Skip to main content
SpringerLink
Log in

Induced flow field of randomly moving nanoparticles: a statistical perspective

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

Abstract

Thermal transport in nanofluids, i.e., suspensions of nanoparticles in a base fluid, is a subject of dispute in the literature with no conclusion as to the governing mechanisms describing it. The interaction between the suspended particles and the base fluid has been cited as the main contributor to the phenomenon. However, the exact cause of the enhancement of heat transfer in nanofluids is still not fully understood. In this study, a simplified computational approach for a nanofluid simulation is proposed. The fluid motions induced by the random Brownian motions of suspended particles are examined from a statistical perspective. The results confirm that the motions of the suspended particles induce a random flow field within the fluid and provide a statistical assessment of this field. As the Brownian time-step is reduced, the statistics of the fluid phase slowly converge. The statistics also indicate the existence of local convective eddies throughout the fluid phase as particles move about. Parameters related to the computational setup do not affect the statistics of the induced fluid velocity. However, implementation of the slip assumption affects the results of the simulation. The calculated local fluid disturbance varies with the particle size with the location of maximum depending on the slip assumption. Finally, it was observed that higher fluid temperature will have a stronger effect on the induced flow field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. Using a one-pass algorithm for the standard deviation calculation eliminates the need to store all of the velocity data from the beginning of the simulation, thus reducing the computational cost of the simulations.

  2. Excess kurtosis equals kurtosis minus 3, for which 3 is the kurtosis of a normal distribution.

Abbreviations

C :

Arbitrary constant

D :

Diffusivity of particles

Fo :

Fourier number

m :

Mass

P :

Pressure

r :

Radial distance

R :

Particle radius

Re :

Reynolds number

ΔS :

Displacement of particles

t :

Elapsed time since particle movement

Δt :

Size of time-step

U :

Velocity of discrete phase

V :

Velocity of continuous phase

δ :

Distance from particle surface

Λ :

Sample size

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

σ :

Standard deviation

τ :

Relaxation time

Δτ :

Sampling frequency

φ :

Polar angle

ψ :

Stream function

ω :

Random number (normally distributed)

0.05:

Location of 5 % of free-stream velocity

D :

Diameter

fluid:

Fluid

max:

Maximum

part:

Particle

r :

Radial distance

SS:

Steady state

TS:

Transient

θ :

Azimuthal angle

φ :

Polar angle

*:

Dimensionless quantity

\(\bar{\alpha }\) :

Mean of quantity α

References

  • Abouali O, Ahmadi G (2012) Computer simulations of natural convection of single phase nanofluids in simple enclosures: a critical review. Appl Therm Eng 36:1–13

    Article  Google Scholar 

  • Batchelor GK (1976) Brownian diffusion of particles with hydrodynamic interaction. J Fluid Mech 74(01):1–29

    Article  MATH  MathSciNet  Google Scholar 

  • Behzadmehr A, Saffar-Avval M, Galanis N (2007) Prediction of turbulent forced convection of a nanofluid in a tube with uniform heat flux using a two phase approach. Int J Heat Fluid Flow 28(2):211–219

    Article  Google Scholar 

  • Bocquet L, Barrat JL (2007) Flow boundary conditions from nano- to micro-scales. Soft Matter 3(6):685–693

    Article  Google Scholar 

  • Cheng WL, Sadr R (2013) A numerical approach in predicting flow field induced by randomly moving nano-particles. Proceedings of the ASME 2013 4th Micro/Nanoscale Heat and Mass Transfer International Conference, Technical Paper MNHMT2013

  • Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of ASME International Mechanical Engineering Congress and Exposition. 66:99–105

  • Chon CH, Kihm KD, Lee SP, Choi SUS (2005) Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett 87(15):1–3

    Article  Google Scholar 

  • Cichocki B, Felderhof BU (1994) Long-time collective motion of rigid bodies immersed in a viscous fluid. Phys A 211(1):25–36

    Article  MathSciNet  Google Scholar 

  • Cichocki B, Felderhof BU (2000) Long-time tails in the solid-body motion of a sphere immersed in a suspension. Phys Rev E 62(4):5383–5388

    Article  MathSciNet  Google Scholar 

  • Das SK, Putra N, Thiesen P, Roetzel W (2003) Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transfer 125:567–574

