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Analytical investigation of nanoparticle migration in a duct considering thermal radiation

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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.

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Abbreviations

\(B_{0}\) :

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)

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

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

\(T\) :

Thermal quantity

\(f\) :

Base fluid

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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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Authors and Affiliations

  1. School of Engineering, Ocean University of China, Qingdao, 266110, China

    Zhixiong Li

  2. School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia

    Zhixiong Li

  3. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    S. Saleem

  4. Public Authority of Applied Education & Training, College of Technological Studies, Applied Science Department, Shuwaikh, Kuwait

    Ahmad Shafee

  5. Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    Ali J. Chamkha

  6. RAK Research and Innovation Center, American University of Ras Al Khaimah, Ras Al Khaimah, United Arab Emirates

    Ali J. Chamkha

  7. College of Mining Technology, Taiyuan University of Technology, Yingze West St. 79, Taiyuan, 030024, P. R. China

    Sunwen Du

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  1. Zhixiong Li
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  2. S. Saleem
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Correspondence to Zhixiong Li.

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Li, Z., Saleem, S., Shafee, A. et al. Analytical investigation of nanoparticle migration in a duct considering thermal radiation. J Therm Anal Calorim 135, 1629–1641 (2019). https://doi.org/10.1007/s10973-018-7517-z

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