraction

b:

Bulk

dr:

Drift

eff:

Effective

f:

Base fluid

k:

Summation index

m:

Mixture

0:

Inlet condition

p:

Particle

r:

Radial direction

w:

Wall

θ:

Angular direction

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Sistan and Baluchestan, P.O. Box 98164-161, Zahedan, Iran

    S. Alikhani & A. Behzadmehr

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Avenue, P.O. Box 15875-4413, Tehran, Iran

    M. Saffar-Avval

Authors
  1. S. Alikhani
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  2. A. Behzadmehr
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  3. M. Saffar-Avval
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Correspondence to A. Behzadmehr.

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Alikhani, S., Behzadmehr, A. & Saffar-Avval, M. Numerical study of nanofluid mixed convection in a horizontal curved tube using two-phase approach. Heat Mass Transfer 47, 107–118 (2011). https://doi.org/10.1007/s00231-010-0677-4

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