    Article  Google Scholar 

  • Dufresne ER, Squires TM, Brenner MP, Grier DG (2000) Hydrodynamic coupling of two brownian spheres to a planar surface. Phys Rev Lett 85(15):3317

    Article  Google Scholar 

  • Eapen J, Williams WC, Buongiorno J, Hu LW, Yip S, Rusconi R, Piazza R (2007) Mean-field versus microconvection effects in nanofluid thermal conduction. Phys Rev Lett 99(9):095901

    Article  Google Scholar 

  • Evans W, Fish J, Keblinski P (2006) Role of Brownian motion hydrodynamics on nanofluid thermal conductivity. Appl Phys Lett 88(9):093116

    Article  Google Scholar 

  • Feng X, Johnson DW (2012) Mass transfer in SiO2 nanofluids: a case against purported nanoparticle convection effects. Int J Heat Mass Transfer 55(13–14):3447–3453

    Article  Google Scholar 

  • Gad-el-Hak M (1999) The fluid mechanics of microdevices—The freeman scholar lecture. J Fluids Eng 121(1):5–33

    Article  Google Scholar 

  • Ghaffari O, Behzadmehr A, Ajam H (2010) Turbulent mixed convection of a nanofluid in a horizontal curved tube using a two-phase approach. Int Comm Heat Mass 37(10):1551–1558

    Article  Google Scholar 

  • Gharagozloo PE, Eaton JK, Goodson KE (2008) Diffusion, aggregation, and the thermal conductivity of nanofluids. Appl Phys Lett 93(10):103110

    Article  Google Scholar 

  • Happel J, Brenner H (1973) Low Reynolds number hydrodynamics. Noordhoff International Publishing, Leyden, The Netherlands

    Google Scholar 

  • He Y, Men Y, Zhao Y, Lu H, Ding Y (2009) Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions. Appl Therm Eng 29(10):1965–1972

    Article  Google Scholar 

  • Jang SP, Choi SUS (2007) Effects of various parameters on nanofluid thermal conductivity. J Heat Transfer 129:617–623

    Article  Google Scholar 

  • Kalteh M, Abbassi A, Saffar-Avval M, Harting J (2011) Eulerian-eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel. Int J Heat Fluid Flow 32(1):107–116

    Article  Google Scholar 

  • Karthikeyan NR, Philip J, Raj B (2008) Effect of clustering on the thermal conductivity of nanofluids. Mater Chem Phys 109(1):50–55

    Article  Google Scholar 

  • Keblinski P, Prasher R, Eapen J (2008) Thermal conductance of nanofluids: is the controversy over. J Nanopart Res 10:1089–1097

    Article  Google Scholar 

  • Kondaraju S, Jin EK, Lee JS (2011) Effect of the multi-sized nanoparticle distribution on the thermal conductivity of nanofluids. Microfluid Nanofluid 10:133–144

    Article  Google Scholar 

  • Koo J, Kleinstreuer C (2005) Laminar nanofluid flow in microheat-sinks. Int J Heat Mass Transfer 48(13):2652–2661

    Article  MATH  Google Scholar 

  • Krishnamurthy S, Bhattacharya P, Phelan PE, Prasher RS (2006) Enhanced mass transport in nanofluids. Nano Lett 6(3):419–423

    Article  Google Scholar 

  • Kumar DH, Patel HE, Kumar VRR, Sundararajan T, Pradeep T, Das SK (2004) Model for heat conduction in nanofluids. Phys Rev Lett 93(14):144301

    Article  Google Scholar 

  • Kwak K, Kim C (2005) Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol. Korea-Aust Rheol J 17(2):35–40

    MathSciNet  Google Scholar 

  • Lee S, Choi SUS, Li S, Eastman JA (1999) Measuring thermal conductivity of fluids containing oxide nanoparticles. J Heat Transfer 121(2):280–289

    Article  Google Scholar 

  • Li CH, Peterson GP (2007) Mixing effect on the enhancement of the effective thermal conductivity of nanoparticle suspensions (Nanofluids). Int J Heat Mass Transfer 50(23–24):4668–4677

    Article  MATH  Google Scholar 

  • Ling RF (1974) Comparison of several algorithms for computing sample means and variances. J Am Stat Assoc 69(348):859–866

    Article  MATH  Google Scholar 

  • Maïga SEB, Palm SJ, Nguyen CT, Roy G, Galanis N (2005) Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow 26(4):530–546

