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Application of Atangana–Baleanu fractional derivative to MHD channel flow of CMC-based-CNT's nanofluid through a porous medium

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  • Saqib, Muhammad
  • Khan, Ilyas
  • Shafie, Sharidan

Abstract

The objective of this article is to apply the Atangana–Baleanu derivative fractional in Caputo sense to convective flow of Carboxy–Methyl–Cellulose (CMC) based Carbon nanotubes (CNT's) nanofluid in a vertical microchannel. The magnetohydrodynamic (MHD) flow through a porous medium together with heat transfer is considered. The Atangana–Baleanu fractional derivative without singular and the non-local kernel is used in the mathematical formulation to get the time fractional governing equations subject to physical initial and boundary conditions. The Laplace transform technique is used to obtain the exact analytical solutions for velocity and temperature distributions. Finally, the influence of parameters of interest is studied through plots and discussed physically.

Suggested Citation

  • Saqib, Muhammad & Khan, Ilyas & Shafie, Sharidan, 2018. "Application of Atangana–Baleanu fractional derivative to MHD channel flow of CMC-based-CNT's nanofluid through a porous medium," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 79-85.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:79-85
    DOI: 10.1016/j.chaos.2018.09.007
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    References listed on IDEAS

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    1. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    2. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    3. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    4. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
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    Cited by:

    1. Shit, G.C. & Maiti, S. & Roy, M. & Misra, J.C., 2019. "Pulsatile flow and heat transfer of blood in an overlapping vibrating atherosclerotic artery: A numerical study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 432-450.
    2. Mehmet Yavuz & Ndolane Sene & Mustafa Yıldız, 2022. "Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    3. Firas A. Alwawi & Hamzeh T. Alkasasbeh & Ahmed M. Rashad & Ruwaidiah Idris, 2020. "A Numerical Approach for the Heat Transfer Flow of Carboxymethyl Cellulose-Water Based Casson Nanofluid from a Solid Sphere Generated by Mixed Convection under the Influence of Lorentz Force," Mathematics, MDPI, vol. 8(7), pages 1-21, July.
    4. Dongmin Yu & Rijun Wang, 2022. "An Optimal Investigation of Convective Fluid Flow Suspended by Carbon Nanotubes and Thermal Radiation Impact," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    5. Panda, Sumati Kumari & Abdeljawad, Thabet & Ravichandran, C., 2020. "A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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