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Heat Transfer Enhancement through Thermodynamical Activity of H 2 O/Clay Nanofluid Flow over an Infinite Upright Plate with Caputo Fractional-Order Derivative

Author

Listed:
  • J. Kayalvizhi

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India)

  • A. G. Vijaya Kumar

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India)

  • Hakan F. Öztop

    (Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig 23119, Turkey
    Department of Mechanical Engineering, Engineering Faculty, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ndolane Sene

    (Department of Mathematics, Institut des Politiques Publiques, Cheikh Anta Diop University, Dakar Fann BP 5683, Senegal)

  • Nidal H. Abu-Hamdeh

    (Department of Mechanical Engineering, Engineering Faculty, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    K. A. CARE Energy Research and Innovation Center, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper presents a modelling of nanofluid flow using Caputo fractional derivatives through conservative equations of mass and momentum, and provides an exact solution on un-steady convective flow over a vertical plate with the mass diffusion effect, in association with an energy equation. H 2 O is the base liquid with clay nanoparticles floating in it in a uniform way. Boussinessq’s approach is used in the momentum equation for pressure gradient. The non-dimensional fluid temperature, species concentration and fluid transport are derived together with Jacob Fourier sine and Laplace transform techniques in terms of exponential decay function, and the inverse is computed further in terms of the Mittag-Leffler function. The impact of various physical quantities is interpreted with the fractional order of the Caputo derivatives. The obtained temperature, transport and species concentration profiles show behaviors for 0 < α < 1, where α is the fractional parameter. The rate of heat and mass transfer coefficients for the significance of physical quantities of interest are also obtained and presented through graphs. The impact of the nanoparticle volume fraction on the flow field is observed. At larger values of the fractional parameter, the velocity, temperature, and concentration distributions grow more quickly. In addition to that, it is found the concentration profiles behave in the opposite way for the volume fraction of nanofluids.

Suggested Citation

  • J. Kayalvizhi & A. G. Vijaya Kumar & Hakan F. Öztop & Ndolane Sene & Nidal H. Abu-Hamdeh, 2022. "Heat Transfer Enhancement through Thermodynamical Activity of H 2 O/Clay Nanofluid Flow over an Infinite Upright Plate with Caputo Fractional-Order Derivative," Energies, MDPI, vol. 15(16), pages 1-18, August.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:16:p:6082-:d:894478
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    References listed on IDEAS

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    1. Nadeem Abbas & Wasfi Shatanawi, 2022. "Heat and Mass Transfer of Micropolar-Casson Nanofluid over Vertical Variable Stretching Riga Sheet," Energies, MDPI, vol. 15(14), pages 1-20, July.
    2. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
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