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Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative

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  • Ghalib, M. Mansha
  • Zafar, Azhar A.
  • Riaz, M. Bilal
  • Hammouch, Z.
  • Shabbir, Khurram

Abstract

This study investigates the unsteady magnetohydrodynamics (MHD) flow of a viscous fluid. The fluid is passing over a vertical plate through porous medium. Additionally conjugate effects of heat and mass transfer with ramped temperatures, slip effect and influence of thermal radiation in the energy equation are taken into account. The dimensionless fractional-order governing equations, in the Caputo–Fabrizio sense, are solved with the help of Laplace transformation. Moreover, semi analytical technique is used to investigate the velocity field. Some results which present in literature are recovered as limiting cases. Influences of different parameters on the velocity profiles for the case of f(t)=t and f(t)=sinωt are highlighted. The novelty of the manuscript is the use of the most recent definition of the non integer order derivative operator i.e. Caputo–Fabrizio derivative operator, the use of generalized boundary conditions in terms of general function f(t), from our general results, several particular cases for instance when f(t) is a linear or sinusoidal function could be recovered.

Suggested Citation

  • Ghalib, M. Mansha & Zafar, Azhar A. & Riaz, M. Bilal & Hammouch, Z. & Shabbir, Khurram, 2020. "Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
  • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437119321788
    DOI: 10.1016/j.physa.2019.123941
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    2. Islam M. Eldesoky, 2012. "Slip Effects on the Unsteady MHD Pulsatile Blood Flow through Porous Medium in an Artery under the Effect of Body Acceleration," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-26, September.
    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.
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