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Flow and migration of nanoparticle in a single channel

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Abstract

A numerical simulation based on a combined Euler and Lagrange method is investigated in this work to simulate the flow and migration of nanoparticles in a single channel. The motion of discrete nanoparticles is determined by the Lagrangian trajectory method based on the Newton’s second law that includes the influence of the body force, various hydrodynamic forces, the Brownian motion and the thermophoresis force. The coupling of discrete particles with continuous flow is realized through the modification of the source term of the continuous equation. The results reveal the two-phase flow nature of nanoparticle suspensions and their implications to the convective heat transfer of nanofluids.

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Abbreviations

c :

Specific heat (J/kg K)

C s :

Coefficient in Eq. 17

C t :

Coefficient in Eq. 17

C m :

Coefficient in Eq. 17

d p :

Particle diameter (m)

d ij :

Deformation tensor

D T,p :

Thermophoretic coefficient

F :

Force acting on the particle (N/kg)

F D :

Drag force (N/kg)

F G :

Gravity (N/kg)

F B :

Brownian force (N/kg)

F T :

Thermophoretic force (N/kg)

F L :

Saffman’s lift force (N/kg)

F P :

Pressure gradient force (N/kg)

F V :

Virtual mass force (N/kg)

g :

Gravity acceleration (m/s2)

I :

Unit vector

k :

Thermal conductivity of nanofluid (W/mK)

k p :

Particle thermal conductivity (W/mK)

K :

Thermal conductivity ratio (k/k p)

k B :

Boltzmann constant

K n :

Knudsen number

K s :

Coefficient

m p :

Mass of the particle (kg)

p :

Pressure of liquid phase (Pa)

Pe :

Peclet number

R :

Radius (m)

Re :

Reynolds number

S 0 :

Spectral intensity basis

S n,ij :

Spectral intensity

S p :

Source term

t :

Time (s)

T l :

Stress tensor of nanofluids

T :

Temperature (K)

v :

Velocity of nanofluid (m/s)

v l :

Fluid phase velocity (m/s)

v p :

Particle velocity (m/s)

Β :

Inter-phase momentum exchange coefficient

ρ l :

Fluid density (kg/m3)

λ :

Mean free path of the fluid (m)

δ ij :

Kronecker delta function

ζ i :

Zero-mean, unit-variance-independent Gaussian random number

μ l :

Dynamic viscosity of nanofluids (kg/ms)

ν :

Kinetic viscosity (m2/s)

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Acknowledgments

The authors would like to extend their thanks to EPSRC for financial support under Grant EP/E065449/1.

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Authors and Affiliations

  1. School of Engineering and Materials Science, Queen Mary University of London, London, E1 4NS, UK

    Dongsheng Wen & Li Zhang

  2. School of Chemical Engineering, Harbin Institute of Technology, Harbin, China

    Yurong He

Authors
  1. Dongsheng Wen
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  2. Li Zhang
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  3. Yurong He
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Correspondence to Dongsheng Wen.

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Wen, D., Zhang, L. & He, Y. Flow and migration of nanoparticle in a single channel. Heat Mass Transfer 45, 1061–1067 (2009). https://doi.org/10.1007/s00231-009-0479-8

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  • DOI: https://doi.org/10.1007/s00231-009-0479-8

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