    Article  Google Scholar 

  • Matthews MT, Hill JM (2006) Flow around nanospheres and nanocylinders. Q J Mech Appl Math 59(2):191–210

    Article  MATH  MathSciNet  Google Scholar 

  • Matthews MT, Hill JM (2007) Nano boundary layer equation with nonlinear navier boundary condition. J Math Anal Appl 333(1):381–400

    Article  MATH  MathSciNet  Google Scholar 

  • Mirmasoumi S, Behzadmehr A (2008) Numerical study of laminar mixed convection of a nanofluid in a horizontal tube using two-phase mixture model. Appl Therm Eng 28(7):717–727

    Article  Google Scholar 

  • Padding JT, Louis AA (2006) Hydrodynamic interactions and brownian forces in colloidal suspensions: coarse-graining over time and length scales. Phys Rev E 74(3):031402

    Article  Google Scholar 

  • Pakravan HA, Yaghoubi M (2011) Combined thermophoresis, Brownian motion and dufour effects on natural convection of nanofluids. Int J Therm Sci 50(3):394–402

    Article  Google Scholar 

  • Poulikakos D, Maruyama S (2003) Molecular dynamics simulation in nanoscale heat transfer: a review. Microscale Thermophys Eng 7:181–206

    Article  Google Scholar 

  • Prasher R, Bhattacharya P, Phelan PE (2006a) Brownian-motion-based convective-conductive model for the effective thermal conductivity of nanofluids. J Heat Transfer 128(6):588–595

    Article  Google Scholar 

  • Prasher R, Evans W, Meakin P, Fish J, Phelan P, Keblinski P (2006b) Effect of aggregation on thermal conduction in colloidal nanofluids. Appl Phys Lett 89(14):143119

    Article  Google Scholar 

  • Qian T, Wang X (2005) Driven cavity flow: from molecular dynamics to continuum hydrodynamics. Multiscale Model Sim 3(4):749–763

    Article  MATH  MathSciNet  Google Scholar 

  • Sadr R, Li H, Yoda M (2005) Impact of hindered Brownian diffusion on the accuracy of particle-image velocimetry using evanescent-wave illumination. Exp Fluids 38:90–98

    Article  Google Scholar 

  • Schmidt JR, Skinner JL (2003) Hydrodynamic boundary conditions, the stokes-einstein law, and long-time tails in the Brownian limit. J Chem Phys 119(15):8062–8068

    Article  Google Scholar 

  • Van Gorder RA, Sweet E, Vajravelu K (2010) Nano boundary layers over stretching surfaces. Commun Nonlinear Sci Numer Simul 15(6):1494–1500

    Article  MATH  MathSciNet  Google Scholar 

  • Vinogradova OI (1999) Slippage of water over hydrophobic surfaces. Int J Miner Process 56(1):31–60

    Article  Google Scholar 

  • Vladkov M, Barrat JL (2006) Modeling transient absorption and thermal conductivity in a simple nanofluid. Nano Lett 6(6):1224–1228

    Article  Google Scholar 

  • Yang YT, Lai FH (2010) Numerical study of heat transfer enhancement with the use of nanofluids in radial flow cooling system. Int J Heat Mass Transfer 53(25):5895–5904

    Article  MATH  Google Scholar 

  • Zhu H, Zhang C, Liu S, Tang Y, Yin Y (2006) Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3O4 aqueous nanofluids. Appl Phys Lett 89(2):023123

    Article  Google Scholar 

Download references

Acknowledgments

This publication was made possible by the NPRP award 09-1183-2-461 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors. The HPC (and/or scientific visualization) resources and services used in this work were provided by the IT research computing group at Texas A&M University at Qatar. IT research computing is funded by the Qatar Foundation for education, science, and community development. The authors would like to express their sincere appreciation for the valuable technical advice from Professor J. N. Reddy, Texas A&M University.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University at Qatar, P. O. Box 23874, Qatar Foundation Education City, Doha, Qatar

    Way Lee Cheng & Reza Sadr

Authors
  1. Way Lee Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reza Sadr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reza Sadr.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, W.L., Sadr, R. Induced flow field of randomly moving nanoparticles: a statistical perspective. Microfluid Nanofluid 18, 1317–1328 (2015). https://doi.org/10.1007/s10404-014-1531-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-014-1531-7

Keywords

Search

Navigation