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Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials

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  • Abdulhameed, M.
  • Muhammad, M.M.
  • Gital, A.Y.
  • Yakubu, D.G.
  • Khan, I.

Abstract

By using the Caputo–Fabrizio time fractional derivative, unsteady flows of an incompressible viscous through a circular tube are developed. Flows are generated due to the combination of electroosmotic, pressure and magnetic forces. The derived fractional momentum equation incorporating the electromagnetic body force resulting from the electric double layer (EDL) field was solved using the Laplace transform technique, Riemann-sum approximation method, and the Stehfest’s algorithm. The solution obtained is validated by assenting comparisons between the Riemann-sum approximation method and Stehfest’s algorithm. Based upon the velocity field solution, the energy equation is analyzed by taking the viscous dissipation, thermal radiative, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect into account. Numerical simulations and graphical illustrations were carried out using the software package Mathcad. The results highlights that, fractional models of fluid-flow and heat transfer with fractional derivatives bring significant differences compared to the ordinary model. The variations of fluid velocity, fluid temperature, skin friction and Nusselt number with related parameters are interpreted and the results are discussed.

Suggested Citation

  • Abdulhameed, M. & Muhammad, M.M. & Gital, A.Y. & Yakubu, D.G. & Khan, I., 2019. "Effect of fractional derivatives on transient MHD flow and radiative heat transfer in a micro-parallel channel at high zeta potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 42-71.
    • Handle: RePEc:eee:phsmap:v:519:y:2019:i:c:p:42-71
    DOI: 10.1016/j.physa.2018.12.019
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    References listed on IDEAS

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    1. Abdulhameed, M. & Vieru, D. & Roslan, R., 2017. "Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 233-252.
    2. Ranjit, N.K. & Shit, G.C., 2017. "Joule heating effects on electromagnetohydrodynamic flow through a peristaltically induced micro-channel with different zeta potential and wall slip," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 458-476.
    3. Shit, G.C. & Mondal, A. & Sinha, A. & Kundu, P.K., 2016. "Electro-osmotic flow of power-law fluid and heat transfer in a micro-channel with effects of Joule heating and thermal radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1040-1057.
    4. 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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