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Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1629–1641 | Cite as

Analytical investigation of nanoparticle migration in a duct considering thermal radiation

  • Zhixiong LiEmail author
  • S. Saleem
  • Ahmad Shafee
  • Ali J. Chamkha
  • Sunwen Du
Article

Abstract

Buongiorno model is applied to investigate nanofluid migration through a permeable duct in the presence of external forces. Influences of radiation and Joule heating on first law equation are added. Final formulas are solved via differential transform method. Roles of suction, thermophoretic, radiation and Brownian motion parameters, Schmidt number, Hartmann number, Eckert number were presented. Results show that temperature gradient improves with the enhancement of Reynolds number, suction and Radiation parameters. Nu augments with the augmentation of Hartmann and Eckert numbers, while reverse behavior is seen for skin friction coefficient. Also, it can be concluded that Nusselt number enhances with the increase in radiation parameter but it decreases with the increase in Brownian motion.

Keywords

Differential transform method Porous duct Nanoparticle Lorentz forces Buongiorno model 

List of symbols

\(B_{0}\)

Magnetic induction (Tesla)

\(\Pr\)

Prandtl number

\({\text{Rd}}\)

Radiation parameter

\(Ha\)

Hartmann number

\(C_{\text{p}}\)

Specific heat capacity (J/kgK)

\(v,\,u\)

Vertical and horizontal velocities (m/s)

\(q_{\text{r}}\)

Thermal radiation (W)

\(T\)

Fluid temperature (K)

Greek symbols

\(\sigma_{\text{e}}\)

Stefan–Boltzmann constant

\(\mu\)

Dynamic viscosity (Pa s)

\(\phi\)

Volume fraction of nanofluid

\(\alpha\)

Thermal diffusivity (m2 s−1)

\(\eta\)

Similarity-independent variable

\(\beta_{\text{R}}\)

Mean absorption coefficient

\(\sigma\)

Electrical conductivity

Subscripts

\(T\)

Thermal quantity

\(f\)

Base fluid

Notes

Acknowledgements

Authors would like to express their gratitude to King Khalid University, Abha 61413, Saudi Arabia, for providing administrative and technical support.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Zhixiong Li
    • 1
    • 2
    Email author
  • S. Saleem
    • 3
  • Ahmad Shafee
    • 4
  • Ali J. Chamkha
    • 5
    • 6
  • Sunwen Du
    • 7
  1. 1.School of EngineeringOcean University of ChinaQingdaoChina
  2. 2.School of Mechanical, Materials, Mechatronic and Biomedical EngineeringUniversity of WollongongWollongongAustralia
  3. 3.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia
  4. 4.Public Authority of Applied Education & Training, College of Technological StudiesApplied Science DepartmentShuwaikhKuwait
  5. 5.Mechanical Engineering Department, Prince Sultan Endowment for Energy and EnvironmentPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  6. 6.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas Al KhaimahUnited Arab Emirates
  7. 7.College of Mining TechnologyTaiyuan University of TechnologyTaiyuanP. R. China

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